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Title:
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Clique is hard on average for regular resolution
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Author:
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Atserias, Albert; Bonacina, Ilario; Rezende, Susanna F. de; Lauria, Massimo; Nordström, Jakob; Razborov, Alexander
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Ciències de la Computació; Universitat Politècnica de Catalunya. ALBCOM - Algorismia, Bioinformàtica, Complexitat i Mètodes Formals |
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Abstract:
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We prove that for k ≪4√n regular resolution requires length nΩ(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 nΩ(k) lower bounds on running time for several state-of-the-art algorithms for finding maximum cliques in graphs. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
-Computational complexity
-Algorithms
-Proof complexity
-Regular resolution
-k-clique
-Erdos-Rényi random
graphs
-Complexitat computacional
-Algorismes |
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Rights:
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Document type:
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Article - Submitted version
Conference Object |
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Published by:
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Association for Computing Machinery (ACM)
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