Large Clique is Hard on Average for Resolution

Shuo Pang

doi:10.1007/978-3-030-79416-3_22

Large Clique is Hard on Average for Resolution

Shuo Pang^*

^*Corresponding author for this work

School of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

5 Citations (Scopus)

Abstract

We prove an exp(Ω(k^(1-ε))) resolution size lower bound for the k-Clique problem on random graphs, for (roughly speaking) k<n^1/3. Towards an optimal resolution lower bound of the problem (i.e. of type n^Ω(k)), we also extend the n^Ω(k)bound in [2] on regular resolution to a stronger model called a-irregular resolution, for k<n^1/3. This model is interesting in that all known CNF families separating regular resolution from general [1, 24] have short proofs in it.

Original language	English
Title of host publication	Computer Science – Theory and Applications
Subtitle of host publication	16th International Computer Science Symposium in Russia, CSR 2021, Sochi, Russia, June 28–July 2, 2021, Proceedings
Publisher	Springer, Cham
Pages	361-380
Number of pages	20
ISBN (Electronic)	9783030794163
ISBN (Print)	9783030794156
DOIs	https://doi.org/10.1007/978-3-030-79416-3_22
Publication status	Published - 17 Jun 2021
Event	16th International Computer Science Symposium in Russia, CSR 2021 - Sochi, Russian Federation Duration: 28 Jun 2021 → 2 Jul 2021 https://logic.pdmi.ras.ru/csr2021/

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	12730
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	16th International Computer Science Symposium in Russia, CSR 2021
Country/Territory	Russian Federation
City	Sochi
Period	28/06/21 → 2/07/21
Internet address	https://logic.pdmi.ras.ru/csr2021/

Research Groups and Themes

Algorithms and Complexity
Resolution
k-Clique
Average-case Lower Bounds

Access to Document

10.1007/978-3-030-79416-3_22

Handle.net

Persistent link

Cite this

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title = "Large Clique is Hard on Average for Resolution",

abstract = "We prove an exp(Ω(k(1-ε))) resolution size lower bound for the k-Clique problem on random graphs, for (roughly speaking) k1/3. Towards an optimal resolution lower bound of the problem (i.e. of type nΩ(k)), we also extend the nΩ(k) bound in [2] on regular resolution to a stronger model called a-irregular resolution, for k1/3. This model is interesting in that all known CNF families separating regular resolution from general [1, 24] have short proofs in it.",

author = "Shuo Pang",

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booktitle = "Computer Science – Theory and Applications",

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Pang, S 2021, Large Clique is Hard on Average for Resolution. in Computer Science – Theory and Applications: 16th International Computer Science Symposium in Russia, CSR 2021, Sochi, Russia, June 28–July 2, 2021, Proceedings. Lecture Notes in Computer Science, vol. 12730, Springer, Cham, pp. 361-380, 16th International Computer Science Symposium in Russia, CSR 2021, Sochi, Russian Federation, 28/06/21. https://doi.org/10.1007/978-3-030-79416-3_22

Large Clique is Hard on Average for Resolution. / Pang, Shuo.
Computer Science – Theory and Applications: 16th International Computer Science Symposium in Russia, CSR 2021, Sochi, Russia, June 28–July 2, 2021, Proceedings. Springer, Cham, 2021. p. 361-380 (Lecture Notes in Computer Science; Vol. 12730).

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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