Chapter

Principles of Distributed Systems

Volume 7702 of the series Lecture Notes in Computer Science pp 151-165

Directed Graph Exploration

  • Klaus-Tycho FörsterAffiliated withComputer Engineering and Networks Laboratory, ETH Zurich
  • , Roger WattenhoferAffiliated withComputer Engineering and Networks Laboratory, ETH Zurich

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Abstract

We study the problem of exploring all nodes of an unknown directed graph. A searcher has to construct a tour that visits all nodes, but only has information about the parts of the graph it already visited. The goal is to minimize the cost of such a tour. In this paper, we present upper and lower bounds for both the deterministic and the randomized online version of exploring all nodes of directed graphs. Our bounds are sharp or sharp up to a small constant, depending on the specific model. Essentially, exploring a directed graph has a multiplicative overhead linear in the number of nodes. If one wants to search for just a node in unweighted directed graphs, a greedy algorithm with quadratic multiplicative overhead can only be improved by a factor of at most two. We were also able to show that randomly choosing a starting point does not improve lower bounds beyond a small constant factor.

Keywords

online algorithms graph exploration mobile agents and autonomous robots