on the communication complexity of sparse set
play

On the communication complexity of sparse set disjointness and - PowerPoint PPT Presentation

Oct 01, 2023 •565 likes •1.94k views

On the communication complexity of sparse set disjointness and exists-equal problems Mert Saglam University of Washington Joint work with Gbor Tardos Communication complexity f(X,Y)=? X Y Alice Bob R: Shared random source R

  1. Our bound: R r (DISJ k ) ≤ O(k log (r) k) Run r rounds ➡ If S’=T’= ∅ , declare DISJOINT ➡ Otherwise, declare INTERSECT • p i = 1 /exp (i) (5 log (r) k) Fact 1 • if S ∩ T= ∅ , in r rounds S’=T’= ∅ Fact 2 |message i | ≤ 5k log (r) k / 2 i |message i | ≤ ∏ i/2 p i-2t+ 1 |S| log 1 /p i For i> 3, t= 1 k log exp (i) ≤ k / 2 i ≤ exp (i- 1 ) exp (i-3)

  2. The lower bound

  3. Exists-equal problem • Stronger lower bound: easier problem exists-equal (EE)

  4. Exists-equal problem • Stronger lower bound: easier problem exists-equal (EE) • Let x,y ∈ [t] n

  5. Exists-equal problem • Stronger lower bound: easier problem exists-equal (EE) • Let x,y ∈ [t] n • EE n (x, y) = 1 iff ∃ i, x i =y i t

  6. Exists-equal problem • Stronger lower bound: easier problem exists-equal (EE) • Let x,y ∈ [t] n • EE n (x, y) = 1 iff ∃ i, x i =y i t x: 3 4 4 5 1 y: 2 3 4 2 4

  7. Exists-equal problem • Stronger lower bound: easier problem exists-equal (EE) • Let x,y ∈ [t] n • EE n (x, y) = 1 iff ∃ i, x i =y i t x: 3 4 4 5 1 y: 2 3 4 2 4 So EE(x,y)= 1

  8. Exists-equal problem • EE n is OR of n equality problems over [t]. t • EE n = DISJ n t tn

  9. Exists-equal problem • EE n is OR of n equality problems over [t]. t • EE n = DISJ n t tn 3 4 4 5 1 2 3 4 2 4

  10. Exists-equal problem • EE n is OR of n equality problems over [t]. t • EE n = DISJ n t tn • • • • ● • 3 4 4 5 1 = ● ● ● ● • • • • • 2 3 4 2 4 ● ● ● ● ●

  11. Exists-equal problem • EE n is OR of n equality problems over [t]. t • EE n = DISJ n t tn • • • • ● • 3 4 4 5 1 = ● ● ● ● • • • • • 2 3 4 2 4 ● ● ● ● ●

  12. Exists-equal problem • EE n is OR of n equality problems over [t]. t • EE n = DISJ n t tn • • • • ● • 3 4 4 5 1 = ● ● ● ● • • • • • 2 3 4 2 4 ● ● ● ● ● |S| = |T| = n S, T ⊂ [nt]

  13. The lower bound • Show: any r-round EE protocol communicates Ω (n log (r) n) bits.

  14. The lower bound • Show: any r-round EE protocol communicates Ω (n log (r) n) bits. • EE is OR of n equality problems, so decompose to subproblems

  15. The lower bound • Show: any r-round EE protocol communicates Ω (n log (r) n) bits. • EE is OR of n equality problems, so decompose to subproblems • Show Ω (log (r) n) lower bound per subproblem

  16. The lower bound • Show: any r-round EE protocol communicates Ω (n log (r) n) bits. • EE is OR of n equality problems, so decompose to subproblems • Show Ω (log (r) n) lower bound per subproblem • Equality has O( 1 ) bit communication protocol

  17. The lower bound • Show: any r-round EE protocol communicates Ω (n log (r) n) bits. • EE is OR of n equality problems, so decompose to subproblems • Show Ω (log (r) n) lower bound per subproblem • Equality has O( 1 ) bit communication protocol

  18. The lower bound • Show: any r-round EE protocol communicates Ω (n log (r) n) bits. • EE is OR of n equality problems, so decompose to subproblems • Show Ω (log (r) n) lower bound per subproblem • Equality has O( 1 ) bit communication protocol • We get super-linear increase in complexity!

