Theory of linear and integer programming
Theory of linear and integer programming
Routing through a dense channel with minimum total wire length
Journal of Algorithms
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Efficient algorithms for finding the maximum number of disjoint paths in grids
Journal of Algorithms
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Edge-Disjoint Routing in Plane Switch Graphs in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width
Journal of Algorithms
Eulerian disjoint paths problem in grid graphs is NP-complete
Discrete Applied Mathematics
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In this paper, we deal with the maximum integer multiflow and the minimum multicut problems in rectilinear grid graphs with uniform capacities on the edges. The first problem is known to be NP-hard when any vertex can be a terminal, and we show that the second one is also NP-hard. Then, we study the case where the terminals are located in a two-sided way on the boundary of the outer face. We prove that, in this case, both problems are polynomial-time solvable. Furthermore, we give two efficient combinatorial algorithms using a primal-dual approach. Our work is based on previous results concerning related decision problems.