Abstract

We propose a family of semidefinite programming (SDP) relaxations of the problem of graph bisection with preferences. That is, given a graph G = (V,E) we wish to partition the vertices into two disjoint sets V = Pi∪P2 so as to minimize the sum of the number of edges cut by the partition and Σi∈Vxidi where xi = +1 if i ∈ P1 and xi = −1 otherwise. The SDP relaxation is related to well‐known SDP and spectral relaxations for graph bisection without preferences. The preference vector d can be used to incorporate important information for recursive bisection for data distribution in parallel computers. This relaxation is analogous to an SDP relaxation of graph partitioning related to the spectral relaxation used to obtain the Fiedler vector.

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