Tree exploration with little memory

  • Authors:

  • Krzysztof Diks;Pierre Fraigniaud;Evangelos Kranakis;Andrzej Pelc

  • Affiliations:

  • Instytut Informatyki, Uniwersytet Warszawski, Banacha 2, 02-097 Warszawa, Poland;CNRS-LRI, Université Paris-Sud, 91405 Orsay, France;School of Computer Science, Carleton University, Ottawa, Ontario K1S 5B6, Canada;Département d'Informatique, Université du Québec en Outaouais, Hull, Québec J8X 3X7, Canada

  • Venue:
  • Journal of Algorithms
  • Year:
  • 2004

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Abstract

A robot with k-bit memory has to explore a tree whose nodes are unlabeled and edge ports are locally labeled at each node. The robot has no a priori knowledge of the topology of the tree or of its size, and its aim is to traverse all the edges. While O(log Δ) bits of memory suffice to explore any tree of maximum degree Δ if stopping is not required, we show that bounded memory is not sufficient to explore with stop all trees of bounded degree (indeed Ω (log log log n) bits of memory are needed for some such trees of size n). For the more demanding task requiring to stop at the starting node after completing exploration, we show a sharper lower bound Ω (log n) on required memory size, and present an algorithm to accomplish this task with O(log2 n)-bit memory, for all n-node trees.