Approximating Maximum Cut on Interval Graphs and Split Graphs beyond Goemans-Williamson

초록

We present a polynomial-time (αGW + ϵ)-approximation algorithm for the Maximum Cut problem on interval graphs and split graphs, where αGW ≈ 0.878 is the approximation guarantee of the Goemans-Williamson algorithm and ϵ > 10-34 is a fixed constant. To attain this, we give an improved analysis of a slight modification of the Goemans-Williamson algorithm for graphs in which triangles can be packed into a constant fraction of their edges. We then pair this analysis with structural results showing that both interval graphs and split graphs either have such a triangle packing or have maximum cut close to their number of edges. We also show that, subject to the Small Set Expansion Hypothesis, there exists a constant c > 0 such that there is no polyomial-time (1-c)-approximation for Maximum Cut on split graphs. © Jungho Ahn, Ian DeHaan, Eun Jung Kim, and Euiwoong Lee; licensed under Creative Commons License CC-BY 4.0.

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