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Small set expansion hypothesis information


The small set expansion hypothesis or small set expansion conjecture in computational complexity theory is an unproven computational hardness assumption. Under the small set expansion hypothesis it is assumed to be computationally infeasible to distinguish between a certain class of expander graphs called "small set expanders" and other graphs that are very far from being small set expanders. This assumption implies the hardness of several other computational problems, and the optimality of certain known approximation algorithms.

The small set expansion hypothesis is related to the unique games conjecture, another unproven computational hardness assumption according to which accurately approximating the value of certain games is computationally infeasible. If the small set expansion hypothesis is true, then so is the unique games conjecture.

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Small set expansion hypothesis

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The small set expansion hypothesis or small set expansion conjecture in computational complexity theory is an unproven computational hardness assumption...

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Parameterized approximation algorithm

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\varepsilon >0} , assuming P ≠ N P {\displaystyle P\neq NP} and the small set expansion hypothesis. It is also W[1]-hard parameterized by the number k {\displaystyle...

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Computational hardness assumption

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edge expansion is minimal. It is known that if SSE is hard to approximate, then so is Unique Label Cover. Hence, the Small Set Expansion Hypothesis, which...

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Dense subgraph

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approximation algorithm is essentially the best possible: assuming the small set expansion hypothesis (a computational complexity assumption closely related to the...

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Unique games conjecture

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Biclique, Maximum Balanced Biclique and Minimum k-Cut from the Small Set Expansion Hypothesis", in Chatzigiannakis, Ioannis; Indyk, Piotr; Kuhn, Fabian; Muscholl...

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Prasad Raghavendra

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satisfaction problems. Together with David Steurer, he developed the small set expansion hypothesis, for which they won the Michael and Shiela Held Prize in 2018...

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David Steurer

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Raghavendra. Together with Prasad Raghavendra, he developed the small set expansion hypothesis, for which they won the Michael and Shiela Held Prize. Together...

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House allocation problem

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n^{\gamma }} for some γ > 0 {\displaystyle \gamma >0} ; if the small set expansion hypothesis is true, then it cannot be approximated to within a factor of...

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Cutwidth

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bisection number, gives the stated approximation ratio. Under the small set expansion hypothesis, it is not possible to achieve a constant approximation ratio...

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Abductive reasoning

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abduction can be seen as a form of set covering. Abductive validation is the process of validating a given hypothesis through abductive reasoning. This...

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Multiregional origin of modern humans

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The multiregional hypothesis, multiregional evolution (MRE), or polycentric hypothesis, is a scientific model that provides an alternative explanation...

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Gaia hypothesis

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The Gaia hypothesis (/ˈɡaɪ.ə/), also known as the Gaia theory, Gaia paradigm, or the Gaia principle, proposes that living organisms interact with their...

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Scientific method

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creating a hypothesis through inductive reasoning, testing it through experiments and statistical analysis, and adjusting or discarding the hypothesis based...

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Bantu expansion

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article presenting these correlations as a reasonable hypothesis. The hypothesized Bantu expansion pushed out or assimilated the hunter-forager proto-Khoisan...

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Score test

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the score—evaluated at the hypothesized parameter value under the null hypothesis. Intuitively, if the restricted estimator is near the maximum of the likelihood...

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Glossary of set theory

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Kelley 2.  Morse–Kelley set theory (also called Kelley–Morse set theory), a set theory with classes KH Kurepa's hypothesis kind Ordinals of the first...

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Statistics

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relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship...

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RNA world

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before the evolution of DNA and proteins. The term also refers to the hypothesis that posits the existence of this stage. Alexander Rich first proposed...

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Austronesian peoples

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originated from a prehistoric seaborne migration, known as the Austronesian expansion, from Taiwan, circa 3000 to 1500 BCE. Austronesians reached the northernmost...

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Khazar hypothesis of Ashkenazi ancestry

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The hypothesis draws on medieval sources such as the Khazar Correspondence, according to which at some point in the 8th–9th centuries, a small number...

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Composition of the Torah

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Priestly phases. By contrast, scholars such as John Van Seters advocate a supplementary hypothesis, which posits that the Torah is the result of two major...

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Flixborough disaster

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consensus for either hypothesis other possible immediate causes have been suggested. The enquiry noted the existence of a small tear in a bellows fragment...

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Ritual Decalogue

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again either by gradual aggregation, or by an individual. The documentary hypothesis identifies the Ritual Decalogue as the work of the Jahwist, from the Kingdom...

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Big Crunch

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of evidence indicates that this hypothesis is not correct. Instead, astronomical observations show that the expansion of the universe is accelerating...

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