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An almost always polynomial time algorithm for the (α, β)-cover problem in bipartite graphs

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2 Author(s)
C. P. Low ; Dept. of Inf. Syst. & Comput. Sci., Nat. Univ. of Singapore, Singapore ; H. W. Leong

The (α, β)-cover problem is the problem of finding a vertex cover SXSY with SXX and SY⊆Y, in a bipartite graph G=(X , Y, E) that satisfies the constraints |Sx|⩽α|X| and |SY |⩽β|Y| where α, β∈(0, 1). This problem has applications in the repair of large memory chips and has been shown to be NP-complete. The authors a new algorithm for finding (α, β)-covers, improvements to the probabilistic analysis given by W.P. Shi and W.K. Fuchs (1989), and a new probabilistic algorithm which runs almost always in O(|E|√n) on any edge probability. The authors note that the probabilistic algorithm works for any edge probability p(n) while the algorithm of Shi and Fuchs works only when p(n)⩽0.5/n. In particular, the result shows that the (α, β)-cover problem is almost always solvable in polynomial time

Published in:

Circuits and Systems, 1991., IEEE International Sympoisum on

Date of Conference:

11-14 Jun 1991