A strongly polynomial algorithm to solve combinatorial linear programs
Operations Research
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
NP-completeness of some edge-disjoint paths problems
Discrete Applied Mathematics
Connectivity and network flows
Handbook of combinatorics (vol. 1)
The complexity of path coloring and call scheduling
Theoretical Computer Science
The edge-disjoint path problem is NP-complete for series-parallel graphs
Discrete Applied Mathematics - Special issue on selected papers from First Japanese-Hungarian Symposium for Discrete Mathematics and its Applications
The equivalence of theorem proving and the interconnection problem
ACM SIGDA Newsletter
Disjoint paths in symmetric digraphs
Discrete Applied Mathematics
Half-integral five-terminus flows
Discrete Applied Mathematics
Energy saving in fixed wireless broadband networks
INOC'11 Proceedings of the 5th international conference on Network optimization
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We investigate the integral multicommodity flow problem in symmetric directed graphs. In order to complete this study on symmetry, we also investigate the symmetric multicommodity flow problem, where requests are symmetric (a symmetric request is actually a pair of requests with the same required capacity and reversed endpoints). It is known that by using a specificity of symmetric digraphs, it is possible to find 2-commodity flows in polynomial time when one of the requests is of value 1. We show that this specificity does not extend to greater flow values, and prove that the 2-commodity flow problem is NP-complete. When requests are symmetric, we propose a polynomial-time algorithm that finds symmetric 2-commodity flows by using 5 simple flow computations, and prove that the symmetric 3-commodity flow problem is NP-complete.