| 00:00 | no. Okay. So I will a little bit more about sorting sentence |
|
| 00:14 | groups. What do you do So, um all right, talked |
|
| 00:26 | the previous month before, so, these are all sorts that fairly easy |
|
| 00:34 | paralyze and particularly if they have distributed . So if you do things on |
|
| 00:38 | construct, the common ones like heat can quit sort and not so |
|
| 00:45 | Two parallel lines in particular when you distributed data despite the difference in the |
|
| 00:54 | shared memories. Just like to do . I want to know the I'll |
|
| 01:00 | about trading sort 1st and then I'll about the other ones. So this |
|
| 01:11 | an inspector reading sort. So um to so I guess there's not much |
|
| 01:21 | an audience, but do you know trading sort? Is that familiar |
|
| 01:29 | you know? Okay, that's all . So it's do you understand |
|
| 01:38 | So I'm trying to through this So what it does is it basically |
|
| 01:47 | that's the sort of place and it it makes a number of bits that |
|
| 01:56 | being used and the various steps of algorithm. So this particular sideways for |
|
| 02:03 | two sorts of, that's just one . So that column here, best |
|
| 02:12 | specify the number and the first one , the value or the small |
|
| 02:22 | And then the sexual thing is there's much the fact that the border two |
|
| 02:32 | on oh, the value in this of the significant and and what does |
|
| 02:43 | in order from first to last number top to bottom on the side. |
|
| 02:49 | , I looked at the numbers This thing that becomes zero. So |
|
| 02:55 | this is the first one and this the second one and the third and |
|
| 02:59 | fourth one and then one. So is them the bottom. So this |
|
| 03:09 | 6, 7 is a direct order data and domestic duties with respect to |
|
| 03:17 | least significant bits. And then when fermentation. So now in order to |
|
| 03:25 | the least significant to see all the zeros least comfortable with all the ones |
|
| 03:30 | the world. And it's also the that the border in which mm Tes |
|
| 03:40 | significantly zero a person in the initial is preserved and that's the granting a |
|
| 03:50 | fish and that's something known as a source this property that but the keys |
|
| 03:57 | have the same value they want is in the foot. Mhm. Sorted |
|
| 04:04 | , effective disorder respectively. So the step is then to move up and |
|
| 04:12 | to the looks at the next pit you would do the same thing or |
|
| 04:17 | number respectively. Yeah, It's a two from the list. So then |
|
| 04:27 | with zero again first 030 for And then disorder. Alright. And then |
|
| 04:40 | get the fermentation so we'll get What did we respect Now ah next |
|
| 04:47 | those significant bits. So everything is number two. Yeah right there. |
|
| 04:58 | all the lots of fun and I the order is preserved. Notice that |
|
| 05:11 | this second ranting and fermentation clearly things I'll scramble with respect the least significant |
|
| 05:22 | not Important and then go through this like three bits of three places on |
|
| 05:29 | own and they did the same thing reputation and then you can see the |
|
| 05:37 | correct. So this is the reading Calgary reading sport algorithm and then by |
|
| 05:47 | the so that's been quite popular parallel . Um So the next slide here |
|
| 05:58 | and they are the computer now what woman wants to put it back so |
|
| 06:06 | don't have to. That's right. now that in addition to the for |
|
| 06:17 | various that's now the economy, the are not just incinerated to sort but |
|
| 06:28 | around, I'm going to be such time you do it frank. |
|
| 06:33 | determination. And this case for two and so it's your job. It |
|
| 06:42 | is four minutes, 4 minutes at time fermentation of. So that means |
|
| 06:47 | takes eight g to 32 but a of reach Granting on four bits of |
|
| 06:56 | time. Thanks. This is thank . This is the best and then |
|
| 07:07 | time for meditation And then necessarily eight of 46 at the time. So |
|
| 07:15 | don't see the problem Just a factor 63 years, 461 station station. |
|
| 07:28 | I'm interested and then red face and number of it in terms of ah |
|
| 07:46 | don't see that at some point It's number of this for the right it |
|
| 07:57 | affect it on your presentation. So , So one of the summary but |
|
| 08:10 | four hours. So that's and then round the invasion. Right reputation and |
|
| 08:19 | family doctor two of the inside before get all the keys. So, |
|
| 08:35 | the hydrated, it's really definitely that's so and in this case is |
|
| 08:48 | reduces the number of implementations that are costs. Oh, but the rest |
|
| 08:57 | also mm hmm. Talk a little more about it. Right benefits. |
|
| 09:10 | and the questions on rated sort So uh sort of one of the advantages |
|
| 09:19 | it that it's kind of one of oblivious sorts. So there is no |
|
| 09:26 | is blinding. Yes. Because through dataset and faces or it doesn't say |
|
| 09:32 | to credit and that value and so to that. So there's no conditions |
|
| 09:37 | the culture that tends to be good parallel computing because things can get load |
|
| 09:46 | . So back to the shortness, think it's some sort of pretty much |
|
| 09:54 | class we talked about sorting. What's thing Sounds familiar sources and I want |
|
| 10:03 | first one practice all the time enough the officers. They make parts for |
|
| 10:10 | is in the pacific think first And go through the fire and whatever is |
|
| 10:16 | . That's enough. The moment of different That's nothing but about 50 |
|
| 10:22 | So Oh, go through a little of detail and I can do the |
|
| 10:29 | sort of this sort and that comes basis for some of the most effective |
|
| 10:37 | sorting algorithms. So let's quickly do stuff. So the idea is so |
|
| 10:48 | can, you have, your key distributed across the nodes in the system |
|
| 10:56 | what to do to have, you , that the system, the complete |
|
| 11:03 | budgets. So the first step is that each note ah rose the |
|
| 11:12 | It has into the respective puppets. but in a given market, that |
|
