Download presentation

Presentation is loading. Please wait.

Published byLisa Benjamin Modified over 2 years ago

1
1 Local Computation Mechanism Design Shai Vardi, Tel Aviv University Joint work with Avinatan Hassidim & Yishay Mansour UC Berekely, February 18 th, 2014

2
2 Motivation Imagine a huge auction, with millions of items and hundreds of thousands of buyers. An item arrives to be shipped. We don’t want to have to compute the result of the entire auction, just to know to which buyer to ship the item…. There is a cloud with millions of computers on which we would like to schedule millions of jobs. We are queried on a job and would like to reply on which machine it should run. But we don’t want to compute the entire schedule….

3
Example – a combinatorial auction

4
Which item does Dudu get?

5
When do we need Local Computation Algorithms (LCAs)? Huge input. Not enough time or space to calculate the entire solution. Only need small parts of the solution at any one time. Local Computation Algorithms 5

6
6 LCAs implement query access to a global solution. We require LCAs to be: Fast – at most polylogarithmic in the input size per query. Space-efficient – at most polylogarithmic overall. Replies to all queries are consistent with the same solution.

7
7 Related work Local computation of PageRank contributions Andersen et al., 2008. Property-preserving data reconstruction Ailon et al., 2008. On the efficiency of local decoding procedures for error- correcting codes Katz and Trevisan, 2000.

8
8 Previous work on LCAs Fast local computation algorithms Rubinfeld, Tamir, V and Xie, 2011. Space-efficient local computation algorithms Alon, Rubinfeld, V and Xie, 2012. Converting online algorithms to local computation algorithms Mansour, Rubinstein, V and Xie, 2012. Tighter bounds for local computations Reingold and V, 2014.

9
Local computation mechanism design

10
Mechanisms without payment Usually, the allocation is harder to find than the payments. This is especially true considering the large volume of work on calculating payments in the past few years, e.g., Babaioff, Kleinberg, Silvkins, EC ‘10, EC ‘13. Therefore, I won’t get into payments in this talk. I will focus on mechanisms without payments.

11
Stable matching The problem: There is a group of men and women. Each man has a preference list over the women, and each woman has a preference list over the men. A stable matching is one in which there is no man and woman who both prefer each other over their matched partner.

12
Stable matching The Gale-Shapley algorithm (’62) (male courtship): Each man goes to his most preferred woman. Each woman chooses which man to keep. The rejected men go to their next-preferred woman. Each woman once again chooses which man to keep, and so on.

13
Stable matching

14
14 Restrictions

15
Restrictions for stable matching 1 2 1 2 2 1 1 2 1 2 2 1 1 2 1 2 1 2 2 1 1 2 1 2 2 1 1 22 1 1 1 1 2 1

16
Local mechanism for stable matching

17
Previous work Truncation strategies in matching markets. Roth and Rothblum,1999. A parallel iterative improvement stable matching algorithm. Lu and Zheng, 2003. Marriage, honesty, and stability. Immorlica and Mahdian, 2005. Almost stable matchings by truncating the Gale-Shapley algorithm. Floreen et al., 2010.

18
Stable matching LCA

20
Proof intuition – why is it local?

22
Stable matching LCA

23
How many men are left unmatched? k=1

24
k=2

25
Stable matching LCA

26
Proof of 3)

27
From monotonicity

28
Stable matching LCA recap

29
Some more local computation mechanisms

30
The non-local case We show how to apply our techniques to the non-local case.

31
Approximating the Gale-Shapley algorithm

34
2-approximating the Gale-Shapley algorithm

39
Part 1 of the proof

40
Part 2 of the proof

43
Gale-Shapley approximation recap

44
44 Thank you for listening! Questions?

Similar presentations

OK

CSCI 256 Data Structures and Algorithm Analysis Lecture 2 Some slides by Kevin Wayne copyright 2005, Pearson Addison Wesley all rights reserved, and some.

CSCI 256 Data Structures and Algorithm Analysis Lecture 2 Some slides by Kevin Wayne copyright 2005, Pearson Addison Wesley all rights reserved, and some.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on resistance temperature detectors Ppt on obesity diet medications Download ppt on wastewater management Ppt on holographic technology companies Ppt on online banking in india Download ppt on the changing world of visual arts Seminar ppt on bluetooth technology Slideshare download ppt on pollution Ppt on polynomials of 900 Ppt on famous places in india