Concurrent flow and concurrent connectivity on graphs
Graph theory with applications to algorithms and computer science
The maximum concurrent flow problem
Journal of the ACM (JACM)
Sparsest cuts and bottlenecks in graphs
Discrete Applied Mathematics - Computational combinatiorics
The Cross Product of Interconnection Networks
IEEE Transactions on Parallel and Distributed Systems
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
The complexity status of problems related to sparsest cuts
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Euclidean prize-collecting steiner forest
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
The complexity of finding uniform sparsest cuts in various graph classes
Journal of Discrete Algorithms
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A cut [S, S] is a sparsest cut of a graph G if its cut value |S||S|/|[S, S]| is maximum (this is the reciprocal of the well-known edge-density of the cut). In the (undirected) uniform concurrent flow problem on G, between every vertex pair of G flow paths with a total flow of 1 have to be established. The objective is to minimize the maximum amount of flow through an edge (edge congestion). The minimum congestion value of the uniform concurrent flow problem on G is an upper bound for the maximum cut value of cuts in G. If both values are equal, G is called a bottleneck graph. The bottleneck properties of cartesian product graphs G × H are studied. First, a flow in G × H is constructed using optimal flows in G and H, and proven to be optimal. Secondly, two cuts are constructed in G × H using sparsest cuts of G and H. It is shown that one of these cuts is a sparsest cut of G × H. As a consequence, we can prove that G × H is (not) a bottleneck graph if both G and H are (not) bottleneck graphs.