FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2269638945> ?p ?o ?g. }

• W2269638945 endingPage "1095" @default.
• W2269638945 startingPage "1079" @default.
• W2269638945 abstract "The problem of finding large cliques in random graphs and its variant, where one wants to recover a clique of size ω > log (n) added to an Erdo's-Renyi graph G ~ G(n, 1/2), have been intensely studied. Nevertheless, existing polynomial time algorithms can only recover planted cliques of size ω = Ω([EQUATION]). By contrast, information theoretically, one can recover planted cliques so long as ω > log (n).In this work, we continue the investigation of algorithms from the sum of squares hierarchy for solving the planted clique problem begun by Meka, Potechin, and Wigderson [MPW15] and Deshpande and Montanari [DM15b]. Our main results improve upon both these previous works by showing:1. Degree four SoS does not recover the planted clique unless ω >[EQUATION] polylog n, improving upon the bound ω > n1/3 due to [DM15b].2. For [EQUATION], degree 2d SoS does not recover the planted clique unless ω > n1/(d+1)/(2d polylog n), improving upon the bound due to [MPW15].Our proof for the second result is based on a fine spectral analysis of the certificate used in the prior works [MPW15, DM15b, FK03] by decomposing it along an appropriately chosen basis. Along the way, we develop combinatorial tools to analyze the spectrum of random matrices with dependent entries and to understand the symmetries in the eigenspaces of the set symmetric matrices inspired by work of Grigoriev [Gri01a].An argument of Kelner shows that the first result cannot be proved using the same certificate. Rather, our proof involves constructing and analyzing a new certificate that yields the nearly tight lower bound by correcting the certificate of [MPW15, DM15b, FK03]." @default.
• W2269638945 created "2016-06-24" @default.
• W2269638945 creator A5001123654 @default.
• W2269638945 creator A5044412015 @default.
• W2269638945 creator A5053469573 @default.
• W2269638945 creator A5068103506 @default.
• W2269638945 creator A5081583404 @default.
• W2269638945 date "2016-01-10" @default.
• W2269638945 modified "2023-09-23" @default.
• W2269638945 title "On the integrality gap of degree-4 sum of squares for planted clique" @default.
• W2269638945 cites W1028870867 @default.
• W2269638945 cites W134347045 @default.
• W2269638945 cites W134727942 @default.
• W2269638945 cites W1521197246 @default.
• W2269638945 cites W1550811836 @default.
• W2269638945 cites W1575824241 @default.
• W2269638945 cites W1580213736 @default.
• W2269638945 cites W1581035799 @default.
• W2269638945 cites W1649634100 @default.
• W2269638945 cites W1828524803 @default.
• W2269638945 cites W1885038349 @default.
• W2269638945 cites W1897704527 @default.
• W2269638945 cites W1967344706 @default.
• W2269638945 cites W1972894929 @default.
• W2269638945 cites W1972913305 @default.
• W2269638945 cites W1985123706 @default.
• W2269638945 cites W1987406389 @default.
• W2269638945 cites W2002025272 @default.
• W2269638945 cites W2010601719 @default.
• W2269638945 cites W2012805418 @default.
• W2269638945 cites W2020632401 @default.
• W2269638945 cites W2022749269 @default.
• W2269638945 cites W2028085501 @default.
• W2269638945 cites W2028932986 @default.
• W2269638945 cites W2031923588 @default.
• W2269638945 cites W2033515640 @default.
• W2269638945 cites W2053885701 @default.
• W2269638945 cites W2062307640 @default.
• W2269638945 cites W2078758709 @default.
• W2269638945 cites W2095315734 @default.
• W2269638945 cites W2096448465 @default.
• W2269638945 cites W2107052785 @default.
• W2269638945 cites W2110180651 @default.
• W2269638945 cites W2112575355 @default.
• W2269638945 cites W2115318789 @default.
• W2269638945 cites W2133404041 @default.
• W2269638945 cites W2138163102 @default.
• W2269638945 cites W2143724791 @default.
• W2269638945 cites W2144362128 @default.
• W2269638945 cites W2146777332 @default.
• W2269638945 cites W2151395725 @default.
• W2269638945 cites W2161185760 @default.
• W2269638945 cites W2163925208 @default.
• W2269638945 cites W2166536886 @default.
• W2269638945 cites W2166602562 @default.
• W2269638945 cites W2171194443 @default.
• W2269638945 cites W2187412414 @default.
• W2269638945 cites W2569174811 @default.
• W2269638945 cites W2600681475 @default.
• W2269638945 cites W2962704928 @default.
• W2269638945 cites W2963048722 @default.
• W2269638945 cites W58673994 @default.
• W2269638945 doi "https://doi.org/10.5555/2884435.2884511" @default.
• W2269638945 hasPublicationYear "2016" @default.
• W2269638945 type Work @default.
• W2269638945 sameAs 2269638945 @default.
• W2269638945 citedByCount "21" @default.
• W2269638945 countsByYear W22696389452016 @default.
• W2269638945 countsByYear W22696389452017 @default.
• W2269638945 countsByYear W22696389452018 @default.
• W2269638945 countsByYear W22696389452019 @default.
• W2269638945 countsByYear W22696389452020 @default.
• W2269638945 countsByYear W22696389452021 @default.
• W2269638945 countsByYear W22696389452022 @default.
• W2269638945 crossrefType "proceedings-article" @default.
• W2269638945 hasAuthorship W2269638945A5001123654 @default.
• W2269638945 hasAuthorship W2269638945A5044412015 @default.
• W2269638945 hasAuthorship W2269638945A5053469573 @default.
• W2269638945 hasAuthorship W2269638945A5068103506 @default.
• W2269638945 hasAuthorship W2269638945A5081583404 @default.
• W2269638945 hasConcept C105795698 @default.
• W2269638945 hasConcept C114614502 @default.
• W2269638945 hasConcept C118615104 @default.
• W2269638945 hasConcept C121332964 @default.
• W2269638945 hasConcept C132525143 @default.
• W2269638945 hasConcept C134306372 @default.
• W2269638945 hasConcept C158693339 @default.
• W2269638945 hasConcept C162324750 @default.
• W2269638945 hasConcept C24890656 @default.
• W2269638945 hasConcept C2775997480 @default.
• W2269638945 hasConcept C2777035058 @default.
• W2269638945 hasConcept C31170391 @default.
• W2269638945 hasConcept C33923547 @default.
• W2269638945 hasConcept C34447519 @default.
• W2269638945 hasConcept C47458327 @default.
• W2269638945 hasConcept C49847556 @default.
• W2269638945 hasConcept C62520636 @default.
• W2269638945 hasConcept C77553402 @default.

• next