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- W2295468341 abstract "Previous chapter Next chapter Full AccessProceedings 2006 Proceedings of the Workshop on Analytic Algorithmics and Combinatorics (ANALCO)Semirandom Models as Benchmarks for Coloring AlgorithmsMichael Krivelevich and Dan VilenchikMichael KrivelevichSchool Of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, IsraelSchool of Computer Science, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, IsraelSearch for more papers by this author and Dan VilenchikSchool Of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, IsraelSchool of Computer Science, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, IsraelSearch for more papers by this authorpp.211 - 221Chapter DOI:https://doi.org/10.1137/1.9781611972962.4PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Semirandom models generate problem instances by blending random and adversarial decisions, thus intermediating between the worst-case assumptions that may be overly pessimistic in many situations, and the easy pure random case. In the Gn,p,k random graph model, the n vertices are partitioned into k color classes each of size n/k. Then, every edge connecting two different color classes is included with probability p = p(n). In the semirandom variant, G*n,p,k, an adversary may add edges as long as the planted coloring is respected. Feige and Killian prove that unless NP ⊆ BPP, no polynomial time algorithm works whp when np < (1 – ε) ln n, in particular when np is constant. Therefore, it seems like G*n,p,k is not an interesting benchmark for polynomial time algorithms designed to work whp on sparse instances (np a constant). We suggest two new criteria, using semirandom models, to serve as benchmarks for such algorithms. We also suggest two new coloring heuristics and compare them with the coloring heuristics suggested by Alon and Kahale 1997 and by Böttcher 2005. We prove that in some explicit sense both our heuristics are preferable to the latter. Previous chapter Next chapter RelatedDetails Published:2006eISBN:978-1-61197-296-2 https://doi.org/10.1137/1.9781611972962Book Series Name:ProceedingsBook Code:PR123Book Pages:185-279" @default.
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- W2295468341 title "Semirandom Models as Benchmarks for Coloring Algorithms" @default.
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