  19. The lower bound By Yao’s lemma, sufficient to consider deterministic protocols with random input

  20. The lower bound By Yao’s lemma, sufficient to consider deterministic protocols with random input ๏ Set t=4n

  21. The lower bound By Yao’s lemma, sufficient to consider deterministic protocols with random input ๏ Set t=4n ๏ Hard distribution ν : (x,y) ∈ [t] n x [t] n , uniform random

  22. The lower bound By Yao’s lemma, sufficient to consider deterministic protocols with random input ๏ Set t=4n ๏ Hard distribution ν : (x,y) ∈ [t] n x [t] n , uniform random ๏ 3/4 ⩽ Pr (x,y) ~ ν [EE(x,y)=0] = ( 1 - 1 /(4n)) n ⩽ e - 1 /4 < 0.78

  23. The lower bound By Yao’s lemma, sufficient to consider deterministic protocols with random input ๏ Set t=4n ๏ Hard distribution ν : (x,y) ∈ [t] n x [t] n , uniform random ๏ 3/4 ⩽ Pr (x,y) ~ ν [EE(x,y)=0] = ( 1 - 1 /(4n)) n ⩽ e - 1 /4 < 0.78 ๏ ⇒ Any 0-round protocol has 0.22 error

  24. Round elimination Thm: No r-round C = O(n log (r) n)-bits protocol for EE n t Induction on r:

  25. Round elimination Thm: No r-round C = O(n log (r) n)-bits protocol for EE n t Induction on r: r-round C= 𝛇 n log (r) n-bits t protocol for EE n

  26. ⇒ Round elimination Thm: No r-round C = O(n log (r) n)-bits protocol for EE n t Induction on r: r-round C= 𝛇 n log (r) n-bits construct t protocol for EE n

  27. ⇒ Round elimination Thm: No r-round C = O(n log (r) n)-bits protocol for EE n t Induction on r: r-round C= 𝛇 n log (r) n-bits construct t protocol for EE n (r- 1 )-round 1 0C-bits protocol for EE n’ where t’ n’=n/B and t’=t/B B =2 C/n

  28. ⇒ Round elimination Thm: No r-round C = O(n log (r) n)-bits protocol for EE n t Induction on r: r-round C= 𝛇 n log (r) n-bits construct t protocol for EE n (r- 1 )-round 1 0C-bits protocol for EE n’ where t’ n’=n/B and t’=t/B B =2 C/n Observe 1 0C= 𝛑 (n’ log (r- 1 ) n’) Contradicts induction hypothesis!

  29. ⇒ Round elimination Thm: No r-round C = O(n log (r) n)-bits protocol for EE n t Induction on r: r-round C= 𝛇 n log (r) n-bits construct t protocol for EE n (r- 1 )-round 1 0C-bits protocol for EE n’ where t’ n’=n/B and t’=t/B B =2 C/n Observe 1 0C= 𝛑 (n’ log (r- 1 ) n’) Note: Contradicts induction hypothesis! t’=4n’

  30. Fixing the first message x 1 x 2 x 3 x 4 x 5 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ x t n

  31. Fixing the first message x 1 x 2 x 3 x 4 x 5 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ x t n

  32. Fixing the first message x 1 x 2 x 3 • Throw x 0 , Pr y [P(x 0 ,y) ≠ EE(x 0 ,y)] ≥ 2 δ x 4 x 5 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ x t n

  33. Fixing the first message x 1 x 2 x 3 • Throw x 0 , Pr y [P(x 0 ,y) ≠ EE(x 0 ,y)] ≥ 2 δ x 4 x 5 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ x t n

  34. Fixing the first message x 1 x 2 x 3 • Throw x 0 , Pr y [P(x 0 ,y) ≠ EE(x 0 ,y)] ≥ 2 δ x 4 x 5 ⋮ • At most half the inputs are gone ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ x t n

  35. Fixing the first message x 1 x 2 x 3 • Throw x 0 , Pr y [P(x 0 ,y) ≠ EE(x 0 ,y)] ≥ 2 δ x 4 x 5 ⋮ • At most half the inputs are gone ⋮ ⋮ ⋮ • Fix the most frequent message m* ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ x t n

  36. Fixing the first message x 1 x 2 x 3 • Throw x 0 , Pr y [P(x 0 ,y) ≠ EE(x 0 ,y)] ≥ 2 δ x 4 x 5 ⋮ • At most half the inputs are gone ⋮ ⋮ ⋮ • Fix the most frequent message m* ⋮ ⋮ ⋮ • Let S ⊆ [t] n be inputs on which m* is sent ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ x t n

