The Complexity of Multiterminal Cuts 论文

1994SIAM Journal on Computing引用 661
Complexity and Algorithms in GraphsComputational Geometry and Mesh GenerationVLSI and FPGA Design Techniques

详细信息

发表期刊/会议
SIAM Journal on Computing
发表日期
1994-08-01
发表年份
1994

关键词

Complexity and Algorithms in GraphsComputational Geometry and Mesh GenerationVLSI and FPGA Design Techniques

摘要

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.