greedy maximal independent sets via local limits
play

Greedy maximal independent sets via local limits Peleg Michaeli Tel - PowerPoint PPT Presentation

Nov 01, 2023 •481 likes •1.57k views

Greedy maximal independent sets via local limits Peleg Michaeli Tel Aviv University Workshop on Local Algorithms WOLA 2019 ETH Zurich, July 21, 2019 Joint work with Michael Krivelevich, Tams Mszros and Clara Shikhelman Peleg Michaeli

  1. General framework Decay of correlation = a.a.s. Develop a machinery to calculate the probability that the root is red. Peleg Michaeli (TAU) Greedy MIS July 21, 2019 7 / 18 We wish to calculate the asymptotics of ι ( G n ) . We fjrst calculate E ( ι ( G n )) = P ( ρ n ∈ I ( G n )) for ρ n chosen u.a.r. We hope that this is determined by a small neighbourhood of ρ n . This local view of ρ n is captured by the local limit of G n .

  2. General framework Decay of correlation = Develop a machinery to calculate the probability that the root is red. Peleg Michaeli (TAU) Greedy MIS July 21, 2019 7 / 18 We wish to calculate the asymptotics of ι ( G n ) . We fjrst calculate E ( ι ( G n )) = P ( ρ n ∈ I ( G n )) for ρ n chosen u.a.r. We hope that this is determined by a small neighbourhood of ρ n . This local view of ρ n is captured by the local limit of G n . ⇒ ι ( G n ) ∼ E ( ι ( G n )) a.a.s.

  3. General framework Decay of correlation = Develop a machinery to calculate the probability that the root is red. Peleg Michaeli (TAU) Greedy MIS July 21, 2019 7 / 18 We wish to calculate the asymptotics of ι ( G n ) . We fjrst calculate E ( ι ( G n )) = P ( ρ n ∈ I ( G n )) for ρ n chosen u.a.r. We hope that this is determined by a small neighbourhood of ρ n . This local view of ρ n is captured by the local limit of G n . ⇒ ι ( G n ) ∼ E ( ι ( G n )) a.a.s.

  4. Local limits Peleg Michaeli (TAU) Greedy MIS July 21, 2019 8 / 18 We say that a (random) graph sequence G n locally converges to a random rooted graph ( U, ρ ) , if for every r ≥ 0 , the ball B r ( G, ρ n ) converges in distribution to B r ( U, ρ ) , where ρ n is a uniform vertex of G n .

  5. Local limits Peleg Michaeli (TAU) Greedy MIS July 21, 2019 8 / 18 We say that a (random) graph sequence G n locally converges to a random rooted graph ( U, ρ ) , if for every r ≥ 0 , the ball B r ( G, ρ n ) converges in distribution to B r ( U, ρ ) , where ρ n is a uniform vertex of G n .

  6. Local limits Peleg Michaeli (TAU) Greedy MIS July 21, 2019 8 / 18 We say that a (random) graph sequence G n locally converges to a random rooted graph ( U, ρ ) , if for every r ≥ 0 , the ball B r ( G, ρ n ) converges in distribution to B r ( U, ρ ) , where ρ n is a uniform vertex of G n .

  7. Local limits Peleg Michaeli (TAU) Greedy MIS July 21, 2019 8 / 18 We say that a (random) graph sequence G n locally converges to a random rooted graph ( U, ρ ) , if for every r ≥ 0 , the ball B r ( G, ρ n ) converges in distribution to B r ( U, ρ ) , where ρ n is a uniform vertex of G n .

  8. Local limits Peleg Michaeli (TAU) Greedy MIS July 21, 2019 8 / 18 We say that a (random) graph sequence G n locally converges to a random rooted graph ( U, ρ ) , if for every r ≥ 0 , the ball B r ( G, ρ n ) converges in distribution to B r ( U, ρ ) , where ρ n is a uniform vertex of G n .

