A competitive algorithm to find all defective edges in a graph

Authors:
Frank K. Hwang
Affiliations:
Department of Applied Mathematics, National Chiao-Tung University, Hsin-Chu, Taiwan, Republic of China
Venue:
Discrete Applied Mathematics
Year:
2005

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Abstract

Consider a graph G(V, E) where a subset D ∈ E is called the set of defective edges. The problem is to identify D with a small number of edge tests, where an edge test takes an arbitrary subset S and asks whether the subgraph G(S) induced by S intersects D (contains a defective edge).Recently, Johann gave an algorithm to find all d defective edges in a graph assuming d = |D| is known. We give an algorithm with d unknown which requires at most d(⌈log2|E|⌉ + 4) + 1 tests. The information-theoretic bound, knowing d, is about d log2(|E|/d). For d fixed, our algorithm is competitive with coefficient 1.