  37. Fixing the first message x 1 x 2 x 3 • Throw x 0 , Pr y [P(x 0 ,y) ≠ EE(x 0 ,y)] ≥ 2 δ x 4 x 5 ⋮ • At most half the inputs are gone ⋮ ⋮ ⋮ • Fix the most frequent message m* ⋮ ⋮ ⋮ • Let S ⊆ [t] n be inputs on which m* is sent ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ x t n

  38. Fixing the first message x 1 x 2 x 3 • Throw x 0 , Pr y [P(x 0 ,y) ≠ EE(x 0 ,y)] ≥ 2 δ x 4 x 5 ⋮ • At most half the inputs are gone ⋮ ⋮ ⋮ • Fix the most frequent message m* ⋮ ⋮ ⋮ • Let S ⊆ [t] n be inputs on which m* is sent ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ x t n

  39. Fixing the first message x 1 x 2 x 3 • Throw x 0 , Pr y [P(x 0 ,y) ≠ EE(x 0 ,y)] ≥ 2 δ x 4 x 5 ⋮ • At most half the inputs are gone ⋮ ⋮ ⋮ • Fix the most frequent message m* ⋮ ⋮ ⋮ • Let S ⊆ [t] n be inputs on which m* is sent ⋮ ⋮ ⋮ ⋮ ⋮ • C-bits protocol ⇒ ≤ 2 C different messages ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ x t n

  40. Fixing the first message x 1 x 2 x 3 • Throw x 0 , Pr y [P(x 0 ,y) ≠ EE(x 0 ,y)] ≥ 2 δ x 4 x 5 ⋮ • At most half the inputs are gone ⋮ ⋮ ⋮ • Fix the most frequent message m* ⋮ ⋮ ⋮ • Let S ⊆ [t] n be inputs on which m* is sent ⋮ ⋮ ⋮ ⋮ ⋮ • C-bits protocol ⇒ ≤ 2 C different messages ⋮ ⋮ ⋮ ⋮ ⋮ • |S| ≥ t n /2 C+ 1 ⋮ x t n

  41. r-round protocol for EE n ⇒ t (r- 1 )-round protocol for t’ B = 2 C/n [t] n n’ = n/B S S u,v ∈ [t’] n’ S u B u X Randomness repeat B times v v B S S Y

  42. r-round protocol for EE n ⇒ t (r- 1 )-round protocol for t’ B = 2 C/n [t] n n’ = n/B S S u,v ∈ [t’] n’ S u B u X Randomness repeat B times v v B S S Y

  43. r-round protocol for EE n ⇒ t (r- 1 )-round protocol for t’ B = 2 C/n [t] n n’ = n/B S X’ S u,v ∈ [t’] n’ S u B u X Randomness repeat B times v v B S S Y

  44. r-round protocol for EE n ⇒ t (r- 1 )-round protocol for t’ B = 2 C/n [t] n n’ = n/B S X’ S u,v ∈ [t’] n’ S u B u X Randomness repeat B times v v B S S Y ① EE(u,v) ≈ EE(X’, Y)

  45. r-round protocol for EE n ⇒ t (r- 1 )-round protocol for t’ B = 2 C/n [t] n n’ = n/B S X’ S u,v ∈ [t’] n’ S u B u X Randomness repeat B times v v B S S Y ① EE(u,v) ≈ EE(X’, Y) ② Y | X’ is ≈ uniform

  46. r-round protocol for EE n ⇒ t (r- 1 )-round protocol for t’ B = 2 C/n [t] n n’ = n/B S X’ S u,v ∈ [t’] n’ S u B u X Randomness repeat B times v v B S S Y ① EE(u,v) ≈ EE(X’, Y) ② Y | X’ is ≈ uniform ③ X’ ∈ S ⇒ first message fixed

  47. t’ Protocol for EE n’ :

  48. t’ Protocol for EE n’ : Given u,v ∈ [t’] n’

  49. t’ Protocol for EE n’ : Given u,v ∈ [t’] n’ u: 2 3 1 4 2 1 v: 4 2 3 4 1 3

  50. t’ Protocol for EE n’ : Recall n’ = n/B B =2 C/n Given u,v ∈ [t’] n’ u: 2 3 1 4 2 1 v: 4 2 3 4 1 3

