Tree exploration with logarithmic memory

Christoph Ambühl, Leszek Ga̧sieniec, Andrzej Pelc, Tomasz Radzik, Xiaohui Zhang

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


We consider the task of network exploration by a mobile agent (robot) with small memory. The agent has to traverse all nodes and edges of a network (represented as an undirected connected graph), and return to the starting node. Nodes of the network are unlabeled and edge ports are locally labeled at each node. The agent has no a priori knowledge of the topology of the network or of its size, and cannot mark nodes in any way. Under such weak assumptions, cycles in the network may prevent feasibility of exploration, hence we restrict attention to trees. We present an algorithm to accomplish tree exploration (with return) using O(log n)-bit memory for all n-node trees. This strengthens the result from Diks et al. [2004], where O(log2 n)-bit memory was used for tree exploration, and matches the lower bound on memory size proved there. We also extend our O(log n)-bit memory traversal mechanism to a weaker model in which ports at each node are ordered in circular manner, however, the explicit values of port numbers are not available.

Original languageEnglish (US)
Article number17
JournalACM Transactions on Algorithms
Issue number2
StatePublished - Mar 2011
Externally publishedYes


  • Distributed algorithms
  • Graph exploration
  • Small memory

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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