The complexity of finding two disjoint paths with min-max objective function
Discrete Applied Mathematics
Finding Two Disjoint Paths Between Two Pairs of Vertices in a Graph
Journal of the ACM (JACM)
A Polynomial Solution to the Undirected Two Paths Problem
Journal of the ACM (JACM)
Solving covering problems using LPR-based lower bounds
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Graph Algorithms
Single-source unsplittable flow
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Functional vector generation for HDL models using linear programming and Boolean satisfiability
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient Algorithms for k-Disjoint Paths Problems on DAGs
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
On Shortest Disjoint Paths in Planar Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Minimum-cost multiple paths subject to minimum link and node sharing in a network
IEEE/ACM Transactions on Networking (TON)
Proceedings of the Second Symposium on Information and Communication Technology
On shortest disjoint paths in planar graphs
Discrete Optimization
Robust architectures for embedded wireless network control and actuation
ACM Transactions on Embedded Computing Systems (TECS)
On the complexity and approximation of the min-sum and min-max disjoint paths problems
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Hi-index | 0.00 |
Given a number α with 0 α G = (V, E) and two nodes s and t in G, we consider the problem of finding two disjoint paths P1 and P2 from s to t such that length(P1) ≤ length(P2) and length(P1)+α·length(P2) is minimized. The paths may be node-disjoint or edge-disjoint, and the network may be directed or undirected. This problem has applications in reliable communication. We prove an approximation ratio ${1+\alpha} \over {2\alpha}$ for all four versions of this problem, and also show that this ratio cannot be improved for the two directed versions unless P = NP. We also present Integer Linear Programming formulations for all four versions of this problem. For a special case of this problem, we give a polynomial-time algorithm for finding optimal solutions.