  51. t’ Protocol for EE n’ : Recall n’ = n/B B =2 C/n Given u,v ∈ [t’] n’ Repeat each coordinate B times u: 2 3 1 4 2 1 v: 4 2 3 4 1 3

  52. t’ Protocol for EE n’ : Recall n’ = n/B B =2 C/n Given u,v ∈ [t’] n’ Repeat each coordinate B times u B : u: 2 3 1 4 2 1 2 2 2 2 3 3 3 3 1 1 1 1 4 4 4 4 2 2 2 2 1 1 1 1 v B : v: 4 2 3 4 1 3 4 4 4 4 2 2 2 2 3 3 3 3 4 4 4 4 1 1 1 1 3 3 3 3

  53. t’ Protocol for EE n’ : Recall n’ = n/B B =2 C/n Given u,v ∈ [t’] n’ Repeat each coordinate B times u B : u: 2 3 1 4 2 1 2 2 2 2 3 3 3 3 1 1 1 1 4 4 4 4 2 2 2 2 1 1 1 1 v B : v: 4 2 3 4 1 3 4 4 4 4 2 2 2 2 3 3 3 3 4 4 4 4 1 1 1 1 3 3 3 3 Pick a random function f i : [t’] ↦ [t] for each i ∈ [n]

  54. t’ Protocol for EE n’ : Recall n’ = n/B B =2 C/n Given u,v ∈ [t’] n’ Repeat each coordinate B times u B : u: 2 3 1 4 2 1 2 2 2 2 3 3 3 3 1 1 1 1 4 4 4 4 2 2 2 2 1 1 1 1 v B : v: 4 2 3 4 1 3 4 4 4 4 2 2 2 2 3 3 3 3 4 4 4 4 1 1 1 1 3 3 3 3 Pick a random 4 2 7 9 2 7 3 6 2 5 2 6 9 3 1 7 6 7 8 4 2 6 9 3 function f i : [t’] ↦ [t] 6 3 1 3 8 7 1 5 4 7 8 9 9 3 1 7 2 1 3 6 9 2 2 1 for each i ∈ [n] : Phantom match ⦁

  55. t’ Protocol for EE n’ : Recall n’ = n/B B =2 C/n Given u,v ∈ [t’] n’ Repeat each coordinate B times u B : u: 2 3 1 4 2 1 2 2 2 2 3 3 3 3 1 1 1 1 4 4 4 4 2 2 2 2 1 1 1 1 v B : v: 4 2 3 4 1 3 4 4 4 4 2 2 2 2 3 3 3 3 4 4 4 4 1 1 1 1 3 3 3 3 Pick a random 4 2 7 9 2 7 3 6 2 5 2 6 9 3 1 7 6 7 8 4 2 6 9 3 function f i : [t’] ↦ [t] 6 3 1 3 8 7 1 5 4 7 8 9 9 3 1 7 2 1 3 6 9 2 2 1 for each i ∈ [n] : Phantom match ⦁ Permute coordinates randomly

  56. t’ Protocol for EE n’ : Recall n’ = n/B B =2 C/n Given u,v ∈ [t’] n’ Repeat each coordinate B times u B : u: 2 3 1 4 2 1 2 2 2 2 3 3 3 3 1 1 1 1 4 4 4 4 2 2 2 2 1 1 1 1 v B : v: 4 2 3 4 1 3 4 4 4 4 2 2 2 2 3 3 3 3 4 4 4 4 1 1 1 1 3 3 3 3 Pick a random 4 2 7 9 2 7 3 6 2 5 2 6 9 3 1 7 6 7 8 4 2 6 9 3 function f i : [t’] ↦ [t] 6 3 1 3 8 7 1 5 4 7 8 9 9 3 1 7 2 1 3 6 9 2 2 1 for each i ∈ [n] : Phantom match ⦁ Permute 3 2 8 1 5 9 2 3 3 7 6 3 9 7 6 9 7 7 4 2 5 9 5 8 coordinates randomly 1 8 3 1 7 3 9 3 1 1 2 1 2 7 5 3 1 7 6 3 7 9 7 3

