Small set expansion hypothesis
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 … 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’.
Small set expansion hypothesis
Did you know?
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) … 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
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). WebThe Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of …
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 … 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 …
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
WebJun 26, 2012 · The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge … fm1270 rechargeable battery buy houstonWebthe 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), greensands community transportWebFollowing 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. fm 1240 falls county txWebDec 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 … greensands corfe castleWebMay 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 … greensand ridge bedfordshireAs 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… fm1270 rechargeable batteryWebcan 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 … fm 1-28 design wind loads