Graph Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Finding small simple cycle separators for 2-connected planar graphs.
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
A linear-time heuristic for improving network partitions
DAC '82 Proceedings of the 19th Design Automation Conference
Approximation algorithms for NP-complete problems on planar graphs
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Graph Bisection Algorithins With Good Average Case Behavior
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Lower bounds for the partitioning of graphs
IBM Journal of Research and Development
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A k-ratio edge separator is a set of edges which separates a weighted graph into two disconnected sets of components neither of which contains more than k-1/k of the original graph's weight. An optimal quotient separator is an edge separator where the size of the separator (i.e., the number of edges) divided by the weight of the smaller set of components is minimized. An optimal quotient k-ratio separator is an edge separator where the size of the separator (i.e., the number of edges) divided by the smaller of either 1/k of the total weight or the weight of the smaller set of components is minimized. In this paper we present an algorithm that finds the optimal quotient k-ratio separator for any k ≥ 3. We use the optimal quotient algorithm to obtain approximation algorithms for finding optimal k-ratio edge separators for any k ≥ 3. Given a planar graph with a size OPT k-ratio separator, we describe an algorithm which a finds k-ratio separator which costs less than O(OPT log n). More importantly the algorithm finds ck-ratio separators (for any c 1) which cost less than C(c)OPT, where C(c) depends only on c.