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Optimal algorithms for finding connected components of an unknown graph

  • Weiping Shi
  • Douglas B. West
Session 3A: Graph Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)

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 SV, 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.

Keywords

Deterministic Algorithm Input Distribution Input Instance Active Interval Connection Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Weiping Shi
    • 1
  • Douglas B. West
    • 2
  1. 1.Department of Computer ScienceUniversity of North TexasDentonUSA
  2. 2.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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