  9. Local limits Peleg Michaeli (TAU) Greedy MIS July 21, 2019 8 / 18 We say that a (random) graph sequence G n locally converges to a random rooted graph ( U, ρ ) , if for every r ≥ 0 , the ball B r ( G, ρ n ) converges in distribution to B r ( U, ρ ) , where ρ n is a uniform vertex of G n . · · ·

  10. Peleg Michaeli (TAU) Local limits Greedy MIS July 21, 2019 8 / 18 We say that a (random) graph sequence G n locally converges to a random rooted graph ( U, ρ ) , if for every r ≥ 0 , the ball B r ( G, ρ n ) converges in distribution to B r ( U, ρ ) , where ρ n is a uniform vertex of G n . · · · � ➪ ➪

  11. Peleg Michaeli (TAU) Local limits Greedy MIS July 21, 2019 8 / 18 We say that a (random) graph sequence G n locally converges to a random rooted graph ( U, ρ ) , if for every r ≥ 0 , the ball B r ( G, ρ n ) converges in distribution to B r ( U, ρ ) , where ρ n is a uniform vertex of G n . · · · � ➪ ➪ � ➪ ➪

  12. Local limits loc July 21, 2019 Greedy MIS Peleg Michaeli (TAU) loc 8 / 18 Examples loc We say that a (random) graph sequence G n locally converges to a random rooted graph ( U, ρ ) , if for every r ≥ 0 , the ball B r ( G, ρ n ) converges in distribution to B r ( U, ρ ) , where ρ n is a uniform vertex of G n . P n , C n − → Z [ n ] d loc → Z d − G ( n, λ / n ) loc − → T λ , a Galton-Watson Pois ( λ ) tree − → the d -regular tree G n,d → ˆ Uniform random tree T n − T 1 , a size-biased GW Pois (1) tree − → the canopy tree Finite d -ary balanced tree loc

  13. Convergence of the greedy independence ratio Theorem (Krivelevich, Mészáros, M., Shikhelman ’19+) loc Peleg Michaeli (TAU) Greedy MIS July 21, 2019 9 / 18 Suppose G n has subfactorial growth. − → ( U, ρ ) then ι ( G n ) → ι ( U, ρ ) a.a.s. If G n

  14. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  15. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  16. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  17. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  18. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  19. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  20. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  21. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  22. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  23. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  24. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  25. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  26. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  27. Decay of correlation Peleg Michaeli (TAU) Greedy MIS July 21, 2019 10 / 18

  28. Let us therefore restrict ourselves to locally tree-like graph sequences, i.e., Locally tree-like but even is still unknown... graph sequences for which is a.s. a tree. Children of the past are roots to independent subtrees. Peleg Michaeli (TAU) Greedy MIS July 21, 2019 11 / 18 We need to calculate ι ( U, ρ ) ,

  29. Let us therefore restrict ourselves to locally tree-like graph sequences, i.e., Locally tree-like graph sequences for which is a.s. a tree. Children of the past are roots to independent subtrees. Peleg Michaeli (TAU) Greedy MIS July 21, 2019 11 / 18 We need to calculate ι ( U, ρ ) , but even ι ( Z 2 ) is still unknown...

  30. Locally tree-like Children of the past are roots to independent subtrees. Peleg Michaeli (TAU) Greedy MIS July 21, 2019 11 / 18 We need to calculate ι ( U, ρ ) , but even ι ( Z 2 ) is still unknown... Let us therefore restrict ourselves to locally tree-like graph sequences, i.e., graph sequences for which ( U, ρ ) is a.s. a tree.

  31. Locally tree-like Children of the past are roots to independent subtrees. Peleg Michaeli (TAU) Greedy MIS July 21, 2019 11 / 18 We need to calculate ι ( U, ρ ) , but even ι ( Z 2 ) is still unknown... Let us therefore restrict ourselves to locally tree-like graph sequences, i.e., graph sequences for which ( U, ρ ) is a.s. a tree. u 1 u 2 · · · u d ρ

  32. Locally tree-like Children of the past are roots to independent subtrees. Peleg Michaeli (TAU) Greedy MIS July 21, 2019 11 / 18 We need to calculate ι ( U, ρ ) , but even ι ( Z 2 ) is still unknown... Let us therefore restrict ourselves to locally tree-like graph sequences, i.e., graph sequences for which ( U, ρ ) is a.s. a tree. u 1 u 2 · · · u d ρ

  33. Systems of ordinary difgerential equations I I I I Peleg Michaeli (TAU) Greedy MIS July 21, 2019 12 / 18 Let ( U, ρ ) be a single-type branching process.