| 11:19 | , every note. So I don't to go and add up how many |
|
| 11:26 | isn't with their respective budgets in the sense. And then you you also |
|
| 11:35 | of reacting to find out what is order in the global focus. So |
|
| 11:41 | is steps and doing this um instagram budget so that um a little bit |
|
| 11:51 | this is about then I have, guess a couple of examples. So |
|
| 12:00 | alright, we're actually sort of about string of numbers they're supposed to sort |
|
| 12:05 | where the steps are supposed to And then so we have in this |
|
| 12:12 | supposed to and you know, correspondent the test numbers, it's important to |
|
| 12:18 | to figure out how many ah expected kind of the first step. Um |
|
| 12:26 | that's just basically so 1-0-1, you do it. Um so this |
|
| 12:36 | there is no role. This is really strange. Let's talk about the |
|
| 12:43 | counties and then the next step is figure out in order to try to |
|
| 12:48 | the total order in terms of all the elements. So That means anything |
|
| 12:54 | inducted into the 3D effect would have something ah that was the numbering for |
|
| 13:01 | order of the elements in practice depends how many elements there are in the |
|
| 13:07 | of projects. So that's what the or So one, There are two |
|
| 13:25 | about zero. Yeah, Number you can start before this practice namaste |
|
| 13:40 | number from 2 to 4. So is, and that's particularly rank corporation |
|
| 13:51 | briefings operates from and then senses known having preclearance operations. So it's a |
|
| 13:59 | common operation that and let's see what is happening here. So no |
|
| 14:10 | If you do this, we're Thank you so much. Right, |
|
| 14:26 | 56. I don't know that's Before and after the first, First |
|
| 14:39 | , 677. Once you have starting for numbering and expected, then you |
|
| 14:45 | then go through and one of them mm hmm to get things sorted. |
|
| 14:56 | , you know, it's basically figuring ah after the permutation of supporting now |
|
| 15:04 | you have the rank order, you where they're supposed to go so that |
|
| 15:09 | best follow them and they end up you're supposed to do lots of areas |
|
| 15:20 | . So this is nothing bad. that's essentially the budget sort and now |
|
| 15:26 | see what else. So, um that's after the presentation and that's what |
|
| 15:35 | got. So how I'm talking about next thing about very sophisticated or how |
|
| 15:45 | . Mhm. And worked in the . So here is just a very |
|
| 15:54 | thing. Let's assume that I have notes. Mhm. Faith buckets. |
|
| 16:00 | just nice and doper not. So line is kind of the bucket. |
|
| 16:10 | it's a note from processing so that oh that's a copy of everybody. |
|
| 16:19 | the sense. So the first step , you know, whatever it is |
|
| 16:26 | buckets and the numbers. Mm mm hmm. Number of justice can |
|
| 16:35 | and make an order supposed to represent number of in the respective oxygen respective |
|
| 16:43 | . So then this is about need then find out, you know, |
|
| 16:47 | how many numbers are there. But one about the two that set and |
|
| 16:52 | on. The next two sides is . A little bit of time to |
|
| 16:56 | that ah in a low balanced way using time essentially some of the primitives |
|
| 17:07 | you're finding for instance FBI. So here is one way of doing it |
|
| 17:16 | there are many ways you can do . But this is one of the |
|
| 17:21 | that happened. Use that A 1000 so between their processors. So what's |
|
| 17:33 | this space for every other back into sort of sports in the world, |
|
| 17:40 | those right to something towards the higher the built in there. So |
|
| 17:52 | it's like a stimulant between the characters uh, between the first day of |
|
| 18:00 | process. No. And one I like it processor. That's |
|
| 18:09 | So it's called one that's something from birth process. We have to do |
|
| 18:18 | second processor for the company expected. one is for every other always don't |
|
| 18:29 | the top. It's for the It's this one that just between parents |
|
| 18:35 | processing and you keep doing that. the next time you do things again |
|
| 18:44 | and he's the guy, he's like , the first player to the left |
|
| 18:55 | the second, right for the So and then you do it one |
|
| 19:04 | time and now the best of the accounts. Ah what's in the first |
|
| 19:12 | sector But it's kind of the balance everything processor. I don't know. |
|
| 19:19 | , it doesn't. Yes. Everything up in single notes is perfect. |
|
| 19:23 | the balance between the process of us . And the communication as well. |
|
| 19:33 | , and then this is just metal on how this thing kind of works |
|
| 19:39 | I'm not but you can look at . I want to do it. |
|
| 19:44 | then, so here is where we up right prostitutes and it was mm |
|
| 20:05 | . Ah so that was that mm It was 24 and the first the |
|
| 20:19 | doctor those sorts of things. So that gets to have a starting |
|
| 20:26 | for each one of the buckets. then it's best to doing things kind |
|
| 20:31 | in reverse and then eventually we end with the order starting order for each |
|
| 20:40 | buckets every processes. So then you do the local assignments. So now |
|
| 20:51 | is just a administration and you and father kind of argument as walking respective |
|
| 20:59 | is a process just so this is of of course this is realistic because |
|
| 21:03 | choose the same number of budget number of processors, everything was hours |
|
| 21:08 | Tuesday, nice and easy. But generalizes so you can do this okay |
|
| 21:14 | it in a number one of this is going to work out what number |
|
| 21:22 | comparisons isn't doing this operation. So always not that one ended up |
|
| 21:33 | But so the back of sort is sort it's easiest to actually make good |
|
| 21:39 | of communication and depending on what the networks are. This particular swapping. |
|
| 21:47 | talked about at 15 before and that's sort of butterflies on paris of |
|
| 21:56 | index bits, bits. also the of process of part two. So |
|
| 22:00 | means if those are connected together using like the butterfly network which has been |
