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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 adding random restrictions to the solution space such that, with non-negligible probability, exactly one solution satisfies the additional restrictions 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.".
- Isolation_lemma thumbnail Linear_optimization_in_a_2-dimensional_polytope.svg?width=300.
- Isolation_lemma wikiPageExternalLink favorite-theorems-unique-witnesses.html.
- Isolation_lemma wikiPageExternalLink summary?doi=10.1.1.16.9300.
- Isolation_lemma wikiPageExternalLink index.html.
- Isolation_lemma wikiPageExternalLink citation.cfm?id=1429791.1429816.
- Isolation_lemma wikiPageExternalLink the-isolation-lemma-and-beyond.
- Isolation_lemma wikiPageExternalLink isolation.pdf.
- Isolation_lemma wikiPageExternalLink proc.pdf.
- Isolation_lemma wikiPageExternalLink r4rw2x4l46476708.
- Isolation_lemma wikiPageID "27295601".
- Isolation_lemma wikiPageRevisionID "569525232".
- Isolation_lemma hasPhotoCollection Isolation_lemma.
- Isolation_lemma subject Category:Combinatorics.
- Isolation_lemma subject Category:Lemmas.
- Isolation_lemma subject Category:Probability_theorems.
- Isolation_lemma type Abstraction100002137.
- Isolation_lemma type Communication100033020.
- Isolation_lemma type Lemma106751833.
- Isolation_lemma type Lemmas.
- Isolation_lemma type Message106598915.
- Isolation_lemma type ProbabilityTheorems.
- Isolation_lemma type Proposition106750804.
- Isolation_lemma type Statement106722453.
- Isolation_lemma type Theorem106752293.
- 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 adding random restrictions to the solution space such that, with non-negligible probability, exactly one solution satisfies the additional restrictions 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".
- Isolation_lemma sameAs m.0bxz26v.
- Isolation_lemma sameAs Q6085965.
- Isolation_lemma sameAs Q6085965.
- Isolation_lemma sameAs Isolation_lemma.
- Isolation_lemma wasDerivedFrom Isolation_lemma?oldid=569525232.
- Isolation_lemma depiction Linear_optimization_in_a_2-dimensional_polytope.svg.
- Isolation_lemma isPrimaryTopicOf Isolation_lemma.
