Small set expansion hypothesis

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August undefined, 2024

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 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

On Set Expansion Problems and the Small Set Expansion Conjecture

WebJun 26, 2012 · The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge … 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. cuda install failed windows 10

arXiv:2203.03858v2 [math.PR] 23 Mar 2024

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 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 … 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 … easter egg hunt bellevue wa

Inapproximability of Maximum Biclique Problems, Minimum

A characterization of approximability for biased CSPs

Web2 days ago · The main expansion was in the form of westward expansion from the center, expanding in a radiating way, which mainly occurred in the Songbei and Dongli Districts (33.71 km 2, 30.02 km 2). From 2010 to 2015, the pace of urban expansion keeps gradually stable, and the area of Harbin city expands by 12.39 km 2 at an average rate of 2.49 km 2. Webcontradict 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’. cuda integrated graphicsWebThe 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 … cuda is not available on macos

"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 … " - Small set expansion hypothesis

Small set expansion hypothesis

A nearly 5/3-approximation FPT algorithm for min- k -cut - ACM …

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

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WebFollowing our work, Khot, Minzer and Safra (2024) proved the “Shortcode Expansion Hypothesis”. Combining their proof with our result and the reduction of Dinur et al. (2016), completes the proof of the 2 to 2 conjecture with imperfect completeness. 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 …

WebApr 10, 2024 · By supporting the construction of agricultural infrastructure, the development of featured agricultural products, the expansion of small and micro enterprises in rural areas, and education and medical care in rural areas, digital financial inclusion will inevitably promote the modernization and clean development of the agricultural industry chain . 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 ...

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). 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 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 ...

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 …

WebThe 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 cuda is not supported as output pixel formatWebThe Small-Set Expansion Hypothesis is equivalent to assuming that the Unique Games Conjecture holds even when the input instances are required to be small set expanders, … easter egg hunt carlisle<2. However, the running time is as large as O(npoly(k=")). Many other efforts have been devoted to designing approximation algorithms in order to ... easter egg hunt auburn caWebthe small-set expansion problem, a close cousin of Khot’s unique games problem, to robust meanestimationandrelatedproblems. Thesereductionsshowthat(a)currentapproaches for … easter egg hunt canton gaWebThe Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of … easter egg hunt cambridge maWebJul 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 … easter egg hunt buckinghamshireWebSep 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. cuda kitchen coupon codes