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**public sources and our publisher partners.**The celebrated Cheeger’s Inequality (Alon and Milman 1985; Alon 1986) establishes a bound on the edge expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of… Expand

Cheeger's fundamental inequality states that any edge-weighted graph has a vertex subset S such that its expansion (a.k.a. conductance) is bounded as follows: [ φ(S) def= (w(S,bar{S}))/(min set(w(S),… Expand

We consider the Degree-Bounded Survivable Network Design Problem: the objective is to find a minimum cost subgraph satisfying the given connectivity requirements as well as the degree bounds on the… Expand

The celebrated Cheeger's Inequality [AM85,a86] establishes a bound on the expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of graphs, based on studying the… Expand

We consider the facility location problem where each facility can serve at most U clients. We analyze a local search algorithm for this problem which uses only the operations of add, delete and swap… Expand

Graph-based semi-supervised learning (SSL) is an important learning problem where the goal is to assign labels to initially unlabeled nodes in a graph. Graph Convolutional Networks (GCNs) have… Expand

We demonstrate that l rounds of the Sherali-Adams hierarchy and 2l rounds of the Lovasz-Schrijver hierarchy suffice to reduce the integrality gap of a natural LP relaxation for Directed Steiner Tree… Expand

We consider two generalizations of the problem of finding a sparsest cut in a graph. The first is to find a partition of the vertex set into m parts so as to minimize the sparsity of the partition… Expand

In many real-world network datasets such as co-authorship, co-citation, email communication, etc., relationships are complex and go beyond pairwise. Hypergraphs provide a flexible and natural… Expand

We give O(log^2 n)-approximation algorithm based on the cut-matching framework of [10, 13, 14] for computing the sparsest cut on directed graphs. Our algorithm uses only O(log^2 n) single commodity… Expand