Small set expansion hypothesis

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August undefined, 2024

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 … 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

[1011.2586] Reductions Between Expansion Problems

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 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 … covid 19 usa update today live

Reductions Between Expansion Problems - ResearchGate

Webthe small-set expansion problem, a close cousin of Khot’s unique games problem, to robust meanestimationandrelatedproblems. Thesereductionsshowthat(a)currentapproaches for … WebNov 11, 2010 · The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge … 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 … maggot brain guitarist

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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 ... WebSep 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). covid 19 update today arizonaWeb2 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. covid19 usa news

"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), " - Small set expansion hypothesis

Small set expansion hypothesis

Reductions Between Expansion Problems - TTIC

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 … 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.

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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. <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 ...

WebThe 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, … 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’.

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. 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 …

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 …

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 . maggot brain guitar soloWebJan 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]. covid 19 vaccination animal pet minkWebApr 13, 2024 · Assuming Small Set Expansion Hypothesis (or Strong Unique Games Conjecture), it is NP-hard to approximate Bipartite Minimum Maximal Matching with a … maggot cartoon imagesWebThe 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 … covid 19 vaccination appointment singaporeWebIn 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 … covid 19 vaccination alberta update todayWebApr 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) covid 19 vaccination cards imagesWebSep 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. maggot commando