Small set expansion hypothesis

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August undefined, 2024

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.

Reductions Between Expansion Problems - ResearchGate

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 … WebApr 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, … north county post office

On non-optimally expanding sets in 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 … <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 ... 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 north county police car stolen

On Set Expansion Problems and the Small Set Expansion Conjecture

WebMar 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) … 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 … north county physical therapy prunedale caWebHypothesis 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 how to reset your msi laptop

"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… " - Small set expansion hypothesis

Small set expansion hypothesis

[1011.2586] Reductions Between Expansion Problems

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

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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 . 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 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 …

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 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 …

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 …

WebThe Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of … how to reset your maintenance light toyotaWebThe Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of … north county oral surgeon escondidoWeb1 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). north county public defenderWebJun 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 … north county pool sebastian flWebMay 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 … how to reset your mint accountWebhardness): 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 to reset your minehut servers worldWebcorrectness 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 how to reset your monitors