The complexity of finding two disjoint paths with min-max objective function
Discrete Applied Mathematics
Finding minimum-cost flows by double scaling
Mathematical Programming: Series A and B
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Addressing Network Survivability Issues by Finding the K-best Paths through a Trellis Graph
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
On network design problems: fixed cost flows and the covering steiner problem
ACM Transactions on Algorithms (TALG)
On the complexity of and algorithms for finding the shortest path with a disjoint counterpart
IEEE/ACM Transactions on Networking (TON)
Design and implementation of the HPCS graph analysis benchmark on symmetric multiprocessors
HiPC'05 Proceedings of the 12th international conference on High Performance Computing
On shortest disjoint paths in planar graphs
Discrete Optimization
| Hi-index | 0.00 |
Motivated by a security problem in geographic information systems, we study the following graph theoretical problem: given a graph G, two special nodes s and t in G, and a number k, find k paths from s to t in G so as to minimize the number of edges shared among the paths. This is a generalization of the well-known disjoint paths problem. While disjoint paths can be computed efficiently, we show that finding paths with minimum shared edges is NP-hard. Moreover, we show that it is even hard to approximate the minimum number of shared edges within a factor of $2^{\log^{1-\varepsilon}n}$ , for any constant 驴0. On the positive side, we show that there exists a (k驴1)-approximation algorithm for the problem, using an adaption of a network flow algorithm. We design some heuristics to improve the quality of the output, and provide empirical results.