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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

46:08 so the numbers here. So the thing you get five or 3 And

46:17 next time we get 087 and the smaller than 1st and and we need

46:27 take down because it was smaller than the next one is 5 12 that

46:36 like in order so that the speed and then just take penalties on the

46:41 way. Oh Justin And the father 061 and that's smaller than ourselves.

46:52 it's that's turning yet. So I'm but it's called the largest number the

47:09 according to. That's right. That's . Okay. Ah So they're among

47:19 actors. That's that same goal standing for. But in order to

47:38 So, so I can think about time and then, but they're sorting

47:44 pulls things out. And the reason I say that essentially the sequential because

47:49 the start at the top of the , you get one number at the

47:53 . There is no mechanism to consider whole bunch of numbers. Except there's

47:58 story. There was a complication again to he has women's I've talked

48:09 So that's one sentence inherently sequential in structure. It doesn't mean one student

48:16 something on the top That was # . Just take down and property surrounded

48:22 take new numbers. So, but some of the propositions that can be

48:26 maternal, but we still have the that this can tell the limits.

48:33 fine. So, so that's why it's quick sorters kind of similar

48:45 So they're not necessarily the best of to organize and that's what I have

48:51 sorting. And I have a few to talk about the next stop.

48:55 kind of want to bring up. only one more lecture. So I

49:01 that would be something that is generally general interest in the city. No

49:15 trying to. All right. So switch of topics. So, so

49:28 just um, this stuff which just they have a hard time distributing data

49:35 notes in the system or potentially so long threads that should get more

49:40 get the balance in health. So far we've talked mostly about simple

49:48 drugs. All right. Thanks Talked about matrices and there's these two

49:55 kind of blocking and columns by sub blocks and so on. Has

50:00 straightforward. But if you have more datasets, the all the problems petition

50:15 subsets and gets assigned to the different . So this is the topic when

50:22 was going to try to address the next we are, I guess

50:33 my background, scientific and engineering Some kind of element stuff influence remains

50:41 arbitrary shapes. There's no simple way saying by rows and columns because there's

50:49 such thing. So then what do do go through? And there's a

50:55 set of methods that people have tried I'll do the simple things first.

51:02 No one on that position. And are tools out there that don't talk

51:08 it. Hopefully get to today. we talked about it next time.

51:16 , um, so the point is what these things and depending upon your

51:25 . One or the other are but one obvious thing that I always

51:29 about is to try to make sure they're about the same amount of work

51:33 also otherwise the slowest nobody substance always the time of things. Johnson go

51:41 . Each note has roughly the same of work to do so again to

51:46 close to the average time. The part also want to do it in

51:52 a way that can minimize the amount data that needs to move, need

51:57 be moved between the nose because the networks that usually is the performance in

52:05 busters. Some applications don't need to much communication. It's not that many

52:12 . The network traffic is the thing wanted the ones to kind of get

52:18 amounts the same amount of work but and at the same time minimize the

52:23 of messages or some aspect of the government system. So that's something objective

52:32 do this data partitioning so and naive you just randomly assign things and that

52:40 get pretty good balance but the communication like bring it out because it doesn't

52:47 any notional ricardo and most of all computational matches behalf for solving ah physics

52:56 engineering competition so basically works on neighborhood we talked about that. We're talking

53:01 Jacoby Kobe was some shadow ridge and on this one because it's communication between

53:09 cells have this differentiation stance on the thing and enables processing you have some

53:15 of that's also what data you combined it doesn't go all over the

53:20 So here is just our pictures and what people do come from most of

53:26 science domain, some people do in case investment models. So you're calling

53:36 into some elements for which of differential that felt it was supposed to happen

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

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

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

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

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

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

58:15 question. So it just says that a plane a graph no matter which

58:20 is, no matter the size, can find something that's roughly a little

58:25 on the square of the number of . So, so alexander gives you

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

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

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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