  34. Systems of ordinary difgerential equations I I I Peleg Michaeli (TAU) Greedy MIS July 21, 2019 12 / 18 Let ( U, ρ ) be a single-type branching process. y ( x ) = P ( ρ ∈ I ( U, ρ ) ∧ σ ρ < x )

  35. I Systems of ordinary difgerential equations Peleg Michaeli (TAU) Greedy MIS July 21, 2019 12 / 18 Let ( U, ρ ) be a single-type branching process. y ( x ) = P ( ρ ∈ I ( U, ρ ) ∧ σ ρ < x ) = x · P ( ρ ∈ I ( U, ρ ) | σ ρ < x ) ∫ x = P ( ρ ∈ I ( U, ρ ) | σ ρ = z ) dz 0

  36. Systems of ordinary difgerential equations Peleg Michaeli (TAU) Greedy MIS July 21, 2019 12 / 18 Let ( U, ρ ) be a single-type branching process. y ( x ) = P ( ρ ∈ I ( U, ρ ) ∧ σ ρ < x ) = x · P ( ρ ∈ I ( U, ρ ) | σ ρ < x ) ∫ x = P ( ρ ∈ I ( U, ρ ) | σ ρ = z ) dz 0 y ′ ( x ) = P ( ρ ∈ I ( U, ρ ) | σ ρ = x )

  37. Systems of ordinary difgerential equations Peleg Michaeli (TAU) July 21, 2019 Greedy MIS 12 / 18 Let ( U, ρ ) be a single-type branching process. y ( x ) = P ( ρ ∈ I ( U, ρ ) ∧ σ ρ < x ) = x · P ( ρ ∈ I ( U, ρ ) | σ ρ < x ) ∫ x = P ( ρ ∈ I ( U, ρ ) | σ ρ = z ) dz 0 y ′ ( x ) = P ( ρ ∈ I ( U, ρ ) | σ ρ = x ) Thus, if y is a unique solution of ) ℓ )( 1 − y ( x ) ξ <x = ℓ ∑ y ′ ( x ) = ( y (0) = 0 , P , x ℓ ∈ N then, ι ( U, ρ ) = y (1) .

  38. Systems of ordinary difgerential equations Peleg Michaeli (TAU) July 21, 2019 Greedy MIS 12 / 18 Let ( U, ρ ) be a multi-type branching process. y ( x ) = P ( ρ ∈ I ( U, ρ ) ∧ σ ρ < x ) = x · P ( ρ ∈ I ( U, ρ ) | σ ρ < x ) ∫ x = P ( ρ ∈ I ( U, ρ ) | σ ρ = z ) dz 0 y ′ ( x ) = P ( ρ ∈ I ( U, ρ ) | σ ρ = x ) Thus, if y is a unique solution of ) ℓ j )( 1 − y j ( x ) ( ∑ ∏ ξ <x y ′ k ( x ) = k → j = ℓ j y k (0) = 0 , P , x ℓ ∈ N T j ∈ T then, ι ( U, ρ ) = E ( y k (1)) .

  39. Size-biased Galton-Watson branching processes Kolchin, Grimmett: the sequence of uniform random trees locally Peleg Michaeli (TAU) Greedy MIS July 21, 2019 13 / 18 converges to the size-biased Galton-Watson Pois (1) tree.

  40. Size-biased Galton-Watson branching processes Kolchin, Grimmett: the sequence of uniform random trees locally Peleg Michaeli (TAU) Greedy MIS July 21, 2019 13 / 18 converges to the size-biased Galton-Watson Pois (1) tree.

  41. Size-biased Galton-Watson branching processes Kolchin, Grimmett: the sequence of uniform random trees locally Peleg Michaeli (TAU) Greedy MIS July 21, 2019 13 / 18 converges to the size-biased Galton-Watson Pois (1) tree.

  42. Size-biased Galton-Watson branching processes Kolchin, Grimmett: the sequence of uniform random trees locally Peleg Michaeli (TAU) Greedy MIS July 21, 2019 13 / 18 converges to the size-biased Galton-Watson Pois (1) tree.

  43. Size-biased Galton-Watson branching processes Kolchin, Grimmett: the sequence of uniform random trees locally Peleg Michaeli (TAU) Greedy MIS July 21, 2019 13 / 18 converges to the size-biased Galton-Watson Pois (1) tree.

  44. Size-biased Galton-Watson branching processes Kolchin, Grimmett: the sequence of uniform random trees locally Peleg Michaeli (TAU) Greedy MIS July 21, 2019 13 / 18 converges to the size-biased Galton-Watson Pois (1) tree.

  45. Size-biased Galton-Watson branching processes Kolchin, Grimmett: the sequence of uniform random trees locally Peleg Michaeli (TAU) Greedy MIS July 21, 2019 13 / 18 converges to the size-biased Galton-Watson Pois (1) tree.

