Approximating unweighted connectivity problems in parallel
Information and Computation
Approximating minimum size {1,2}-connected networks
Discrete Applied Mathematics
Discrete Applied Mathematics - Special issue: Special issue devoted to the fifth annual international computing and combinatories conference (COCOON'99) Tokyo, Japan 26-28 July 1999
Hereditary systems and greedy-type algorithms
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
A global approach for designing reliable WDM networks and grooming the traffic
Computers and Operations Research
Max-Weight Integral Multicommodity Flow in Spiders and High-Capacity Trees
Approximation and Online Algorithms
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
k-edge-connectivity: approximation and LP relaxation
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
On approximating the d-girth of a graph
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
On approximating the d-girth of a graph
Discrete Applied Mathematics
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An efficient heuristic is presented for the problem of finding a minimum-size k-connected spanning subgraph of a given (undirected or directed) graph G=(V,E). There are four versions of the problem, depending on whether G is undirected or directed, and whether the spanning subgraph is required to be k-node connected (k-NCSS) or k-edge connected (k-ECSS). The approximation guarantees are as follows: min-size k-NCSS of an undirected graph 1+[1/k], min-size k-NCSS of a directed graph 1+[1/k], min-size k-ECSS of an undirected graph 1+[7/k], & min-size k-ECSS of a directed graph 1+[4//spl radic/k]. The heuristic is based on a subroutine for the degree-constrained subgraph (b-matching) problem. It is simple, deterministic, and runs in time O(k|E|/sup 2/). For undirected graphs and k=2, a (deterministic) parallel NC version of the heuristic finds a 2-node connected (or a-edge connected) spanning subgraph whose size is within a factor of (1.5+/spl epsiv/) of minimum, where /spl epsiv/0 is a constant.