Abstract
We want to find the connected components of an unknown graph G with a known vertex set V. We learn about G by sending an oracle a query set S⊂V, and the oracle tells us the vertices connected to S. We want to use the minimum number of queries, adaptively, to find the components. The problem is also known as interconnect diagnosis of wiring networks in VLSI. The graph has n vertices and k components, but k is not part of the input. We present a deterministic algorithm using O(min{k,log n}) queries and a randomized algorithm using expected O(min{k, log k+log log n}) queries. We also prove matching lower bounds.
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© 1995 Springer-Verlag Berlin Heidelberg
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Shi, W., West, D.B. (1995). Optimal algorithms for finding connected components of an unknown graph. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030827
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DOI: https://doi.org/10.1007/BFb0030827
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