|
| 22:08 | or the other sort of more sophisticated that also have direct connect connection links |
|
| 22:17 | things for a notice that may be in any one of the obvious picks |
|
| 22:24 | that the communication and pattern in that maps through experience existing links the underlying |
|
| 22:32 | connecting notes. All right. Stop questions on dr sort and that's in |
|
| 22:45 | in a way underlying the sample sort was the rest is practical sorted for |
|
| 22:53 | a few years and then there hasn't one of our door in a tweet |
|
| 23:04 | bit over the years. Yeah, was kind of the last resort and |
|
| 23:09 | was invented. So um so the is kind of it's very similar to |
|
| 23:21 | bucket sort I would say the difference that there is respect in which you |
|
| 23:34 | to define the bucket sizes but done so um oh From the previous slide |
|
| 23:43 | just used the integral 0-9 um and go back in for each one of |
|
| 23:50 | . Thus find sometimes in instagram they're on instagram for some projects of data |
|
| 24:00 | well here's the revenge of data and divided the equal number intervals of |
|
| 24:06 | The market size is the banks of hint of all. But in general |
|
| 24:13 | one of those you know, tease may not be uniformly distributed. So |
|
| 24:17 | box it may have a lot more and many other things. So the |
|
| 24:22 | sort is trying to mitigate that the in terms of finding something but the |
|
| 24:29 | of known as the Lakers in the of the sample sort of trying to |
|
| 24:39 | . So some buckets have a larger of keys and others with the hope |
|
| 24:46 | I went back to roughly the same of keys by the justice the bucket |
|
| 24:54 | . So the worry that's being done you kind of randomly select fees or |
|
| 25:03 | on your happiness done collection of keys want to sort and then you're randomly |
|
| 25:11 | a bunch of she's and hope that keys would be good to define bucket |
|
| 25:21 | . So that's the notion of pleasures um now okay it says on the |
|
| 25:31 | right there there and said please you as ah many buckets as you have |
|
| 25:40 | and your system so that's great in case every node eventually have one but |
|
| 25:46 | the end So N -1 splitters. know, dividers that makes us in |
|
| 25:54 | of potential but but it turns out sometimes it's good to create more splinters |
|
| 26:04 | things get more refined than things that's low balance if you have a carton |
|
| 26:07 | their own practice and every note. for certain you know, not just |
|
| 26:13 | budget but the future budgets depending on the over something. So after when |
|
| 26:21 | had you know done this random selection teas from the collection of keys that |
|
| 26:27 | have there is no it takes the . So you need the best to |
|
| 26:34 | them and then figure out prompted constructed dark. So that's of course the |
|
| 26:43 | selection active in every note, choose few splinters of the past. So |
|
| 26:48 | a totally parallel operation then um the is but it's a small sector because |
|
| 26:57 | you know maybe a few small multiple the number of no such a hat |
|
| 27:02 | you don't have billions of keys and now and then hundreds of thousands of |
|
| 27:08 | and so it's considerably lower so that's and for that you can use surveying |
|
| 27:14 | for instance that are possible. So then you know communicators. So every |
|
| 27:24 | knows all the bucket boundaries, all pictures then it's the same thing as |
|
| 27:32 | in the back to sort every note science, it's set of keys to |
|
| 27:38 | buckets and then the best. So they have assumed that there is a |
|
| 27:47 | that there are as many buckets as processors basically. Then the idea is |
|
| 27:55 | you that's the same the bucket that it's going to be accumulated by another |
|
| 28:04 | or note to that processor. So know whatever 10 notes This process of |
|
| 28:12 | buckets And these are you know processing seven To keep number seven and all |
|
| 28:19 | other partners gets sent to respect the . So after that permutation, you |
|
| 28:24 | processor one, it does all the that goes into back in one from |
|
| 28:32 | the other process accepted the petition and to the local sort after that and |
|
| 28:38 | things are ordered In each note and ordered with respect to each other. |
|
| 28:43 | no two has larger keys and 100 . And just it's ending sequence that |
|
| 28:50 | want. So here is a little but their opponents again oh, it's |
|
| 29:02 | so easy to find. So all the activity, the numbers in terms |
|
| 29:11 | wow excited for this. Just the here. So now what is the |
|
| 29:26 | ? Mm hmm. Mentioned up. back to the expansion means the if |
|
| 29:35 | are perfect, every processor unknown. , the total number of keys divided |
|
| 29:44 | the number of processors. So it's average number there was hope in practice |
|
| 29:50 | doesn't happen perfectly. So some process all that more elements than the average |
|
| 29:58 | still work. So the bucket expansion to deal with how much to order |
|
| 30:05 | buckets or on average then the But taking the whole number divided by |
|
| 30:14 | number. So the expansion. So shows episode entirely over example directory |
|
| 30:22 | The closer you get to kind of purpose of hotels where everybody knows eventually |
|
| 30:28 | up close to the average number of . And then of course there is |
|
| 30:33 | deviation from the average. Uh Greatest stuff in any one of |
|
| 30:39 | And also the maximum appropriate number. is also in terms of the loan |
|
| 30:55 | and these are the system and that's probability statistics. Thank you. Figure |
|
| 31:08 | what the largest expected expansion. So it. There's a very high |
|
| 31:22 | Never just so don't stop. he said uh the second last |
|
| 31:41 | Rather than from using it should be careful exchange of data between the process |
|
| 31:47 | seems a little bit Okay. That's let's particular fence um Oh, |
|
| 32:00 | coincidence on. Yeah. So In the end, what you need |
|
| 32:06 | do is a presentation because you want the elements in this case and dr |
