Small set expansion hypothesis

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August undefined, 2024

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, … 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.

Inapproximability of Maximum Biclique Problems, Minimum

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 … 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 ... shark typhoon combo

CiteSeerX — Reductions between expansion problems

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. 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 is equivalent to assuming that the Unique Games Conjecture holds even when the input instances are required to be small set expanders, … shark types images

On non-optimally expanding sets in Grassmann graphs

Optimal Analysis of Subset-Selection Based Low-Rank …

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 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 … shark typhoon leyline binding shark types game

"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). " - Small set expansion hypothesis

Small set expansion hypothesis

Reductions Between Expansion Problems - NASA/ADS

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

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. 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 …

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 … 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 …

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 ...

WebJun 26, 2012 · The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge … shark typhoon modern deckWebSep 4, 2024 at 12:45 In this paper, people.math.ethz.ch/~abandeira/TenLecturesFortyTwoProblems.pdf, at the chapter 3, … shark typhoon mtgWebThe 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 shark typhoon deckWeb2 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. shark typhoon mtg priceWebJun 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 ... shark typhoon modernWebNov 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. population of ardmore okWebcontradict 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’. population of arimo idaho