Approximation Ratio of the Min-Degree Greedy Algorithm for Maximum Independent Set on Interval and Chordal Graphs
arxiv(2024)
摘要
In this article we prove that the minimum-degree greedy algorithm, with
adversarial tie-breaking, is a (2/3)-approximation for the Maximum
Independent Set problem on interval graphs. We show that this is tight, even on
unit interval graphs of maximum degree 3. We show that on chordal graphs, the
greedy algorithm is a (1/2)-approximation and that this is again tight. These
results contrast with the known (tight) approximation ratio of
3/Δ+2 of the greedy algorithm for general graphs of maximum
degree Δ.
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