  57. t’ Protocol for EE n’ : Recall n’ = n/B B =2 C/n Given u,v ∈ [t’] n’ Repeat each coordinate B times u B : u: 2 3 1 4 2 1 2 2 2 2 3 3 3 3 1 1 1 1 4 4 4 4 2 2 2 2 1 1 1 1 v B : v: 4 2 3 4 1 3 4 4 4 4 2 2 2 2 3 3 3 3 4 4 4 4 1 1 1 1 3 3 3 3 Pick a random 4 2 7 9 2 7 3 6 2 5 2 6 9 3 1 7 6 7 8 4 2 6 9 3 function f i : [t’] ↦ [t] 6 3 1 3 8 7 1 5 4 7 8 9 9 3 1 7 2 1 3 6 9 2 2 1 for each i ∈ [n] : Phantom match ⦁ Permute X: 3 2 8 1 5 9 2 3 3 7 6 3 9 7 6 9 7 7 4 2 5 9 5 8 coordinates Y: randomly 1 8 3 1 7 3 9 3 1 1 2 1 2 7 5 3 1 7 6 3 7 9 7 3

  58. Step 2: Rounding to S B = 2 C/n [t] n n’ = n/B S S u,v ∈ [t’] n’ S u B u X Randomness repeat B times v v B S S Y ① EE(u,v) ≈ EE(X’, Y) ② Y | X’ is ≈ uniform ③ X’ ∈ S ⇒ first message fixed

  59. Step 2: Rounding to S B = 2 C/n [t] n n’ = n/B S X’ S u,v ∈ [t’] n’ S u B u X Randomness repeat B times v v B S S Y ① EE(u,v) ≈ EE(X’, Y) ② Y | X’ is ≈ uniform ③ X’ ∈ S ⇒ first message fixed

  60. • N x = S ∩ Ball ( X, n( 1-1 /B) ) S N x • X’: uniform in N X

  61. • N x = S ∩ Ball ( X, n( 1-1 /B) ) S N x • X’: uniform in N X ③ X’ ∈ S ⇒ first message fixed

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Data Streams &amp; Communication Complexity Lecture 3: Communication Complexity and Lower Bounds

Data Streams &amp; Communication Complexity Lecture 3: Communication Complexity and Lower Bounds

Data Streams &amp; Communication Complexity Lecture 3: Communication Complexity and Lower Bounds Andrew McGregor, UMass Amherst 1/23 Basic Communication Complexity Three friends Alice, Bob, and Charlie each have some information x , y , z

1.11k views • 98 slides
Communication Complexity BASICS Summer School 2015 Communication

Communication Complexity BASICS Summer School 2015 Communication

Communication Complexity BASICS Summer School 2015 Communication Complexity of Relations Direct Sum Lower Bounds for Disjointness Asymmetric Communication Complexity and Data Structures d H ( x, y ) 0

1.7k views • 154 slides
A Stable Marriage Requires Communication Complexity Communication Complexity Proofs Yannai A.

A Stable Marriage Requires Communication Complexity Communication Complexity Proofs Yannai A.

Background Query A Stable Marriage Requires Communication Complexity Communication Complexity Proofs Yannai A. Gonczarowski Open Problems The Hebrew University of Jerusalem and Microsoft Research January 5, 2015 Joint work with: Noam

1.48k views • 121 slides
Communication Complexity Lecture 23 Computing with remote inputs 1 Communication Complexity

Communication Complexity Lecture 23 Computing with remote inputs 1 Communication Complexity

Communication Complexity Lecture 23 Computing with remote inputs 1 Communication Complexity 2 Communication Complexity Setting 2 Communication Complexity Setting Alice wants to compute f(x,y) 2 Communication Complexity Setting

1.58k views • 105 slides
Scalable Communication Protocols for Dynamic Sparse Data Exchange Torsten Hoefler, Christian

Scalable Communication Protocols for Dynamic Sparse Data Exchange Torsten Hoefler, Christian

Scalable Communication Protocols for Dynamic Sparse Data Exchange Torsten Hoefler, Christian Siebert, Andrew Lumsdaine PPoPP 2010, Bangalore, India The Sparse Data Exchange Problem Defines a generic communication problem Assume a set of

545 views • 26 slides
Managing Complexity in the Parallel Sparse Grid Combination Technique J. W. Larson 1 P. E.

Managing Complexity in the Parallel Sparse Grid Combination Technique J. W. Larson 1 P. E.