|
| 32:15 | To be on no, zero and you want. So wherever they are |
|
| 32:24 | the system, they need to go . So that is the problem. |
|
| 32:30 | , do that implement that station? is not said so every time like |
|
| 32:41 | . Uh huh we talked about once the bags and connect between the |
|
| 32:52 | Well, that's what's known as the . The factory connection, like the |
|
| 32:59 | we see all around and that's like computer science stream Branson and Branson |
|
| 33:08 | So, um that's it. Something look at the connective, what they |
|
| 33:15 | in the hierarchy of bottle lips because are so many of these um the |
|
| 33:20 | just that one has to So factory a property that's a number of links |
|
| 33:27 | as we go towards the road to with the reason, you know, |
|
| 33:33 | science are upside down trees and they at the bottom. And so I |
|
| 33:38 | get a source of closer to the . The bandwidth of the next |
|
| 33:44 | So a factory, it's Food Factory . This council has to go on |
|
| 33:50 | street. So especially didn't have a what's for system? Uh huh. |
|
| 34:09 | that would work. Um a quarter the of the system that could About |
|
| 34:16 | knows it. So, so it never worse than actually for that sort |
|
| 34:21 | one thing. So in principle it sustain computation without conference. The second |
|
| 34:30 | is uh contract, he's randomized routing track the whole balance and the whole |
|
| 34:38 | in the first. So when that because the marathon machine balance itself. |
|
| 34:47 | in that case we never awarded trying figure out clever for different data distributions |
|
| 34:54 | we're trying to build concurrency from the . It depends on the interconnect. |
|
| 35:01 | , Absolutely. So to do something mm hmm. So they're not too |
|
| 35:14 | machines after that have actually produced But there has been So this was |
|
| 35:21 | of the system and people vendors are nervous about using randomization. And I |
|
| 35:27 | because it's not clear, it's very to prove that it's deadlocked. So |
|
| 35:35 | I avoid want to avoid that. that pretty much. And there were |
|
| 35:41 | earlier machines to that actually that's the kind of butterfly network. It's |
|
| 35:49 | And in that case when we talked the SST was started with an input |
|
| 35:55 | And then it's very prestigious STD and there's the output. So the action |
|
| 36:01 | what people used it kind of processing on one side of this network and |
|
| 36:06 | other one was memory. That's and the randomized assignment from data and that |
|
| 36:14 | also the actual machine being. So any other questions on that. |
|
| 36:26 | so this was about the over sampling this is again from this particular |
|
| 36:32 | And so to differentiate where time with function for what was that? So |
|
| 36:45 | you can see in front of this protection part, there's no sense of |
|
| 36:51 | for this platform. What? And then exhorted exhorted speakers. And |
|
| 37:04 | was surprised that more pictures to He's uh he's a number of ah |
|
| 37:22 | The local store for $50. Over something. Is that the note |
|
| 37:32 | smaller is number of buckets in the part of the system. So as |
|
| 37:45 | think the maximum number in the Oh and the finance start conservatives |
|
| 37:57 | All right. I love this. even though the candidates sort is performed |
|
| 38:06 | a smaller number of data elements but interconnect cost of doing that is |
|
| 38:12 | That's why it's alright. That's all had and then it goes up |
|
| 38:19 | Thanks for for that pete. And I think this feels a little bit |
|
| 38:45 | and this was somewhere in here for me. Um So in this case |
|
| 39:00 | processor processor more dominating sequential. Um But we're also seeing his startup |
|
| 39:14 | 30 work four for the former central reasonable over time. And the |
|
| 39:48 | Once the sorting of the keys are we'll catch the keys. So this |
|
| 39:54 | kind of the basic idea that has about creating a load balance of his |
|
| 40:01 | persistence and as I said, there a winner and the number of competitions |
|
| 40:05 | a long time and I think of different Mary as well as and this |
|
| 40:11 | just um, then we implemented some on this particular machine. So |
|
| 40:17 | Okay, right. That's the So the benefit americans going too far |
|
| 40:34 | to give you some sense. this is for one of these, |
|
| 40:42 | a picture of this with the so it's a little bit in the |
|
| 40:56 | and this is especially comparing and really of, that is good sort. |
|
| 41:03 | . Yes. Right. And the , so I want you to be |
|
| 41:17 | of share short, I talked to last time. It's simple to |
|
| 41:21 | These are not very complicated an um, there's no way you're getting |
|
| 41:30 | balance in the system. So a of more things about sorting and I'm |
|
| 41:41 | to switch topics. So, this works also in Australia, is |
|
| 41:57 | to an award dinner? That's you know, so it was just |
|
| 42:05 | sort is a very simple idea and as much for the ideas for the |
|
| 42:11 | algorithm about sort. And the idea something worth Trying to remember this |
|
| 42:22 | So, again, so here's the idea that the americans back to |
|
| 42:32 | that term iconic sort. Mm hmm based on first to emerge on. |
|
| 42:39 | the sequence and then reversed the intelligent together. And so so the idea |
|
| 42:45 | this place stand by me on the splitters. So, but in this |
|
| 42:53 | most straightforward version Union Friends, some and they have the length of the |
|
| 43:01 | from equals the number of sub lists that's the square root of the |
|
| 43:06 | I guess we have something with someone roots sometimes by that number of |
|
| 43:13 | These two sequences are supposed to merge sequences sorted. So then what it |
|
| 43:20 | is first and find everybody. And they're yeah, there are solid someone |
|
| 43:26 | know that already increasing or decreasing whatever but you don't know how to do |
|
| 43:36 | relate to each other. So then to do is get start to work |
|
| 43:41 | this splitters. Again, the square that divided them into chunks and then |
