In this paper, we bound the integrality gap and the approximation ratio for maximum plane multiflow problems and deduce bounds on the flow-cut-gap. Planarity means here that the union of the supply and demand graph is planar. We first prove that there exists a multiflow of value at least half of the capacity of a minimum multicut. We then show how to convert any multiflow into a half-integer one of value at least half of the original multiflow. Finally, we round any half-integer multiflow into an integer multiflow, losing again at most half of the value, in polynomial time, achieving a 1/4-approximation algorithm for maximum integer multiflows in the plane, and an integer-flow-cut gap of 8.
CITATION STYLE
Garg, N., Kumar, N., & Sebő, A. (2020). Integer Plane Multiflow Maximisation: Flow-Cut Gap and One-Quarter-Approximation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12125 LNCS, pp. 144–157). Springer. https://doi.org/10.1007/978-3-030-45771-6_12
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