Tree exploration with logarithmic memory

Leszek Gąsieniec, Andrzej Pelc, Tomasz Radzik, Xiaohui Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

36 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 [15], where O(log2 n)-bit memory was used for tree exploration, and matches the lower bound on memory size proved there.

Original languageEnglish (US)
Title of host publicationProceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007
PublisherAssociation for Computing Machinery
Number of pages10
ISBN (Electronic)9780898716245
StatePublished - 2007
Externally publishedYes
Event18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007 - New Orleans, United States
Duration: Jan 7 2007Jan 9 2007

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Conference18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007
Country/TerritoryUnited States
CityNew Orleans

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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