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We present an approximation algorithm for the problem of finding a minimum-cost k-vertex connected spanning subgraph, assuming that the number of vertices is at least 6k 2. The approximation guarantee is six times the kth harmonic number (which is O(log k)), and this is also an upper bound on the integrality ratio for a standard linear programming(More)
We give a 17 12-approximation algorithm for the following NP-hard problem: Given a simple undirected graph, nd a 2-edge connected spanning subgraph that has the minimum number of edges. The best previous approximation guarantee was 3 2. If the well known 4 3 conjecture for the metric TSP holds, then the optimal value (minimum number of edges) is at most 4 3(More)
An eecient heuristic is presented for the problem of nding a minimum-size k-connected spanning subgraph of an (undirected or directed) simple graph G = (V; E). There are four versions of the problem, and the approximation guarantees are as follows: minimum-size k-node connected spanning subgraph of an undirected graph 1 + 1=k], minimum-size k-node connected(More)
A k-separator (k-shredder) of an undirected graph is a set of k nodes whose removal results in two or more (three or more) connected components. Let the given (undirected) graph be k-node connected, and let n denote the number of nodes. Solving an open question, we show that the problem of counting the number of k-separators is #P-complete. However, we(More)
Given an undirected graph <i>G</i>(<i>V</i>, <i>E</i>) with terminal set <i>T</i> &#8838; <i>V</i>, the problem of packing element-disjoint Steiner trees is to find the maximum number of Steiner trees that are disjoint on the nonterminal nodes and on the edges. The problem is known to be NP-hard to approximate within a factor of &#937;(log <i>n</i>), where(More)
We design and analyse approximation algorithms for the minimum-cost connected T-join problem: given an undirected graph G=(V,E) with nonnegative costs on the edges, and a set of nodes T⊆V, find (if it exists) a spanning connected subgraph H of minimum cost such that every node in T has odd degree and every node not in T has even degree; H may have multiple(More)