Finding cliques using few probes

Uriel Feige; David Gamarnik; Joe Neeman; Miklós Z. Rácz; Prasad Tetali

doi:10.1002/rsa.20896

Finding cliques using few probes

Uriel Feige, David Gamarnik, Joe Neeman, Miklós Z. Rácz, Prasad Tetali

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Consider algorithms with unbounded computation time that probe the entries of the adjacency matrix of an n vertex graph, and need to output a clique. We show that if the input graph is drawn at random from (Formula presented.) (and hence is likely to have a clique of size roughly (Formula presented.)), then for every δ<2 and constant ℓ, there is an α<2 (that may depend on δ and ℓ) such that no algorithm that makes n^δ probes in ℓ rounds is likely (over the choice of the random graph) to output a clique of size larger than (Formula presented.).

Original language	English (US)
Pages (from-to)	142-153
Number of pages	12
Journal	Random Structures and Algorithms
Volume	56
Issue number	1
DOIs	https://doi.org/10.1002/rsa.20896
State	Published - Jan 1 2020

All Science Journal Classification (ASJC) codes

Software
General Mathematics
Computer Graphics and Computer-Aided Design
Applied Mathematics

Keywords

adaptive query model
cliques
random graphs

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10.1002/rsa.20896

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abstract = "Consider algorithms with unbounded computation time that probe the entries of the adjacency matrix of an n vertex graph, and need to output a clique. We show that if the input graph is drawn at random from (Formula presented.) (and hence is likely to have a clique of size roughly (Formula presented.)), then for every δ<2 and constant ℓ, there is an α<2 (that may depend on δ and ℓ) such that no algorithm that makes nδ probes in ℓ rounds is likely (over the choice of the random graph) to output a clique of size larger than (Formula presented.).",

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AU - Feige, Uriel

AU - Gamarnik, David

AU - Neeman, Joe

AU - Rácz, Miklós Z.

AU - Tetali, Prasad

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Consider algorithms with unbounded computation time that probe the entries of the adjacency matrix of an n vertex graph, and need to output a clique. We show that if the input graph is drawn at random from (Formula presented.) (and hence is likely to have a clique of size roughly (Formula presented.)), then for every δ<2 and constant ℓ, there is an α<2 (that may depend on δ and ℓ) such that no algorithm that makes nδ probes in ℓ rounds is likely (over the choice of the random graph) to output a clique of size larger than (Formula presented.).

AB - Consider algorithms with unbounded computation time that probe the entries of the adjacency matrix of an n vertex graph, and need to output a clique. We show that if the input graph is drawn at random from (Formula presented.) (and hence is likely to have a clique of size roughly (Formula presented.)), then for every δ<2 and constant ℓ, there is an α<2 (that may depend on δ and ℓ) such that no algorithm that makes nδ probes in ℓ rounds is likely (over the choice of the random graph) to output a clique of size larger than (Formula presented.).

KW - adaptive query model

KW - cliques

KW - random graphs

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ER -

Finding cliques using few probes

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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