Approximating minimum-size k-connected spanning subgraphs via matching

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:457660

Cheriyan, J ^[1]; Thurimella, R ^[2]

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1. Univ. of Waterloo, Ontario (Canada)
2. Univ. of Denver, CO (United States)

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/{radical}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{vert_bar}E{vert_bar}{sup 2}). The analyses hinge on theorems of Mader and Cai. For undirected graphs and k = 2, a (deterministic) parallel NC version of the heuristic finds a 2-node connected (or 2-edge connected) spanning subgraph whose size is within a factor of (1.5 + {epsilon}) of minimum, where {epsilon} > 0 is a constant.

• OSTI ID: 457660
• Report Number(s): CONF-961004--; CNN: Grant OGP0138432; Grant CCR-9210604
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
DIAGRAMS
MATHEMATICAL LOGIC