Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
The complexity of finding two disjoint paths with min-max objective function
Discrete Applied Mathematics
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
An Approximation Algorithm for the Disjoint Paths Problem in Even-Degree Planar Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Finding min-sum disjoint shortest paths from a single source to all pairs of destinations
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Finding two disjoint paths in a network with normalized α+-MIN-SUM objective function
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Multilayer survivable optical network design
INOC'11 Proceedings of the 5th international conference on Network optimization
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Given a graph G = (V, E)andk source-sink pairs {(s1, t1),..., (sk, tk)} with each s, ti ∈ V, the Min-Sum Disjoint Paths problem asks k disjoint paths to connect all the source-sink pairs with minimized total length, while the Min-Max Disjoint Paths problem asks also k disjoint paths to connect all source-sink pairs but with minimized length of the longest path. In this paper we show that the weighted Min-Sum Disjoint Paths problem is FPNP-complete in general graph, and the uniform Min-Sum Disjoint Paths and uniform Min-Max Disjoint Paths problems can not be approximated within Ω(m1-ε) for any constant ε 0 even in planar graph if P ≠ NP, where m is the number of edges in G. Then we give at the first time a simple bicriteria approximation algorithm for the uniform Min-Max Edge-Disjoint Paths and the weighted Min-Sum Edge-Disjoint Paths problems, with guaranteed performance ratio O(log k/ log log k) and O(1) respectively. Our algorithm is based on randomized rounding.