|
| 43:47 | to pick it up where say one the boundaries or borders and boundaries, |
|
| 43:56 | they related to the others? So is my picture of trying to point |
|
| 44:02 | so you the for the sequence of sequence that's part of the division of |
|
| 44:13 | . But this time and then if and we are on this and then |
|
| 44:21 | the marge the solvents together. Not where you search all of these. |
|
| 44:32 | . So and once you have so you're not understanding From one piece |
|
| 44:38 | the other this. But this is very general idea that we're finding a |
|
| 44:51 | of algorithms and it's a good way thinking things that you have things. |
|
| 44:56 | do you emerged from business and it be fired? It was very silly |
|
| 45:01 | of in terms of theoretical balancing one the most efficient, very simple. |
|
| 45:09 | I want to get to be aware it in terms of how things can |
|
| 45:18 | and then I just have one more I guess in terms of sorting and |
|
| 45:23 | sort of thing. But this is about it, wow, I'm just |
|
| 45:29 | you before I don't spend time on inherent in this part of the collection |
|
| 45:36 | so on. It doesn't mean you play games with it but it's not |
|
| 45:41 | obvious and that's why the other sorts be new to you and not something |
|
| 45:47 | been talking to some other force but simple. Alright. So here is |
|
| 45:55 | instant so I just went through this so deep sort as human but it's |
|
| 46:03 | of general in the heat for a heat. This kind of water respectively |
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| 46:08 | so the numbers here. So the thing you get five or 3 And |
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| 46:17 | next time we get 087 and the smaller than 1st and and we need |
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| 46:27 | take down because it was smaller than the next one is 5 12 that |
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| 46:36 | like in order so that the speed and then just take penalties on the |
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| 46:41 | way. Oh Justin And the father 061 and that's smaller than ourselves. |
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| 46:52 | it's that's turning yet. So I'm but it's called the largest number the |
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| 47:09 | according to. That's right. That's . Okay. Ah So they're among |
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| 47:19 | actors. That's that same goal standing for. But in order to |
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| 47:38 | So, so I can think about time and then, but they're sorting |
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| 47:44 | pulls things out. And the reason I say that essentially the sequential because |
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| 47:49 | the start at the top of the , you get one number at the |
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| 47:53 | . There is no mechanism to consider whole bunch of numbers. Except there's |
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| 47:58 | story. There was a complication again to he has women's I've talked |
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| 48:09 | So that's one sentence inherently sequential in structure. It doesn't mean one student |
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| 48:16 | something on the top That was # . Just take down and property surrounded |
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| 48:22 | take new numbers. So, but some of the propositions that can be |
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| 48:26 | maternal, but we still have the that this can tell the limits. |
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| 48:33 | fine. So, so that's why it's quick sorters kind of similar |
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| 48:45 | So they're not necessarily the best of to organize and that's what I have |
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| 48:51 | sorting. And I have a few to talk about the next stop. |
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| 48:55 | kind of want to bring up. only one more lecture. So I |
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| 49:01 | that would be something that is generally general interest in the city. No |
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| 49:15 | trying to. All right. So switch of topics. So, so |
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| 49:28 | just um, this stuff which just they have a hard time distributing data |
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| 49:35 | notes in the system or potentially so long threads that should get more |
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| 49:40 | get the balance in health. So far we've talked mostly about simple |
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| 49:48 | drugs. All right. Thanks Talked about matrices and there's these two |
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| 49:55 | kind of blocking and columns by sub blocks and so on. Has |
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| 50:00 | straightforward. But if you have more datasets, the all the problems petition |
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| 50:15 | subsets and gets assigned to the different . So this is the topic when |
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| 50:22 | was going to try to address the next we are, I guess |
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| 50:33 | my background, scientific and engineering Some kind of element stuff influence remains |
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| 50:41 | arbitrary shapes. There's no simple way saying by rows and columns because there's |
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| 50:49 | such thing. So then what do do go through? And there's a |
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| 50:55 | set of methods that people have tried I'll do the simple things first. |