Managing Complexity in the Parallel Sparse Grid Combination Technique J. W. Larson 1 P. E. Strazdins 2 M. Hegland 1 B. Harding 1 S. Roberts 1 L. Stals 1 A. P. Rendell 2 M. Ali 2 J. Southern 3 1 Mathematical Sciences Institute, The Australian

570 views • 25 slides
On Characterizing the Relationship between Lower Bound Methods in Communication Complexity

On Characterizing the Relationship between Lower Bound Methods in Communication Complexity

On Characterizing the Relationship between Lower Bound Methods in Communication Complexity Jiahui Liu, Prayaag Venkat Columbia University, University of Maryland College Park Thursday, August 10 Introduction: Communication Complexity

480 views • 29 slides
The Input/Output Complexity of Sparse Matrix Multiplication Rasmus Pagh, Morten St ockel IT

The Input/Output Complexity of Sparse Matrix Multiplication Rasmus Pagh, Morten St ockel IT

The Input/Output Complexity of Sparse Matrix Multiplication Rasmus Pagh, Morten St ockel IT University of Copenhagen September 9 2014 Pagh, St ockel September 9 2014 1 / 29 Sparse matrix multiplication Problem description Sparse

572 views • 32 slides
Reducing computational complexity of sparse grid stochastic collocation methods Peter Jantsch

Reducing computational complexity of sparse grid stochastic collocation methods Peter Jantsch

Reducing computational complexity of sparse grid stochastic collocation methods Peter Jantsch QUIET Workshop, Trieste July 19, 2017 Joint work with C. Webster, A. Teckentrup, M. Gunzburger, D. Galindo, G. Zhang Supported by the US Dept. of

179 views • 6 slides
Communication Complexity with Small Advantage Thomas Watson University of Memphis

Communication Complexity with Small Advantage Thomas Watson University of Memphis

Communication Complexity with Small Advantage Thomas Watson University of Memphis Communication complexity F : { 0 , 1 } n { 0 , 1 } n { 0 , 1 } Communication complexity F : { 0 , 1 } n { 0 , 1 } n { 0 , 1 } (Alice: x ) (Bob: y )

910 views • 66 slides
Communication Complexity of Learning Discrete Distributions Krzysztof Onak IBM T.J. Watson

Communication Complexity of Learning Discrete Distributions Krzysztof Onak IBM T.J. Watson

Communication Complexity of Learning Discrete Distributions Krzysztof Onak IBM T.J. Watson Research Center Joint work with Ilias Diakonikolas , Elena Grigorescu , and Abhiram Natarajan . Krzysztof Onak (IBM Research) Communication Complexity of

634 views • 50 slides
Robust Lower Bounds for Communication and Stream Computation Amit Chakrabarti Dartmouth

Robust Lower Bounds for Communication and Stream Computation Amit Chakrabarti Dartmouth

Robust Lower Bounds for Communication and Stream Computation Amit Chakrabarti Dartmouth College Graham Cormode AT&amp;T Labs Andrew McGregor UC San Diego Communication Complexity Communication Complexity

1.21k views • 67 slides
On the Communication Complexity of Multilateral Trading Nicolas Maudet Ulle Endriss Universit

On the Communication Complexity of Multilateral Trading Nicolas Maudet Ulle Endriss Universit

On the Communication Complexity of Multilateral Trading AAMAS-2004 On the Communication Complexity of Multilateral Trading Nicolas Maudet Ulle Endriss Universit e Paris Dauphine Imperial College London maudet@lamsade.dauphine.fr

445 views • 10 slides
Distributed Frank-Wolfe Algorithm A Unified Framework for Communication-Efficient Sparse Learning

Distributed Frank-Wolfe Algorithm A Unified Framework for Communication-Efficient Sparse Learning

Distributed Frank-Wolfe Algorithm A Unified Framework for Communication-Efficient Sparse Learning elien Bellet 1 Aur Joint work with Yingyu Liang 2 , Alireza Bagheri Garakani 1 , Maria-Florina Balcan 3 and Fei Sha 1 1 University of Southern

440 views • 28 slides
Communication-avoiding sparse direct solvers for linear systems &amp; Sherry Li graph problems

Communication-avoiding sparse direct solvers for linear systems &amp; Sherry Li graph problems

hpcgarage.org/uiuc20 Slides are here right now Piyush Sao get em while theyre hot (ORNL) Communication-avoiding sparse direct solvers for linear systems &amp; Sherry Li graph problems (LBNL) Ramki Kannan Richard (Rich) Vuduc

