A Weighted Planar Graph Separator
نویسندگان
چکیده
Given a weighted planar graph, we construct a simple separating cycle C whose interior and exterior both weigh at most 2/3 of the total weight. The cycle C uses k jumps across the faces and ordinary edges with cost O(1=k) of the total edge cost. This theorem is the main component of a PTAS for the weighted TSP problem 4].
منابع مشابه
NP-completeness of the Planar Separator Problems
For a given graph G, the Separator Problem asks whether a vertex or edge set of small cardinality (or weight) exists whose removal partitions G into two disjoint graphs of approximately equal sizes. Called the Vertex Separator Problem when the removed set is a vertex set, and the Edge Separator Problem when it is an edge set, both problems are NP-complete for general unweighted graphs [6]. Desp...
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