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| 51:02 | No one on that position. And are tools out there that don't talk |
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| 51:08 | it. Hopefully get to today. we talked about it next time. |
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| 51:16 | , um, so the point is what these things and depending upon your |
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| 51:25 | . One or the other are but one obvious thing that I always |
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| 51:29 | about is to try to make sure they're about the same amount of work |
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| 51:33 | also otherwise the slowest nobody substance always the time of things. Johnson go |
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| 51:41 | . Each note has roughly the same of work to do so again to |
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| 51:46 | close to the average time. The part also want to do it in |
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| 51:52 | a way that can minimize the amount data that needs to move, need |
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| 51:57 | be moved between the nose because the networks that usually is the performance in |
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| 52:05 | busters. Some applications don't need to much communication. It's not that many |
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| 52:12 | . The network traffic is the thing wanted the ones to kind of get |
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| 52:18 | amounts the same amount of work but and at the same time minimize the |
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| 52:23 | of messages or some aspect of the government system. So that's something objective |
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| 52:32 | do this data partitioning so and naive you just randomly assign things and that |
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| 52:40 | get pretty good balance but the communication like bring it out because it doesn't |
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| 52:47 | any notional ricardo and most of all computational matches behalf for solving ah physics |
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| 52:56 | engineering competition so basically works on neighborhood we talked about that. We're talking |
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| 53:01 | Jacoby Kobe was some shadow ridge and on this one because it's communication between |
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| 53:09 | cells have this differentiation stance on the thing and enables processing you have some |
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| 53:15 | of that's also what data you combined it doesn't go all over the |
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| 53:20 | So here is just our pictures and what people do come from most of |
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| 53:26 | science domain, some people do in case investment models. So you're calling |
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| 53:36 | into some elements for which of differential that felt it was supposed to happen |
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| 53:41 | each one and then you have to a global picture from the simulation and |
|
| 53:45 | just other things that do um and thank you father due to be imagined |
|
| 53:55 | the amount of computation depends on where are. If you're in the right |
|
| 54:00 | , it's probably not much activity going and right probably not but badly close |
|
| 54:11 | it where this just shoots up, there is no longer connectivity. So |
|
| 54:18 | can't necessarily you want the and not to say you want to send them |
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| 54:27 | over the world because they are refined . So here's other things I've seen |
|
| 54:38 | do and I'm trying to figure outside something they did that. And also |
|
| 54:45 | was involved with thinking about what that like constructing aircraft from the field around |
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| 54:51 | aircraft and here's other things about submarines molecular dynamics for that sense. |
|
| 55:00 | they atoms and molecules are not uniformly in space. So in that case |
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| 55:09 | also uneven amount of work getting involved and there's more effects, other |
|
| 55:15 | That's cool skating anyways, so that just trying to motivate that. |
|
| 55:21 | the underlying data structures used for describing problems are not as simple as red |
|
| 55:28 | baseball, all kinds of other So so there are underlying things. |
|
| 55:37 | that the mental model that the competition supposed to happen as the graph nodes |
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| 55:45 | the graph is the computation of the and the edges of the graph is |
|
| 55:50 | data interaction needs to happen between the whatever. So if you know, |
|
| 55:57 | you take a logistics problem that crew , whatever crews and the nose, |
|
| 56:04 | airports and whatever. Living to represent movement of people or goods or whatever |
|
| 56:13 | airport to airport and or traveling salesman . Not sure people know that. |
|
| 56:20 | there's a bunch of cities and roads terms of physics, there may be |
|
| 56:27 | once a few defining elements of computation presenting elements and then the differential equation |
|
| 56:37 | and use variables from other elements. then there's communication that helps the center |
|
| 56:44 | selection between elements. Right? So then that's our concept, they design |
|
| 56:52 | and other things. So this um end up if you represent things that |
|
| 57:00 | , it's also becomes a sparse matrix they thought and very large various force |
|
| 57:07 | . But anyway, so this is of the things so that people started |
|
