Clique Is Hard on Average for Regular Resolution-Reference-Cited by-同舟云学术

Clique Is Hard on Average for Regular Resolution

Published:2021-06-30 Issue:4 Volume:68 Page:1-26
ISSN:0004-5411
Container-title:Journal of the ACM
language:en
Short-container-title:J. ACM

Author:

Atserias Albert¹,Bonacina Ilario¹^ORCID,De Rezende Susanna F.²,Lauria Massimo³,Nordström Jakob⁴,Razborov Alexander⁵

Affiliation:

1. Universitat Politècnica de Catalunya, Barcelona, Spain

2. Institute of Mathematics of the Czech Academy of Sciences, Czech Republic

3. Sapienza - Università di Roma, Roma, Italy

4. University of Copenhagen, Denmark and Lund University, Sweden

5. University of Chicago, USA, and Steklov Mathematical Institute, Moscow, Russia

Abstract

We prove that for k ≪ 4√ n regular resolution requires length n Ω( k ) to establish that an Erdős–Rényi graph with appropriately chosen edge density does not contain a k -clique. This lower bound is optimal up to the multiplicative constant in the exponent and also implies unconditional n Ω( k ) lower bounds on running time for several state-of-the-art algorithms for finding maximum cliques in graphs.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Link

https://dl.acm.org/doi/pdf/10.1145/3449352

Reference58 articles.

1. Finding a large hidden clique in a random graph

2. Clique is hard on average for regular resolution

3. Time-space tradeoffs in resolution: Superpolynomial lower bounds for superlinear space;Beame Paul;SIAM J. Comput.,2016

4. The resolution complexity of independent sets and vertex covers in random graphs;Beame Paul;Comput. Complex.,2007

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