SIAM Journal on Discrete Mathematics
Ring routing and wavelength translation
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A cycle augmentation algorithm for minimum cost multicommodity flows on a ring
Discrete Applied Mathematics
| Hi-index | 0.00 |
In this paper, we introduce the upgrading problem of edge-disjoint paths. In the off-line upgrading problem, a supply graph G with integer capacities and two demand graphs H"1 and H"2 with unit demands are given on the same vertex set. Our task is to determine the maximum size of a set F@?E(H"1)@?E(H"2) such that F has an integer routing in G which can be extended both to an integer routing of H"1 and to an integer routing of H"2. In the online upgrading problem, we are given a supply graph G with integer capacities, a demand graph H with an integer routing, and another demand graph H"2 with unit demands such that E(H)@?E(H"2). Our task is to determine the maximum size of a set F@?E(H) such that the restriction of the given routing to F can be extended to an integer routing of H"2. Thus, depending on whether the graphs are directed or undirected, we have four different versions. We give algorithmic proofs of minimax formulas for the case when G is a ring and the demand graphs are stars with the same center. All four versions are NP-complete for general graphs.