Proceedings 41st Annual Symposium on Foundations of Computer Science (2000)
Redondo Beach, California
Nov. 12, 2000 to Nov. 14, 2000
U. Feige , Dept. of Comput. Sci. & Appl. Math., Weizmann Inst. of Sci., Rehovot, Israel
R. Krauthgamer , Dept. of Comput. Sci. & Appl. Math., Weizmann Inst. of Sci., Rehovot, Israel
A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n/2. The bisection cost is the number of edges connecting the two sets. Finding the bisection of minimum cost is NP-hard. We present an algorithm that finds a bisection whose cost is within ratio of O(log/sup 2/ n) from the optimal. For graphs excluding any fixed graph as a minor (e.g. planar graphs) we obtain an improved approximation ratio of O(log n). The previously known approximation ratio for bisection was roughly /spl radic/n.
computational complexity; graph theory; computational geometry; polylogarithmic approximation; minimum bisection; graph; vertices; vertex partitioning; bisection cost; edges; complexity; approximation ratio
R. Krauthgamer and U. Feige, "A polylogarithmic approximation of the minimum bisection," Proceedings 41st Annual Symposium on Foundations of Computer Science(FOCS), Redondo Beach, California, 2000, pp. 105.