Small set expansion hypothesis

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August undefined, 2024

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 … WebDec 4, 2024 · Small Set Vertex Expansion problem is vertex version of the Small Set Expansion (SSE) problem, in which we are asked to choose a set of k nodes to minimize …

On non-optimally expanding sets in Grassmann graphs

Webthe small-set expansion problem, a close cousin of Khot’s unique games problem, to robust meanestimationandrelatedproblems. Thesereductionsshowthat(a)currentapproaches for … 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. currency exchange fort collins

Inapproximabilty of Densest κ-Subgraph from Average Case …

Websets in disproving the small-set expansion hypothesis. 1. We de ne a combinatorial analog of the spectral gap, and use it to prove the convergence of non-lazy random walks. A … 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 WebSep 4, 2024 at 12:45 In this paper, people.math.ethz.ch/~abandeira/TenLecturesFortyTwoProblems.pdf, at the chapter 3, … currency exchange formula excel

Optimal Analysis of Subset-Selection Based Low-Rank …

WebThe Small Set Expansion Hypothesis is a conjecture which roughly states that it is NP-hard to distinguish between a graph with a small subset of vertices whose (edge) expansion is almost zero and one in which all small subsets of vertices have expansion almost one. In this work, we prove conditional inapproximability results with essentially optimal ratios for … 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 currency exchange frankfurt airportAs well as their cryptographic applications, hardness assumptions are used in computational complexity theory to provide evidence for mathematical statements that are difficult to prove unconditionally. In these applications, one proves that the hardness assumption implies some desired complexity-theoretic statement, instead of proving that the statement is itself true. The best-known assumption of this type is the assumption that P ≠ NP, but others include the expone… currency exchange for japanese yen

"WebJun 26, 2012 · The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge … " - Small set expansion hypothesis

Small set expansion hypothesis

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 … WebDec 15, 2015 · Finally, I will present an example showing the limitations of local graph partitioning algorithms in attacking the small-set expansion hypothesis, disproving a conjecture by Oveis Gharan about evolving sets. I will present a new proof of Cheeger's inequality, which can be generalized to incorporate robust vertex expansion in it. The …

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Web1 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). 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)

Webhardness): assuming the Small Set Expansion hypothesis, we prove that even for 0-1 similarities, there exists ">0, such that it is NP-hard to ap-proximate the [MW17] objective within a factor of (1 "). A summary of our results compared to the previous work is given inTable1. Here we also point out that 1 3 is a simple baseline achieved by a random 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 …

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

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 …

WebAbstract. 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 ... currency exchange forest parkWebJun 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 … currency exchange for indiaWebIn mathematics, the minimum k-cut, is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph to at least k connected components. These edges are referred to as k-cut. The goal is to find the minimum-weight k … currency exchange fort lauderdale airportWebApr 13, 2024 · Assuming Small Set Expansion Hypothesis (or Strong Unique Games Conjecture), it is NP-hard to approximate Bipartite Minimum Maximal Matching with a … currency exchange free apiWebThe 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 currency exchange frisco texasWebJun 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 … currency exchange frisco txWebNov 11, 2010 · The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge … currency exchange franklin park il