  46. Size-biased Galton-Watson branching processes Kolchin, Grimmett: the sequence of uniform random trees locally Peleg Michaeli (TAU) Greedy MIS July 21, 2019 13 / 18 converges to the size-biased Galton-Watson Pois (1) tree.

  47. Size-biased Galton-Watson branching processes Kolchin, Grimmett: the sequence of uniform random trees locally Peleg Michaeli (TAU) Greedy MIS July 21, 2019 13 / 18 converges to the size-biased Galton-Watson Pois (1) tree.

  48. Size-biased Galton-Watson branching processes Kolchin, Grimmett: the sequence of uniform random trees locally Peleg Michaeli (TAU) Greedy MIS July 21, 2019 13 / 18 converges to the size-biased Galton-Watson Pois (1) tree.

  49. Uniform random trees , s t s hence s , and for s s , and we get s Peleg Michaeli (TAU) Greedy MIS July 21, 2019 t s 14 / 18 ∞ ) d ( λx ) d ( 1 − y t ( x ) ∑ = e − λy t ( x ) . y ′ t ( x ) = e λx d ! x d =0 hence y t ( x ) = ln (1 + λx )/ λ . Thus ι ( G ( n, λ / n )) → ι ( T λ ) = y t (1) = ln (1 + λ ) . λ

  50. Uniform random trees and we get July 21, 2019 Greedy MIS Peleg Michaeli (TAU) 14 / 18 ∞ ) d ( λx ) d ( 1 − y t ( x ) ∑ = e − λy t ( x ) . y ′ t ( x ) = e λx d ! x d =0 hence y t ( x ) = ln (1 + λx )/ λ . Thus ι ( G ( n, λ / n )) → ι ( T λ ) = y t (1) = ln (1 + λ ) . λ t ( x ) = (1 − y s ( x )) e − λy t ( x ) = 1 − y s ( x ) y ′ s ( x ) = (1 − y s ( x )) y ′ 1 + λx , hence y s ( x ) = 1 − (1 + λx ) − 1/ λ , and for λ = 1 , y s (1) = 1 − (1 + x ) − 1 , T 1 ) = y s (1) = 1 ι ( T n ) → ι ( ˆ 2 .

  51. Simulations don’t lie red: 125 (50%), green: 92 ( 37%), blue: 32 ( 13%), black: 1 Peleg Michaeli (TAU) Greedy MIS July 21, 2019 15 / 18

  52. Simulations don’t lie Peleg Michaeli (TAU) Greedy MIS July 21, 2019 15 / 18 red: 125 (50%), green: 92 ( ≈ 37%), blue: 32 ( ≈ 13%), black: 1

  53. Simulations don’t lie (but I do) Peleg Michaeli (TAU) Greedy MIS July 21, 2019 15 / 18 red: 125 (50%), green: 92 ( ≈ 37%), blue: 32 ( ≈ 13%), black: 1

  54. Greedy independence ratio – results Flory ’39, Page ’59 July 21, 2019 Greedy MIS Peleg Michaeli (TAU) (same for functional digraphs) KMMS ’19+ Lauer & Wormald ’07 16 / 18 McDiarmid ’84 Wormald ’95 ι ( P n ) → 1 2 (1 − e − 2 ) ι ( G ( n, λ / n )) → ln (1 + λ )/ λ ι ( G n,d ) → 1 ( 1 − ( d − 1) − 2/( d − 2) ) 2 ( d -regular graphs with girth → ∞ )

  55. Greedy independence ratio – results Flory ’39, Page ’59 July 21, 2019 Greedy MIS Peleg Michaeli (TAU) (same for functional digraphs) KMMS ’19+ Lauer & Wormald ’07 16 / 18 McDiarmid ’84 Wormald ’95 ✓ ι ( P n ) → 1 2 (1 − e − 2 ) ι ( G ( n, λ / n )) → ln (1 + λ )/ λ ι ( G n,d ) → 1 ( 1 − ( d − 1) − 2/( d − 2) ) 2 ( d -regular graphs with girth → ∞ )

