Approximation of satisfactory bisection problems
نویسندگان
چکیده
The Satisfactory Bisection problem means to decide whether a given graph has a partition of its vertex set into two parts of the same cardinality such that each vertex has at least as many neighbors in its part as in the other part. A related variant of this problem, called Co-Satisfactory Bisection, requires that each vertex has at most as many neighbors in its part as in the other part. A vertex satisfying the degree constraint above in a partition is called ‘satisfied’ or ‘co-satisfied’, respectively. After stating the NP -completeness of both problems, we study approximation results in two directions. We prove that maximizing the number of (co-)satisfied vertices in a bisection has no polynomial-time approximation scheme (unless P = NP ), whereas constant approximation algorithms can be obtained in polynomial time. Moreover, minimizing the difference of the cardinalities of vertex classes in a bipartition that (co-)satisfies all vertices has no polynomial-time approximation scheme either.
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عنوان ژورنال:
- J. Comput. Syst. Sci.
دوره 74 شماره
صفحات -
تاریخ انتشار 2008