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- Isolation_lemma abstract "In theoretical computer science, the term isolation lemma (or isolating lemma) refers to randomized algorithms that reduce the number of solutions to a problem to one, should a solution exist.This is achieved by constructing random constraints such that, with non-negligible probability, exactly one solution satisfies these additional constraints if the solution space is not empty.Isolation lemmas have important applications in computer science, such as the Valiant–Vazirani theorem and Toda's theorem in computational complexity theory.The first isolation lemma was introduced by Valiant & Vazirani (1986), albeit not under that name.Their isolation lemma chooses a random number of random hyperplanes, and has the property that, with non-negligible probability, the intersection of any fixed non-empty solution space with the chosen hyperplanes contains exactly one element. This suffices to show the Valiant–Vazirani theorem:there exists a randomized polynomial-time reduction from the satisfiability problem for Boolean formulas to the problem of detecting whether a Boolean formula has a unique solution.Mulmuley, Vazirani & Vazirani (1987) introduced an isolation lemma of a slightly different kind:Here every coordinate of the solution space gets assigned a random weight in a certain range of integers, and the property is that, with non-negligible probability, there is exactly one element in the solution space that has minimum weight. This can be used to obtain a randomized parallel algorithm for the maximum matching problem.Stronger isolation lemmas have been introduced in the literature to fit different needs in various settings.For example, the isolation lemma of Chari, Rohatgi & Srinivasan (1993) has similar guarantees as that of Mulmuley et al., but it uses fewer random bits.In the context of the exponential time hypothesis, Calabro et al. (2008) prove an isolation lemma for k-CNF formulas.Noam Ta-Shma gives an isolation lemma with slightly stronger parameters, and gives non-trivial results even when the size of the weight domain is smaller than the number of variables.".
- Isolation_lemma thumbnail Linear_optimization_in_a_2-dimensional_polytope.svg?width=300.
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- Isolation_lemma wikiPageExternalLink isolation.pdf.
- Isolation_lemma wikiPageExternalLink proc.pdf.
- Isolation_lemma wikiPageExternalLink favorite-theorems-unique-witnesses.html.
- Isolation_lemma wikiPageExternalLink summary?doi=10.1.1.16.9300.
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- Isolation_lemma wikiPageWikiLink Category:Combinatorics.
- Isolation_lemma wikiPageWikiLink Category:Lemmas.
- Isolation_lemma wikiPageWikiLink Category:Probability_theorems.
- Isolation_lemma wikiPageWikiLink Clique_problem.
- Isolation_lemma wikiPageWikiLink Computational_complexity_theory.
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- Isolation_lemma wikiPageWikiLink Iff.
- Isolation_lemma wikiPageWikiLink Joel_Spencer.
- Isolation_lemma wikiPageWikiLink Lance_Fortnow.
- Isolation_lemma wikiPageWikiLink Matching_(graph_theory).
- Isolation_lemma wikiPageWikiLink Maximum_matching.
- Isolation_lemma wikiPageWikiLink NL_(complexity).
- Isolation_lemma wikiPageWikiLink Polynomial-time_reduction.
- Isolation_lemma wikiPageWikiLink Randomized_algorithm.
- Isolation_lemma wikiPageWikiLink Richard_J._Lipton.
- Isolation_lemma wikiPageWikiLink Theoretical_computer_science.
- Isolation_lemma wikiPageWikiLink Todas_theorem.
- Isolation_lemma wikiPageWikiLink Tutte_matrix.
- Isolation_lemma wikiPageWikiLink Valiant–Vazirani_theorem.
- Isolation_lemma wikiPageWikiLink File:Linear_optimization_in_a_2-dimensional_polytope.svg.
- Isolation_lemma wikiPageWikiLinkText "isolation lemma".
- Isolation_lemma hasPhotoCollection Isolation_lemma.
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- Isolation_lemma wikiPageUsesTemplate Template:Refbegin.
- Isolation_lemma wikiPageUsesTemplate Template:Refend.
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- Isolation_lemma subject Category:Combinatorics.
- Isolation_lemma subject Category:Lemmas.
- Isolation_lemma subject Category:Probability_theorems.
- Isolation_lemma type Article.
- Isolation_lemma type Article.
- Isolation_lemma type Combinatoric.
- Isolation_lemma type Field.
- Isolation_lemma type Lemma.
- Isolation_lemma type Theorem.
- Isolation_lemma comment "In theoretical computer science, the term isolation lemma (or isolating lemma) refers to randomized algorithms that reduce the number of solutions to a problem to one, should a solution exist.This is achieved by constructing random constraints such that, with non-negligible probability, exactly one solution satisfies these additional constraints if the solution space is not empty.Isolation lemmas have important applications in computer science, such as the Valiant–Vazirani theorem and Toda's theorem in computational complexity theory.The first isolation lemma was introduced by Valiant & Vazirani (1986), albeit not under that name.Their isolation lemma chooses a random number of random hyperplanes, and has the property that, with non-negligible probability, the intersection of any fixed non-empty solution space with the chosen hyperplanes contains exactly one element. ".
- Isolation_lemma label "Isolation lemma".
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- Isolation_lemma sameAs Q6085965.
- Isolation_lemma sameAs Q6085965.
- Isolation_lemma wasDerivedFrom Isolation_lemma?oldid=679433278.
- Isolation_lemma depiction Linear_optimization_in_a_2-dimensional_polytope.svg.
- Isolation_lemma isPrimaryTopicOf Isolation_lemma.