641 views • 47 slides
The Input/Output Complexity of Sparse Matrix Multiplication Rasmus Pagh 1 , Morten St ockel 2 1

The Input/Output Complexity of Sparse Matrix Multiplication Rasmus Pagh 1 , Morten St ockel 2 1

The Input/Output Complexity of Sparse Matrix Multiplication Rasmus Pagh 1 , Morten St ockel 2 1 IT University of Copenhagen, 2 University of Copenhagen SIAM LA, October 26 2015 Pagh, St ockel ITU, DIKU October 26 2015 1 / 30 Sparse matrix

878 views • 35 slides
Joshua Brody and Amit Chakrabarti Dartmouth College 24 th CCC, 2009, Paris Joshua Brody 1

Joshua Brody and Amit Chakrabarti Dartmouth College 24 th CCC, 2009, Paris Joshua Brody 1

Gap-Hamming Lower Bound July 18, 2009 Lower Bounds for Gap-Hamming-Distance and Consequences for Data Stream Algorithms Joshua Brody and Amit Chakrabarti Dartmouth College 24 th CCC, 2009, Paris Joshua Brody 1 Gap-Hamming Lower Bound July

1.28k views • 61 slides
Translating Evidence Into Practice Susan E. Shapiro, PhD, RN Associate Chief Nursing Officer,

Translating Evidence Into Practice Susan E. Shapiro, PhD, RN Associate Chief Nursing Officer,

Translating Evidence Into Practice Susan E. Shapiro, PhD, RN Associate Chief Nursing Officer, Emory susan.shapiro@ emoryhealthcare.org Healthcare Assistant Dean for Strategic Clinical Initiatives, Nell Hodgson Woodruff School of Nursing

276 views • 16 slides
Stochastic Programming Models with Decision Dependent Probabilities David L. Woodruff Graduate

Stochastic Programming Models with Decision Dependent Probabilities David L. Woodruff Graduate

Stochastic Programming Models with Decision Dependent Probabilities David L. Woodruff Graduate School of Management University of California, Davis October 2003 1 Outline Overview of the modeling issues Beyond the state of the art

598 views • 23 slides
Communication Complexity David P. Woodruff IBM Almaden Talk Outline 1. Information Theory

Communication Complexity David P. Woodruff IBM Almaden Talk Outline 1. Information Theory

Information Theory for Communication Complexity David P. Woodruff IBM Almaden Talk Outline 1. Information Theory Concepts 2. Distances Between Distributions 3. An Example Communication Lower Bound Randomized 1-way Communication

471 views • 25 slides
Navigation and Zooming Navigation and Zooming Histories in a Zoomable Zoomable User Interface

Navigation and Zooming Navigation and Zooming Histories in a Zoomable Zoomable User Interface

Overview Overview Navigation Patterns and Usability of Zoomable Navigation Patterns and Usability of Zoomable User Interfaces with and without an Overview User Interfaces with and without an Overview Domain Name Based Visualization of Web

188 views • 8 slides
Examining Service Excellence in Higher Education for Adult Learners: A Text-mining Analysis Lee

Examining Service Excellence in Higher Education for Adult Learners: A Text-mining Analysis Lee

Examining Service Excellence in Higher Education for Adult Learners: A Text-mining Analysis Lee Yew Haur, Guan Chong and Chia Allan Introduc)on Background and Mo)va)on Higher educa,on is increasingly embraced by

854 views • 27 slides
Local Naming and Scope These slides borrow heavily from Ben Woods

Local Naming and Scope These slides borrow heavily from Ben Woods

Local Naming and Scope These slides borrow heavily from Ben Woods Fall 15 slides, some of which are in turn based on Dan Grossmans material from

585 views • 30 slides
LSST- FRANCE 8 June 2016 Dominique Fouchez, CPPM Supernovae Dark Energy science with LSST The

LSST- FRANCE 8 June 2016 Dominique Fouchez, CPPM Supernovae Dark Energy science with LSST The

News from the The DESC Supernova Working Group LSST- FRANCE 8 June 2016 Dominique Fouchez, CPPM Supernovae Dark Energy science with LSST The DESC SN-WG program Isotropy constraints Dark Energy constraints BAO with supernovae Two LSST

603 views • 22 slides

More recommend