Small set expansion hypothesis

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August undefined, 2024

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 … 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),

Inapproximabilty of Densest κ-Subgraph from Average Case …

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 WebThe Small Set Expansion Hypothesis (SSEH) is a conjecture which roughly states that it is NP-hard to distinguish between a graph with a small set of vertices whose expansion is … fish city grill san pedro

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WebThe Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of … 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 As 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… can a child be an abuser safeguarding adults

On non-optimally expanding sets in Grassmann graphs

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 … can a child be baptized if one parent objectsWebcontradict the Small Set Expansion Hypothesis since γ∗(G) can be computed in time polynomial in the size of the graph. Example 1.5. A popular use of Markov Chain Monte Carlo methods is to sample from the uniform distribution on an exponentially sized subset V of a product space {1,...,r}n (where r ≍ 1 and n is large) using ‘local chains’. fish city grill san antonio tx

"WebSep 24, 2014 · In this talk, we present a Cheeger inequality for vertex expansion (minimum ratio of number of vertices adjacent to a subset to the size of the subset), a parameter of fundamental importance, which is also NP-hard and approximable to within $O (\sqrt {\log n}) OPT$ in polynomial-time. " - Small set expansion hypothesis

Small set expansion hypothesis

Optimal Analysis of Subset-Selection Based Low-Rank …

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 … 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 …

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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

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 … 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 constant better than \frac {3} {2}. Due to space limitations, this result is only presented in the full version of our paper (published on arXiv [ 6 ]). 2 Revisiting the Khot-Regev Reduction

WebThe 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 … Websmall-set expansion problem. In particular, proving the NP-hardness of approximating the 2!q norm is (necessarily) an intermediate goal towards proving the Small-Set Expansion Hypothesis of Raghavendra and Steurer [RS10]. However, relatively few results algorithmic and hardness results are known for ap-proximating hypercontractive norms.

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 …

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 … can a child be a shareholderWebThe Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of … can a child be arrestedWebApr 13, 2024 · Assuming Small Set Expansion Hypothesis (or Strong Unique Games Conjecture), it is NP-hard to approximate Bipartite Minimum Maximal Matching with a … can a child be a pscWebMar 6, 2024 · Moreover, there is some evidence that this approximation algorithm is essentially the best possible: assuming the Small Set Expansion Hypothesis (a computational complexity assumption closely related to the Unique Games Conjecture), then it is NP-hard to approximate the problem to within [math]\displaystyle{ (2 - \epsilon) … can a child be born with autismWebcorrectness 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 fish city grill southlake menuWebApr 13, 2024 · The competitiveness of small modular reactors (SMRs) has been planned based on design simplification, short construction time, passive safety systems, and enabling self-financing by ramp-up construction. Due to the global energy challenges, SMRs have received pervasive attention from a wide range of researchers, designers, … can a child be an abuser of an adultWebJun 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 … fish city grill southlake tx menu