  56. Greedy independence ratio – results Flory ’39, Page ’59 July 21, 2019 Greedy MIS Peleg Michaeli (TAU) (same for functional digraphs) KMMS ’19+ Lauer & Wormald ’07 16 / 18 Wormald ’95 McDiarmid ’84 ✓ ι ( P n ) → 1 2 (1 − e − 2 ) ✓ ι ( G ( n, λ / n )) → ln (1 + λ )/ λ ι ( G n,d ) → 1 ( 1 − ( d − 1) − 2/( d − 2) ) 2 ( d -regular graphs with girth → ∞ )

  57. Greedy independence ratio – results Flory ’39, Page ’59 July 21, 2019 Greedy MIS Peleg Michaeli (TAU) (same for functional digraphs) KMMS ’19+ Lauer & Wormald ’07 16 / 18 Wormald ’95 McDiarmid ’84 ✓ ι ( P n ) → 1 2 (1 − e − 2 ) ✓ ι ( G ( n, λ / n )) → ln (1 + λ )/ λ 1 − ( d − 1) − 2/( d − 2) ) ✓ ι ( G n,d ) → 1 ( 2 ( d -regular graphs with girth → ∞ )

  58. Greedy independence ratio – results Flory ’39, Page ’59 July 21, 2019 Greedy MIS Peleg Michaeli (TAU) (same for functional digraphs) KMMS ’19+ Lauer & Wormald ’07 16 / 18 Wormald ’95 McDiarmid ’84 ✓ ι ( P n ) → 1 2 (1 − e − 2 ) ✓ ι ( G ( n, λ / n )) → ln (1 + λ )/ λ 1 − ( d − 1) − 2/( d − 2) ) ✓ ι ( G n,d ) → 1 ( 2 ( d -regular graphs with girth → ∞ ) ✓

  59. Greedy independence ratio – results Flory ’39, Page ’59 July 21, 2019 Greedy MIS Peleg Michaeli (TAU) (same for functional digraphs) KMMS ’19+ Lauer & Wormald ’07 16 / 18 McDiarmid ’84 Wormald ’95 ✓ ι ( P n ) → 1 2 (1 − e − 2 ) ✓ ι ( G ( n, λ / n )) → ln (1 + λ )/ λ 1 − ( d − 1) − 2/( d − 2) ) ✓ ι ( G n,d ) → 1 ( 2 ( d -regular graphs with girth → ∞ ) ✓ ✸ ι ( T n ) → 1 2

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

Greedy maximal independent sets via local limits Peleg Michaeli Tel Aviv University The 31st

Greedy maximal independent sets via local limits Peleg Michaeli Tel Aviv University The 31st

Greedy maximal independent sets via local limits Peleg Michaeli Tel Aviv University The 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA2020) September 2020 Joint work

1.76k views • 154 slides
Maximal subsemigroups via independent sets Wilf Wilson 26 th April 2017 Maximal subsemigroups? 1

Maximal subsemigroups via independent sets Wilf Wilson 26 th April 2017 Maximal subsemigroups? 1

Maximal subsemigroups via independent sets Wilf Wilson 26 th April 2017 Maximal subsemigroups? 1 2 3 A maximal subsemigroup is * * * formed by removing parts of one D -class. 5 7 It has one of several forms. * * However: A semigroup

345 views • 10 slides
Lower Bounds for Maximal Matchings and Maximal Independent Sets Alkida Balliu Aalto University,

Lower Bounds for Maximal Matchings and Maximal Independent Sets Alkida Balliu Aalto University,

Lower Bounds for Maximal Matchings and Maximal Independent Sets Alkida Balliu Aalto University, Finland Joint work with Sebastian Brandt ETH Zurich Juho Hirvonen Aalto University Dennis Olivetti Aalto University Mikal Rabie LIP6 -

937 views • 64 slides
CS 140: Computation on Graphs Maximal Independent Sets A graph problem: Maximal Independent

CS 140: Computation on Graphs Maximal Independent Sets A graph problem: Maximal Independent

CS 140: Computation on Graphs Maximal Independent Sets A graph problem: Maximal Independent Set Graph with vertices V = {1,2, ,n} 1 2 A set S of vertices is independent if no two vertices in S are neighbors. An independent

345 views • 12 slides
Axiom of Choice, Maximal Independent Sets, Argumentation and Dialogue Games Christof Spanring

Axiom of Choice, Maximal Independent Sets, Argumentation and Dialogue Games Christof Spanring

Axiom of Choice, Maximal Independent Sets, Argumentation and Dialogue Games Christof Spanring Department of Computer Science, University of Liverpool, UK Institute of Information Systems, Vienna University of Technology, Austria PhDs Tea Talk

