Small set expansion hypothesis

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August undefined, 2024

WebApr 13, 2015 · The Small Set Expansion Hypothesis (SSEH)[14] states: for every η>0, there is a δsuch that it is NP-hard to distinguish whether ΦG(δ) >1 − ηor ΦG(δ) WebJul 1, 2024 · Specifically, assuming the Small Set Expansion Hypothesis [18], the problem is hard to approximate to within a factor of n 1 − γ for any constant γ > 0. We also establish …

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WebHypothesis 1.1. For all ε > 0, there exists δ > 0 such that SSEδ(1−ε,ε) is NP-hard. Theorem 1.2. [RS10] The small set expansion hypothesis implies the unique games conjecture. Moreover, the small set expansion hypothesis is shown to be equivalent to a variant of the WebMay 10, 2024 · The Small Set Expansion Hypothesis (SSEH) is a conjecture which roughly states that it is NP-hard to distinguish between a graph with a small subset of vertices … toy weight set

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Webthe tightness result does not rely on the small-set expansion hypothesis. We note that Louis, Raghavendra and Vempala [34] gave an SDP approximation algorithm for vertex expansion with the same approximation guarantee, but their SDP is different from and stronger than that in Definition I.1 (see Lemma III.10), WebJun 10, 2024 · Motivated by the above, we give new approximation and hardness results for . In particular, assuming the Small Set Expansion Hypothesis (SSEH), we show that with arity r and k = µ n is NP-hard to approximate to a factor of … WebJun 15, 2015 · The small set expansion (Sse) problem was studied by Arora, Barak and Steurer in [3] (and also by several other researchers such as [5, 18, [29][30][31]) in an … thermoplongeur 1000w 220v

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WebJun 8, 2024 · We put forth a hypothesis stating that every small set whose expansion is smaller than 1–δ must be correlated with one of a specified list of sets which are … toy weinermobileWeb1 This problem also shows that small syntactic changes in the problem deﬁnition can make a big difference for its computational complexity. The ... (Khot[2002]) or the closely related Small-Set Expansion Hypothesis (Raghavendra and Steurer[2010]). Approximating the maximum cut We now deﬁne the Max Cut problem: 1. Problem (Max Cut). toy welding rig

"WebThe Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of … " - Small set expansion hypothesis

Small set expansion hypothesis

On non-optimally expanding sets in grassmann graphs

Webcan approximate the small set expansion within a constant factor (and in time exponential in rank 1 (P)). Putting this together withTheorem 3.4gives a sub-exponential time … WebApr 13, 2024 · Assuming Small Set Expansion Hypothesis (or Strong Unique Games Conjecture), it is NP-hard to approximate Bipartite Minimum Maximal Matching with a …

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WebNov 11, 2010 · The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge … The small set expansion hypothesis or small set expansion conjecture in computational complexity theory is an unproven computational hardness assumption related to the unique games conjecture. Under the small set expansion hypothesis it is assumed to be computationally infeasible to … See more The small set expansion hypothesis implies the NP-hardness of several other computational problems. Although this does not prove that these problems actually are NP-hard, it nevertheless suggests that it … See more The small set expansion hypothesis was formulated, and connected to the unique games conjecture, by Prasad Raghavendra and David Steurer in 2010. One approach to resolving the small set expansion hypothesis is to seek approximation … See more

Webcorrectness of Small Set Expansion Hypothesis and Exponential Time Hypothesis. The authors also proposed a PTAS (Polynomial Time Approximation Scheme) with (1 + ") approximation ratio when 0 WebJun 8, 2024 · Abstract We study the structure of non-expanding sets in the Grassmann graph. We put forth a hypothesis stating that every small set whose expansion is smaller than 1– δ must be correlated with one of a specified list of sets which are isomorphic to smaller Grassmann graphs.

WebNov 11, 2010 · The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of small sets in graphs. WebSmall-set Expansion hypothesis. Building on the work of Cheeger [29], Alon and Milman [3, 1] proved the discrete Cheeger Inequality, a central inequality in Spectral Graph Theory. This inequality establishes a bound on expansion via the spectrum of the graph: 2 2 6˚ G6 p 2 2 where 2 is the second smallest eigenvalue of the normalized ...

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WebOct 9, 2024 · In the Maximum Balanced Biclique Problem (MBB), we are given an n-vertex graph \(G=(V, E)\), and the goal is to find a balanced complete bipartite subgraph with q vertices on each side while maximizing q.The MBB problem is among the first known NP-hard problems, and has recently been shown to be NP-hard to approximate within a factor … thermo plisseesWebThe main result is that the Small-Set Expansion Hypothesis is in fact equivalent to a variant of the Unique Games Conjecture, and the first strong hardness of approximation results … toy welders for kidsWebJan 28, 2024 · Assuming the Small Set Expansion Hypothesis (SSEH), no polynomial time algorithm can achieve an approximation ratio better than two [9]. Recently, Gupta, Lee and Li [5] gave a 1.9997-approximation FPT algorithm for the min- k -cut parameterized by k. They also improved this approximation ratio to 1.81 [4]. thermoplongeur 2kwWebJun 8, 2024 · We put forth a hypothesis stating that every small set whose expansion is smaller than 1–δ must be correlated with one of a specified list of sets which are isomorphic to smaller Grassmann graphs. We develop a framework of Fourier analysis for analyzing functions over the Grassmann graph, and prove that our hypothesis holds for all sets ... thermoplongeur 300wWebAbstract. We study the structure of non-expanding sets in the Grassmann graph. We put forth a hypothesis stating that every small set whose expansion is smaller than 1 − must be correlated with one of a specified list of sets which are isomorphic to smaller Grassmann graphs. We develop a framework of Fourier analysis for analyzing functions ... thermoplongeur4800w 12-81WebThe Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of small sets in graphs. This hardness assumption is closely connected to the Unique Games Conjecture (Khot, STOC 2002). In Keyphrases expansion problem thermoplongeur 3000wWebSep 30, 2024 · This assumption is crucial for the performance of these algorithms: even a very small fraction of outliers can completely compromise the algorithm’s behavior. ... in the sense that they stumble upon a well-known computational barrier — the so-called small set expansion hypothesis (SSE), closely related to the unique games conjecture (UGC). toywell