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• W2951843400 abstract "Previous chapter Next chapter Full AccessProceedings Proceedings of the 2014 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Hardness of Robust Graph Isomorphism, Lasserre Gaps, and Asymmetry of Random GraphsRyan O'Donnell, John Wright, Chenggang Wu, and Yuan ZhouRyan O'Donnell, John Wright, Chenggang Wu, and Yuan Zhoupp.1659 - 1677Chapter DOI:https://doi.org/10.1137/1.9781611973402.120PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Building on work of Cai, Fürer, and Immerman [18], we show two hardness results for the Graph Isomorphism problem. First, we show that there are pairs of nonisomorphic n-vertex graphs G and H such that any sum-of-squares (SOS) proof of nonisomorphism requires degree Ω(n). In other words, we show an Ω(n)-round integrality gap for the Lasserre SDP relaxation. In fact, we show this for pairs G and H which are not even (1 – 10−14)-isomorphic. (Here we say that two n-vertex, m-edge graphs G and H are α-isomorphic if there is a bijection between their vertices which preserves at least αm edges.) Our second result is that under the R3XOR Hypothesis [23] (and also any of a class of hypotheses which generalize the R3XOR Hypothesis), the robust Graph Isomorphism is hard. I.e. for every ∊ > 0, there is no efficient algorithm which can distinguish graph pairs which are (1 — ∊)-isomorphic from pairs which are not even (1 – ∊0)-isomorphic for some universal constant ∊0. Along the way we prove a robust asymmetry result for random graphs and hypergraphs which may be of independent interest. Previous chapter Next chapter RelatedDetails Published:2014ISBN:978-1-61197-338-9eISBN:978-1-61197-340-2 https://doi.org/10.1137/1.9781611973402Book Series Name:ProceedingsBook Code:PRDA14Book Pages:viii + 1885" @default.
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• W2951843400 date "2013-12-18" @default.
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• W2951843400 title "Hardness of Robust Graph Isomorphism, Lasserre Gaps, and Asymmetry of Random Graphs" @default.
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• W2951843400 doi "https://doi.org/10.1137/1.9781611973402.120" @default.
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