696 views • 36 slides
Axiom of Choice, Maximal Independent Sets, Argumentation and Dialogue Games Christof Spanring

Axiom of Choice, Maximal Independent Sets, Argumentation and Dialogue Games Christof Spanring

Axiom of Choice, Maximal Independent Sets, Argumentation and Dialogue Games Christof Spanring Department of Computer Science, University of Liverpool, UK Institute of Information Systems, Vienna University of Technology, Austria London,

505 views • 14 slides
Small maximal independent sets Jeroen Schillewaert (joint with Jacques Verstrate) Department

Small maximal independent sets Jeroen Schillewaert (joint with Jacques Verstrate) Department

Small maximal independent sets Jeroen Schillewaert (joint with Jacques Verstrate) Department of Mathematics University of Auckland New Zealand J. Schillewaert (University of Auckland) SMIS 1 / 34 Table of Contents Statement of the main

681 views • 35 slides
Distributed Maximal Matching: Greedy is Optimal Jukka Suomela Helsinki Institute for

Distributed Maximal Matching: Greedy is Optimal Jukka Suomela Helsinki Institute for

Distributed Maximal Matching: Greedy is Optimal Jukka Suomela Helsinki Institute for Information Technology HIIT University of Helsinki Joint work with Juho Hirvonen Weizmann Institute of Science, 27 November 2011 Background 2 Maximal

1.26k views • 86 slides
Maximal Independent Set Stefan Schmid @ T-Labs, 2011 What is a MIS? MIS An independent set

Maximal Independent Set Stefan Schmid @ T-Labs, 2011 What is a MIS? MIS An independent set

Foundations of Distributed Systems: Maximal Independent Set Stefan Schmid @ T-Labs, 2011 What is a MIS? MIS An independent set (IS) of an undirected graph is a subset U of nodes such that no two nodes in U are adjacent. An IS is maximal if

958 views • 80 slides
Orbits of D -maximal sets in E . Peter M. Gerdes April 19, 2012 * Joint work with Peter Cholak

Orbits of D -maximal sets in E . Peter M. Gerdes April 19, 2012 * Joint work with Peter Cholak

Background Automorphisms D -maximal sets . Orbits of D -maximal sets in E . Peter M. Gerdes April 19, 2012 * Joint work with Peter Cholak and Karen Lange. . . . . . . Peter M. Gerdes Orbits of D -maximal sets in E Background

249 views • 21 slides
Fully Dynamic Maximal Independent Set with Sublinear Update Time Sepehr Assadi University of

Fully Dynamic Maximal Independent Set with Sublinear Update Time Sepehr Assadi University of

Fully Dynamic Maximal Independent Set with Sublinear Update Time Sepehr Assadi University of Pennsylvania Joint work with: Krzysztof Onak, Baruch Schieber, and Shay Solomon IBM Research Sepehr Assadi (Penn) STOC 2018 The Maximal Independent

1.19k views • 102 slides
Local Limits Crash Course Gorman Lau, P.E. CWEA 2016 P3S Conference February 29, 2016

Local Limits Crash Course Gorman Lau, P.E. CWEA 2016 P3S Conference February 29, 2016

Local Limits Crash Course Gorman Lau, P.E. CWEA 2016 P3S Conference February 29, 2016 Presentation Outline Background Local limit evaluations Local limits update/development Local limits implementation Local limits

1.18k views • 83 slides
Dynamic Programming Greedy. Build up a solution incrementally, myopically optimizing some local

Dynamic Programming Greedy. Build up a solution incrementally, myopically optimizing some local

Algorithmic paradigms Dynamic Programming Greedy. Build up a solution incrementally, myopically optimizing some local criterion. Introduction, Weighted Interval Scheduling Divide-and-conquer. Break up a problem into independent subproblems,

237 views • 7 slides
Algorithms in Nature SOP &amp; MIS Maximal Independent Set (MIS) A fundamental problem in

Algorithms in Nature SOP &amp; MIS Maximal Independent Set (MIS) A fundamental problem in

Algorithms in Nature SOP &amp; MIS Maximal Independent Set (MIS) A fundamental problem in distributed computing: - Often required to establish wireless networks - Used for routing messages, grouping sensors etc. For a set of nodes

749 views • 29 slides
Maximal Vector Computation in Large Data Sets Parke Godfrey 1 Ryan Shipley 2 Jarek Gryz 1 1 York