| 57:14 | look at then. So if you this type of perhaps instructors, That's |
|
| 57:20 | of one question. one question of traditions like to answer. So you |
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| 57:26 | how good split if I want to things into parts of the two |
|
| 57:33 | So what is the best possible splitter can get in terms of separating the |
|
| 57:38 | into two pieces. Um So that's that's very famous. It's called |
|
| 57:48 | Um separate separate sergeant Preston goes arbitrary graph to explain her. So |
|
| 58:06 | is the best possible? Everyone's Don't tell you how to find |
|
| 58:11 | But just a while if I find is good or bad, the answers |
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| 58:15 | question. So it just says that a plane a graph no matter which |
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| 58:20 | is, no matter the size, can find something that's roughly a little |
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| 58:25 | on the square of the number of . So, so alexander gives you |
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| 58:34 | points when you want to fight. to separate the theorem is something you |
|
| 58:38 | have heard about in terms of computer in general because it's used in many |
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| 58:44 | contexts but also comes up and how for about data structures and pieces. |
|
| 58:52 | huh. All right. Mhm. right. Yeah, almost system |
|
| 59:04 | Ecstatic and honest. Mostly documents study compositions dynamic, you know, as |
|
| 59:11 | said, if you look at the problem that shop fronts then investment makes |
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| 59:17 | big partition in the space, depending much of a front moves because when |
|
| 59:22 | shock happens, that loss of computing the other part of it Lester. |
|
| 59:31 | So that's what the dynamic positioning and many ways to do that and you |
|
| 59:38 | , let's talk about that next So and here's a whole, this |
|
| 59:41 | a different grades do it. So I was grateful. First wave |
|
| 59:52 | . Very simple. Uh what's up being used for breakfast for perspective traditional |
|
| 60:06 | there are some methods out there that to that and the one that has |
|
| 60:12 | need for it certainly wearable and protection . So here's first the idea or |
|
| 60:21 | things on the graph just nodes and principle. All of those different ways |
|
| 60:29 | in different amounts of work. Uh represents and then the represents so much |
|
| 60:37 | has been transferred to also they're waiting something. They just and there they |
|
| 60:46 | currently so you get about the same of. Also this is one particular |
|
| 60:56 | you can look at the one american . Um Yeah. So basically |
|
| 61:10 | Okay. Ah That was on the work and and we're referencing on the |
|
| 61:29 | . That is very soft. Uh so this is work. Thanks. |
|
| 61:42 | hmm. Two more. Yes, a cartoon. And and the next |
|
| 61:49 | shows you Yes. By the simple of if you go thanks. That's |
|
| 61:57 | versus saying that this this conversation. . Conservative system. General. Oh |
|
| 62:14 | do that. Um So now I'm to quickly for someone. So when |
|
| 62:31 | read it visitors you will find things don't separate it and it's separated depending |
|
| 62:36 | what works the data structure is from the other and what better. So |
|
| 62:42 | this that one and if you think the what the what and then that |
|
| 63:08 | under under. But now so that's the key. Um So most of |
|
| 63:23 | things is talked about, it's usually no separators are supposed to be |
|
| 63:33 | So the simplest thing is again, you have a geometry but and face |
|
| 63:40 | take this Bruce scheduling problem that I coordinates doesn't have any need for |
|
| 63:50 | If you do some physical domain you know, many people going to |
|
| 63:57 | out what you know similar so or pressure or something and you have a |
|
| 64:04 | on the other part. Let us out of it Matea or some design |
|
| 64:10 | that has coordinates. In that case have a job but not everything. |
|
| 64:17 | this is you know, if you have a geometry you can petition things |
|
| 64:22 | to according to it. So here a very simple way of how you |
|
| 64:27 | this. So the idea here is work. Okay. Uh so you |
|
| 64:39 | want to test or something to do it. Uh just what's your name |
|
| 64:59 | . You know, it's one. here's what the coordinate perception works. |
|
| 65:05 | there and one of the government actors slow down once and then to do |
|
| 65:19 | other access. But now it looks the supplemental what vertical doesn't institute but |
|
| 65:31 | part you're not ending up why and keep doing that. And then you |
|
| 65:42 | get more and more partitions and that of works okay. And this if |
|
| 65:50 | are nicely aligned before, but then can tweak it on this side. |
|
| 65:55 | that no Hunter was tweeting, we're to get the partitions to be pleased |
|
| 66:02 | meet you. Mhm. I'm just things. And so here's the |
|
| 66:13 | So if you have something that is no longer um oriented and on record |
|
| 66:20 | this box here, I want to is what's more stuff no coordinate |
|
| 66:27 | So they basically tried to reorient the system. So it fits the |
|
| 66:33 | So now you're finally moments of the the structure and then they do the |
|
| 66:38 | respected commonality in terms of moments of . And if you do that now |
|
| 66:44 | get the slice like this since they the comments, the xy four |
|
| 66:51 | And then yes, but it's basically same idea. But instead of just |
|
| 66:55 | taking recording system, you find moments inertia and figure out this to get |
|
| 66:59 | coordinates system is more or less the in a sensible way with the structure |
|
| 67:07 | the next few slides is just telling How you can do this thing. |
|
| 67:12 | basically find 2D for simplicity in there's a hyper plane, but basically |
|
| 67:17 | time uh suspects in this case for lions and the that's the that the |
|
| 67:45 | the slides has a bit of that out to do the protection of the |
