On set expansion problems and the small set expansion conjecture
نویسندگان
چکیده
منابع مشابه
On Set Expansion Problems and the Small Set Expansion Conjecture
We study two problems related to the Small Set Expansion Conjecture [14]: the Maximum weight m′-edge cover (MWEC ) problem and the Fixed cost minimum edge cover (FCEC ) problem. In the MWEC problem, we are given an undirected simple graph G = (V,E) with integral vertex weights. The goal is to select a set U ⊆ V of maximum weight so that the number of edges with at least one endpoint in U is at ...
متن کاملOn Set Expansion Problems and the Small Set Expansion
We study two problems related to the Small Set Expansion Conjecture [15]: the Maximum weight m′-edge cover (MWEC) problem and the Fixed cost minimum edge cover (FCEC) problem. In the MWEC problem, we are given an undirected simple graph G = (V,E) with integral vertex weights. The goal is to select a set U ⊆ V of maximum weight so that the number of edges with at least one endpoint in U is at mo...
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The expansion of a hypergraph, a natural extension of the notion of expansion in graphs, is defined as the minimum over all cuts in the hypergraph of the ratio of the number of the hyperedges cut to the size of the smaller side of the cut. We study the Hypergraph Small Set Expansion problem, which, for a parameter δ ∈ (0, 1/2], asks to compute the cut having the least expansion while having at ...
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Consider an irreducible reversible Markov chain on state space V , with |V | = n and invariant distribution π. Let 0 = λ1 ≤ λ2 ≤ · · ·λn ≤ 2 be the eigenvalues of its Laplacian operator. We give a simple spectral condition under which there exists a unit vector f ∈ L(V, π) with ‖f‖1 ≤ δ and 〈f, Lf〉 ≤ . (Using a standard Cheeger inequality, this implies the existence of a set S ⊆ V with measure ...
متن کاملTesting Small Set Expansion in General Graphs
We consider the problem of testing small set expansion for general graphs. A graph G is a (k, φ)expander if every subset of volume at most k has conductance at least φ. Small set expansion has recently received significant attention due to its close connection to the unique games conjecture, the local graph partitioning algorithms and locally testable codes. We give testers with two-sided error...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2015
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.05.028