A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Separators for sphere-packings and nearest neighbor graphs
Journal of the ACM (JACM)
How Good is Recursive Bisection?
SIAM Journal on Scientific Computing
Geometric Separators for Finite-Element Meshes
SIAM Journal on Scientific Computing
Min—max-boundary domain decomposition
Theoretical Computer Science
Spectral partitioning works: planar graphs and finite element meshes
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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Many load balancing problems that arise in scientific computing applications ask to partition a graph with weights on the vertices and costs on the edges into a given number of almost equally-weighted parts such that the maximum boundary cost over all parts is small.Here, this partitioning problem is considered for boundeddegree graphs G ≡ (V,E) with edge costs c: E → R+ that have a p-separator theorem for some p 1, i.e., any (arbitrarily weighted) subgraph of G can be separated into two parts of roughly the same weight by removing separator S⊆V such that the edges incident to S in the subgraph have total cost at most proportional to (Εecpe)1/p, where the sum is over all edges in the subgraph.We show for all positive integers k and weights w that the vertices of G can be partitioned into k parts such that the weight of each part differs from the average weight Εv∈V wvk by less than maxv∈V wv, and the boundary edges of each part have cost at most proportional to (Εe∈ cpe/k)1/p + maxe∈E ce. The partition can be computed in time nearly proportional to the time for computing a separator S of G.Our upper bound on the boundary costs is shown to be tight up to a constant factor for infinitely many instances with a broad range of parameters. Previous results achieved this bound only if one has c ≡ 1, w ≡ 1, and one allows parts with weight exceeding the average by a constant fraction.