Online Graph Exploration: New Results on Old and New Algorithms

  • Nicole Megow
  • Kurt Mehlhorn
  • Pascal Schweitzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)


We study the problem of exploring an unknown undirected connected graph. Beginning in some start vertex, a searcher must visit each node of the graph by traversing edges. Upon visiting a vertex for the first time, the searcher learns all incident edges and their respective traversal costs. The goal is to find a tour of minimum total cost. Kalyanasundaram and Pruhs [23] proposed a sophisticated generalization of a Depth First Search that is 16-competitive on planar graphs. While the algorithm is feasible on arbitrary graphs, the question whether it has constant competitive ratio in general has remained open. Our main result is an involved lower bound construction that answers this question negatively. On the positive side, we prove that the algorithm has constant competitive ratio on any class of graphs with bounded genus. Furthermore, we provide a constant competitive algorithm for general graphs with a bounded number of distinct weights.


Planar Graph Minimum Span Tree Travel Salesman Problem Competitive Ratio Online Algorithm 
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 2011

Authors and Affiliations

  • Nicole Megow
    • 1
  • Kurt Mehlhorn
    • 1
  • Pascal Schweitzer
    • 2
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.The Australian National UniversityCanberraAustralia

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