Abstract
Given an undirected graph with edge costs and a subset of k nodes called terminals, a multiway cut is a subset of edges whose removal disconnects each terminal from the rest. MULTIWAY CUT is the problem of finding a multiway cut of minimum cost. Previously, a very simple combinatorial algorithm due to Dahlhaus, Johnson, Papadimitriou, Seymour, and Yannakakis gave a performance guarantee of 2(1 - 1/k). In this paper, we present a new linear programming relaxation for MULTIWAY CUT and a new approximation algorithm based on it. The algorithm breaks the threshold of 2 for approximating MULTIWAY CUT, achieving a performance ratio of at most 1.5 - 1/k. This improves the previous result for every value of k. In particular, for k = 3 we get a ratio of 7/6 < 4/3.
| Original language | English |
|---|---|
| Pages (from-to) | 564-574 |
| Number of pages | 11 |
| Journal | Journal of Computer and System Sciences |
| Volume | 60 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jun 2000 |
| Externally published | Yes |
| Event | The 30th Annual ACM Symposium on Theory of Computing - Dallas, TX, USA Duration: 23 May 1998 → 26 May 1998 |
Bibliographical note
Funding Information:1Research supported in part by NSF Grant CCR-9319106. 2 Work supported by BSF Grant 96-00402, and by grants from the S. and N. Grand Research Fund, from the Smoler Research Fund, and from the Fund for the Promotion of Research at the Technion.