Random Walks That Find Perfect Objects and the Lovasz Local Lemma

被引:24
|
作者
Achlioptas, Dimitris [1 ]
Iliopoulos, Fotis [2 ]
机构
[1] Univ Calif Santa Cruz, Dept Comp Sci, Santa Cruz, CA 95064 USA
[2] Univ Calif Berkeley, Div Comp Sci, Berkeley, CA 94720 USA
基金
美国国家科学基金会; 欧洲研究理事会;
关键词
Lovasz Local Lemma; LLL; entropic method; ALGORITHMIC APPROACH; CONSTRUCTIVE PROOF;
D O I
10.1145/2818352
中图分类号
TP3 [计算技术、计算机技术];
学科分类号
0812 ;
摘要
We give an algorithmic local lemma by establishing a sufficient condition for the uniform random walk on a directed graph to reach a sink quickly. Our work is inspired by Moser's entropic method proof of the Lovasz Local Lemma (LLL) for satisfiability and completely bypasses the Probabilistic Method formulation of the LLL. In particular, our method works when the underlying state space is entirely unstructured. Similarly to Moser's argument, the key point is that the inevitability of reaching a sink is established by bounding the entropy of the walk as a function of time.
引用
收藏
页数:29
相关论文
共 50 条
  • [1] Random Walks that Find Perfect Objects and the Lovasz Local Lemma
    Achlioptas, Dimitris
    Iliopoulos, Fotis
    [J]. 2014 55TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS 2014), 2014, : 494 - 503
  • [2] Using Lovasz Local Lemma in the space of random injections
    Lu, Linyuan
    Szekely, Laszlo
    [J]. ELECTRONIC JOURNAL OF COMBINATORICS, 2007, 14 (01):
  • [3] Probabilistic Constructions of Computable Objects and a Computable Version of Lovasz Local Lemma
    Rumyantsev, Andrei
    Shen, Alexander
    [J]. FUNDAMENTA INFORMATICAE, 2014, 132 (01) : 1 - 14
  • [4] A Quantum Lovasz Local Lemma
    Ambainis, Andris
    Kempe, Julia
    Sattath, Or
    [J]. STOC 2010: PROCEEDINGS OF THE 2010 ACM SYMPOSIUM ON THEORY OF COMPUTING, 2010, : 151 - 160
  • [5] Revisit the Lovasz Local Lemma
    Chen, J
    [J]. JOURNAL OF THEORETICAL PROBABILITY, 1997, 10 (03) : 747 - 758
  • [6] A Quantum Lovasz Local Lemma
    Ambainis, Andris
    Kempe, Julia
    Sattath, Or
    [J]. JOURNAL OF THE ACM, 2012, 59 (05)
  • [7] Coloring and the Lovasz Local Lemma
    Chen, Xing
    Du, Zhihua
    Meng, Jixiang
    [J]. APPLIED MATHEMATICS LETTERS, 2010, 23 (03) : 219 - 221
  • [8] DETERMINISTIC ALGORITHMS FOR THE LOVASZ LOCAL LEMMA
    Chandrasekaran, Karthekeyan
    Goyal, Navin
    Haeupler, Bernhard
    [J]. SIAM JOURNAL ON COMPUTING, 2013, 42 (06) : 2132 - 2155
  • [9] Deterministic Algorithms for the Lovasz Local Lemma
    Chandrasekaran, Karthekeyan
    Goyal, Navin
    Haeupler, Bernhard
    [J]. PROCEEDINGS OF THE TWENTY-FIRST ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2010, 135 : 992 - +
  • [10] Costas Arrays and the Lovasz Local Lemma
    Correll, Bill, Jr.
    Swanson, Christopher N.
    Ho, Randy W.
    [J]. 2015 IEEE INTERNATIONAL RADAR CONFERENCE (RADARCON), 2015, : 186 - 191