2020/02/25 by Naveen Garg, Garg, Naveen, Nikhil Kumar +3
Computer Science · #Complexity and Algorithms in Graphs #Optimization and Search Problems #Advanced Graph Theory Research
paper · doi:10.48550/arxiv.2002.10927
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.