Survivable network design with degree or order constraints
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximating minimum bounded degree spanning trees to within one of optimal
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Network design for vertex connectivity
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Tight approximation algorithm for connectivity augmentation problems
Journal of Computer and System Sciences
An almost O(log k)-approximation for k-connected subgraphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Graph Reduction Step Preserving Element-Connectivity and Applications
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Approximating connectivity augmentation problems
ACM Transactions on Algorithms (TALG)
Prize-Collecting steiner network problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Node-weighted network design in planar and minor-closed families of graphs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Approximating minimum-cost connectivity problems via uncrossable bifamilies
ACM Transactions on Algorithms (TALG)
Prize-collecting steiner network problems
ACM Transactions on Algorithms (TALG)
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A typical problem in network design is to find a minimum-cost sub-network H of a given network G such that H satisfies some prespecified connectivity requirements. Our focus is on approximation algorithms for designing networks that satisfy vertex connectivity requirements. Our main tool is a linear programming relaxation of the following setpair formulation due to Frank and Jordan: a setpair consists of two subsets of vertices (of the given network G); each setpair has an integer requirement, and the goal is to find a minimum-cost subset of the edges of G sucht hat each setpair is covered by at least as many edges as its requirement. We introduce the notion of skew bisupermodular functions and use it to prove that the basic solutions of the linear program are characterized by “non-crossing families” of setpairs. This allows us to apply Jain’s iterative rounding method to find approximately optimal integer solutions. We give two applications. (1) In the k-vertex connectivity problem we are given a (directed or undirected) graph G=(V,E) with non-negative edge costs, and the task is to find a minimum-cost spanning subgraph H such that H is k-vertex connected. Let n=|V|, and let εk≤(1−ε)n. We give an $$O{\left( {{\sqrt {n/ \in } }} \right)}$$-approximation algorithm for both problems (directed or undirected), improving on the previous best approximation guarantees for k in the range $$\Omega {\left( {{\sqrt n }} \right)} element connectivity problem, matching the previous best approximation guarantee due to Fleischer, Jain and Williamson.