On the complexity of covering vertices by faces in a planar graph
SIAM Journal on Computing
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Planar graph decomposition and all pairs shortest paths
Journal of the ACM (JACM)
Finding k-cuts within twice the optimal
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Flow in Planar Graphs with Multiple Sources and Sinks
SIAM Journal on Computing
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
The planar multiterminal cut problem
Discrete Applied Mathematics
Rounding algorithms for a geometric embedding of minimum multiway cut
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
An improved approximation algorithm for MULTIWAY CUT
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Nonlinear Formulations and Improved Randomized Approximation Algorithms for Multicut Problems
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
The regularity lemma and approximation schemes for dense problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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The minimum k-terminal cut problem is of considerable theoretical interest and arises in several applied areas such as parallel and distributed computing, VLSI circuit design, and networking. In this paper, we present two new approximation and exact algorithms for this problem on an n-vertex undirected weighted planar graph G. For the case when the k terminals are covered by the boundaries of m 1 faces of G, we give a min{O(n2 log n log m), O(m2n1.5 log2 n+kn)} time algorithm with a (2 - 2/k)-approximation ratio (clearly, m ≤ k). For the case when all k terminals are covered by the boundary of one face of G, we give an O(nk3 +(n log n)k2) time exact algorithm, or a linear time exact algorithm if k = 3, for computing an optimal k-terminal cut. Our algorithms are based on interesting observations and improve the previous algorithms when they are applied to planar graphs.