Maximal Vector Computation in Large Data Sets Parke Godfrey 1 Ryan Shipley 2 Jarek Gryz 1 1 York

Maximal Vector Computation in Large Data Sets Parke Godfrey 1 Ryan Shipley 2 Jarek Gryz 1 1 York University 2 College of William and Mary Toronto, C ANADA Williamsburg, USA 30 August 2005 VLDB Trondheim, Norway Maximal VectorGodfrey,

1.07k views • 73 slides
Chapter 16: Greedy Algorithms Greedy is a strategy that works well on optimization problems with

Chapter 16: Greedy Algorithms Greedy is a strategy that works well on optimization problems with

Chapter 16: Greedy Algorithms Greedy is a strategy that works well on optimization problems with the following characteristics: 1. Greedy-choice property: A global optimum can be arrived at by selecting a local optimum. 2. Optimal substructure:

664 views • 24 slides
Self-similar growth-fragmentations as scaling limits of Markov branching processes Benjamin

Self-similar growth-fragmentations as scaling limits of Markov branching processes Benjamin

Self-similar growth-fragmentations as scaling limits of Markov branching processes Benjamin Dadoun Institut fr Mathematik, Universitt Zrich Les probabilits de demain 3 mai 2018 Outline Introduction 1 Motivating example 2

1.38k views • 109 slides
The scaling limit of critical random graphs Christina Goldschmidt Joint work with Louigi

The scaling limit of critical random graphs Christina Goldschmidt Joint work with Louigi

Statistical Mechanics Seminar, Warwick, 18th February 2010 The scaling limit of critical random graphs Christina Goldschmidt Joint work with Louigi Addario-Berry (McGill University) and Nicolas Broutin (INRIA Rocquencourt) Part I : Trees A

1.32k views • 93 slides
Combinatorial structures and algorithms: phase transition, enumeration and sampling Mihyun Kang

Combinatorial structures and algorithms: phase transition, enumeration and sampling Mihyun Kang

W ORKSHOP ON R ANDOMNESS AND E NUMERATION , 24-28 N OVEMBER 2008, C URACAUTN , C HILE Combinatorial structures and algorithms: phase transition, enumeration and sampling Mihyun Kang Institut fr Informatik Institut fr Mathematik

1.66k views • 150 slides
Shedding new light on random chromosome segregation Qi Zheng Department of Epidemiology and

Shedding new light on random chromosome segregation Qi Zheng Department of Epidemiology and

Shedding new light on random chromosome segregation Qi Zheng Department of Epidemiology and Biostatistics 1 Motivation Bacteria were thought to be mono-ploid (haploid), but not any more Ploidy value c is the number of chromosomes per

299 views • 14 slides
Probability Distribu.ons on Structured Objects September 17, 2013

Probability Distribu.ons on Structured Objects September 17, 2013

Probability Distribu.ons on Structured Objects September 17, 2013 Reminder HW1 is due at 11:59pm tonight There was some ambiguity in this assignment

916 views • 66 slides
Branching Processes in Fluid Mechanics: An application to the Navier-Stokes and LANS-alpha

Branching Processes in Fluid Mechanics: An application to the Navier-Stokes and LANS-alpha

Branching Processes in Fluid Mechanics: An application to the Navier-Stokes and LANS-alpha equations. Enrique Thomann Joint work with Larry Chen, Ron Guenther, Ed Waymire (Oregon State University) and Sun-Chul Kim (Chung Ang University)

707 views • 33 slides
Quantum Chromodynamics Lecture 2: Leading order and showers Hadron Collider Physics Summer School

Quantum Chromodynamics Lecture 2: Leading order and showers Hadron Collider Physics Summer School

Quantum Chromodynamics Lecture 2: Leading order and showers Hadron Collider Physics Summer School 2010 John Campbell, Fermilab Tasks for today Discuss a recipe for QCD predictions Leading Order (LO) Monte Carlo. Understand the

592 views • 28 slides
Weighted branching formulas for the hook lengths Matja Konvalinka Vanderbilt University (joint

Weighted branching formulas for the hook lengths Matja Konvalinka Vanderbilt University (joint

Weighted branching formulas for the hook lengths Matja Konvalinka Vanderbilt University (joint with Ionu t Ciocan-Fontanine and Igor Pak) FPSAC 2010, San Francisco, August 2010 Partitions Definition A partition of n is a finite

686 views • 27 slides

More recommend