Abstract
This paper presents polynomial-time approximation algorithms for the problem of computing a maximum independent set in a given map graph G with or without weights on its vertices. If G is given together with a map, then a ratio of 1+δ can be achieved by a quadratic-time algorithm for any given constant δ≥0, no matter whether each vertex of G is given a weight or not. In case G is given without a map, a ratio of 4 can be achieved by a low-degree polynomial-time algorithm if no vertex is given a weight, while a ratio of 5 can be achieved by a low-degree polynomial-time algorithm otherwise.
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