Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Directed network design with orientation constraints
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A note on orientations of mixed graphs
Discrete Applied Mathematics
On the orientation of graphs and hypergraphs
Discrete Applied Mathematics - Submodularity
Combined connectivity augmentation and orientation problems
Discrete Applied Mathematics - Submodularity
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Improved orientations of physical networks
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Optimally orienting physical networks
RECOMB'11 Proceedings of the 15th Annual international conference on Research in computational molecular biology
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We consider connectivity problems with orientation constraints. Given a directed graph D and a collection of ordered node pairs P let P[D]={(u,v)∈P: D contains a uv−path}. In the Steiner Forest Orientation problem we are given an undirected graph G=(V,E) with edge-costs and a set P⊆V ×V of ordered node pairs. The goal is to find a minimum-cost subgraph H of G and an orientation D of H such that P[D]=P. We give a 4-approximation algorithm for this problem. In the Maximum Pairs Orientation problem we are given a graph G and a multi-collection of ordered node pairs P on V. The goal is to find an orientation D of G such that |P[D]| is maximum. Generalizing the result of Arkin and Hassin [DAM'02] for |P|=2, we will show that for a mixed graph G (that may have both directed and undirected edges), one can decide in nO(|P|) time whether G has an orientation D with P[D]=P (for undirected graphs this problem admits a polynomial time algorithm for any P, but it is NP-complete on mixed graphs). For undirected graphs, we will show that one can decide whether G admits an orientation D with |P[D]|≥k in O(n+m)+2O(k·loglogk) time; hence this decision problem is fixed-parameter tractable, which answers an open question from Dorn et al. [AMB'11]. We also show that Maximum Pairs Orientation admits ratio O(log|P|/loglog|P|), which is better than the ratio O(logn/loglogn) of Gamzu et al. [WABI'10] when |P|n. Finally, we show that the following node-connectivity problem can be solved in polynomial time: given a graph G=(V,E) with edge-costs, s,t∈V, and an integer ℓ, find a min-cost subgraph H of G with an orientation D such that D contains ℓ internally-disjoint st-paths, and ℓ internally-disjoint ts-paths.