Finding Optimum k-vertex Connected Spanning Subgraphs: Improved Approximation Algorithms for k=3, 4, 5
نویسندگان
چکیده
The problem of finding a minimum weight k-vertex connected spanning subgraph is considered. For k ≥ 2, this problem is known to be NP-hard. Combining properties of inclusion-minimal k-vertex connected graphs and of k-out-connected graphs (i.e., graphs which contain a vertex from which there exist k internally vertex-disjoint paths to every other vertex), we derive polynomial time approximation algorithms for the cases k = 3, 4, 5. Up to 1990, E. A. Dinic, Moscow. This work was done as a part of the author’s D.Sc. thesis at the Dept. of Mathematics, Technion, Haifa, Israel.
منابع مشابه
Improved Approximation Algorithms for Finding Optimum k-Vertex Connected Spanning Subgraphs
We consider the following problem: given an integer k and a graph with a nonnegative cost function on its edges, nd its minimum weight k-vertex connected spanning subgraph. For k > 1, this problem is known to be NP-hard. For an arbitrary k, the best known approximation algorithm is due to Ravi and Williamson which achieves the approximation ratio 2H(k), where H (k) = 1 + 1 2 + : : : + 1 k is th...
متن کاملApproximation Algorithms for k-Connected Graph Factors
Finding low-cost spanning subgraphs with given degree and connectivity requirements is a fundamental problem in the area of network design. We consider the problem of finding d-regular spanning subgraphs (or d-factors) of minimum weight with connectivity requirements. For the case of k-edge-connectedness, we present approximation algorithms that achieve constant approximation ratios for all d ≥...
متن کاملA 2-Approximation Algorithm for Finding an Optimum 3-Vertex-Connected Spanning Subgraph
The problem of finding a minimum weight k-vertex connected spanning subgraph in a graph G = (V,E) is considered. For k ≥ 2, this problem is known to be NP-hard. Combining properties of inclusionminimal k-vertex connected graphs and of k-out-connected graphs (i.e., graphs which contain a vertex from which there exist k internally vertex-disjoint paths to every other vertex), we derive an auxilia...
متن کاملFinding k-Connected Subgraphs with Minimum Average Weight
We consider the problems of finding k-connected spanning subgraphs with minimum average weight. We show that the problems are NP-hard for k > 1. Approximation algorithms are given for four versions of the minimum average edge weight problem: 1. 3-approximation for k-edge-connectivity, 2. O(logk) approximation for k-node-connectivity 3. 2+ approximation for k-node-connectivity in Euclidian graph...
متن کاملA 17/12-approximation algorithm for 2-vertex-connected spanning subgraphs on graphs with minimum degree at least 3
We obtain a polynomial-time 17 12 -approximation algorithm for the minimum-cost 2-vertexconnected spanning subgraph problem, restricted to graphs of minimum degree at least 3. Our algorithm uses the framework of ear-decompositions for approximating connectivity problems, which was previously used in algorithms for finding the smallest 2-edge-connected spanning subgraph by Cheriyan, Sebo and Szi...
متن کامل