Abstract
In the multiterminal cut problem one is given an edge-weighted graph and a subset of the vertices called terminals, and is asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, max-flow problem, and can be solved in polynomial time. It is shown that the problem becomes NP-hard as soon as k = 3, but can be solved in polynomial time for planar graphs for any fixed k. The planar problem is NP-hard, however, if k is not fixed. A simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2 - 2/k of the optimal cut weight is also described.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 864-894 |
| Number of pages | 31 |
| Journal | SIAM Journal on Computing |
| Volume | 23 |
| Issue number | 4 |
| DOIs | |
| State | Published - Jan 1 1994 |
| Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Computer Science(all)
- Mathematics(all)
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Dahlhaus, E., Johnson, D. S., Papadimitriou, C. H., Seymour, P. D., & Yannakakis, M. (1994). Complexity of multiterminal cuts. SIAM Journal on Computing, 23(4), 864-894. https://doi.org/10.1137/S0097539792225297