Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
On Integer Multiflow Maximization
SIAM Journal on Discrete Mathematics
An improved approximation algorithm for multiway cut
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Rounding algorithms for a geometric embedding of minimum multiway cut
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A simple algorithm for the planar multiway cut problem
Journal of Algorithms
Multiway Cuts in Directed and Node Weighted Graphs
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
A 2-approximation algorithm for the directed multiway cut problem
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Hardness of the undirected edge-disjoint paths problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A linear programming formulation of Mader's edge-disjoint paths problem
Journal of Combinatorial Theory Series B
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Given an edge-capacitated graph and kterminal vertices, the maximum integer multiterminal flow problem (MaxIMTF) is to route the maximum number of flow units between the terminals. For directed graphs, we introduce a new parameter kL ≤ k and prove that MaxIMTF is $\mathcal{NP}$-hard when k = kL = 2 and when kL = 1 and k = 3, and polynomial-time solvable when kL = 0 and when kL = 1 and k = 2. We also give an 2 log2 (kL + 2)-approximation algorithm for the general case. For undirected graphs, we give a family of valid inequalities for MaxIMTF that has several interesting consequences, and show a correspondence with valid inequalities known for MaxIMTF and for the associated minimum multiterminal cut problem.