|
| 67:49 | of the line. Figure out what square distances and, and you go |
|
| 67:55 | the exercise of certain first figure out what the cut is that? |
|
| 68:02 | That let's go along here and then out what happened. That's right this |
|
| 68:08 | of on this side and that's what the 2nd and 4th. And so |
|
| 68:19 | is just showing that these squares kind um, sort of the coordinate with |
|
| 68:28 | bar is the center and then you do this. So this is just |
|
| 68:34 | that obviously is a big construction. don't want to cut this. So |
|
| 68:39 | will be very hard many events whereas want like this. So the orientation |
|
| 68:49 | the Oh, next question. So just under still. That was a |
|
| 68:58 | based. Now the thing that it's lot more flexible in general is to |
|
| 69:10 | an ocean of space filling curves and vertical space been encouraged before. |
|
| 69:18 | So the idea is that you cover in the space that you are interested |
|
| 69:25 | or infrastructure that's a hot. So this simple to the right investment. |
|
| 69:33 | would curve the rocks around some way all the squares or a tube for |
|
| 69:40 | of sub tubes And the elements with elements do something that walks around and |
|
| 69:49 | you order all the points in the . And then the idea is once |
|
| 69:55 | have this map your higher dimensional thing a line then just like up to |
|
| 70:02 | such that the segments of the lines may not be equal length but the |
|
| 70:09 | of points of the work on this of the line is the same and |
|
| 70:12 | your son the statement and there's a of standard works that um Yeah. |
|
| 70:21 | , it was on that one for on space and important. Come on |
|
| 70:32 | introduced. Yeah. Station and then us to the victor understand someone this |
|
| 70:43 | for the next on the one day . So that's one could also check |
|
| 70:49 | the correctness and so on because the . Yeah, the number of the |
|
| 70:54 | between Yes, I found him. , so we'll have a little time |
|
| 71:08 | show you A couple of examples of one. This in some range templates |
|
| 71:24 | then by mr protection uh different. . So that's everything. So you |
|
| 71:48 | 0.9. Yeah. Yeah. So that's one type of uh |
|
| 71:59 | No. Yes. So this is , that's the best the story of |
|
| 72:04 | the structure is flipping and and now are actually related to build structures but |
|
| 72:13 | , so I was a beyond So this is the Hilbert curves, |
|
| 72:18 | it up but not like that at . So usually if you shape and |
|
| 72:27 | is one that's another story and then next slide shows can actually generalize and |
|
| 72:55 | it's gonna be right here and uh and experience and short segments where many |
|
| 73:16 | statement from the owner. I wonder too built in the system and get |
|
| 73:26 | balanced drawing your arms and assistance and picture basically showing another going back to |
|
| 73:36 | that corresponding to this by That's something speaking up. Mhm. Oh |
|
| 73:50 | Because you know the the structure and of looks like what calendars and what's |
|
| 74:02 | illusion that it's not that but this like that the meeting suffering personally. |
|
| 74:27 | that's why I keep forgetting. So kind of another one that's what's so |
|
| 74:32 | . This is fun. Reordering disease without the it's also very strong. |
|
| 74:49 | so uh um maybe expect them all find out organize things in terms of |
|
| 75:00 | memory because that's sort of a very time to minimize and so on. |
|
| 75:08 | compiler of people trying to figure out to do this assignment of data to |
|
| 75:14 | many members of neurons in order to local the reality in terms of memory |
|
| 75:24 | . Hi folks playing around with the . Mhm. Mhm. Now this |
|
| 75:33 | the great code ordering that show but can also build this traverse salon space |
|
| 75:39 | that they're not utilizing number of big that sometimes or a total crypt. |
|
| 75:44 | wanted to show you for people who that are producing these things. So |
|
| 75:50 | are results from some sentiments that's great each one of his for different one |
|
| 76:12 | . Okay. So what's going on ? Is that one thing that is |
|
| 76:22 | interest to the establishment that's the final votes. It's trying to figure out |
|
| 76:29 | surface for volume aspects of the So publicity for a supplement translating communication |
|
| 76:38 | other supplements sister. Mm hmm. the surface and the volume represents work |
|
| 76:48 | to London. Yes. What's the ? They don't start supplements 79 last |
|
| 77:08 | ah company and or domestically vertical direction to the surface. Oh no |
|
| 77:29 | And then they call the one is the most expensive very well, you |
|
| 77:43 | , structures in terms of getting the . It's also yeah, the old |
|
| 77:55 | and sometimes the maximum the average awesome . Absolutely. I'm confused. This |
|
| 78:06 | about 1000 and then there's one more and then I believe that stuff |
|
| 78:16 | What's up? So this uh, more comes out communication which influences from |
|
| 78:23 | the neighbors, carving up the, know, oh hey brian elements in |
|
| 78:33 | final element structure ends up in some notes and then not all of the |
|
| 78:39 | is in some place. So and number of other partitions for each one |
|
| 78:44 | . So they start how many and you call me facing imports. |
|
| 79:02 | uniform. Okay. This was done real computations for them. 57. |
|
| 79:25 | you know, so if one doesn't a simple in the box domain that |
|
| 79:31 | can use uniform partitioning of the domain we want to look at some of |
|
| 79:36 | motion in general petitioning methods being Um, There are packages again after |
|
| 79:46 | , 2 petitions. They don't. right. I don't think so. |
|
| 79:53 | the tradition goes on the moment. don't think anyone investment what produce someone |
|
| 80:06 | about next time. Ah, so might be useful to someone that's, |
|
| 80:15 | , does parallel computation on so many . So any questions on this stop |
|
| 80:36 | for a moment. Mm hmm. can |
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