Small set expansion hypothesis
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. 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
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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). 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 …
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. 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.
WebJun 26, 2012 · The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge … 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 …
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 …
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]. phone number for the dollar treeWebAbstract. 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 ... how do you run scandisk in windows 10Webthe 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), how do you run wire through a wallWebhardness): 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 how do you run your computer as administratorWebcontradict 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’. phone number for the fcc in washington dcWebJun 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 ... how do you rupture a colonWebJul 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 … phone number for the governor\u0027s office