Graph Decomposition for Memoryless Periodic Exploration

Adrian Kosowski; Alfredo Navarra

doi:10.1007/s00453-011-9518-1

Graph Decomposition for Memoryless Periodic Exploration

Abstract

We consider a general framework in which a memoryless robot periodically explores all the nodes of a connected anonymous graph by following local information available at each vertex. For each vertex v, the endpoints of all edges adjacent to v are assigned unique labels within the range 1 to deg (v) (the degree of v). The generic exploration strategy is implemented using a right-hand-rule transition function: after entering vertex v via the edge labeled i, the robot proceeds with its exploration, leaving via the edge having label [i mod deg (v)]+1 at v.A lot of attention has been given to the problem of labeling the graph so as to achieve a periodic exploration having the minimum possible length π. It has recently been proved (Czyzowicz et al., Proc. SIROCCO'09, 2009) that π ≤ 13/3 n holds for all graphs of n vertices. Herein, we provide a new labeling scheme which leads to shorter exploration cycles, improving the general bound to π≤4n−2. This main result is shown to be tight with respect to the class of labellings admitting certain connectivity properties. The labeling scheme is based on a new graph decomposition which may be of independent interest.

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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: ALGORITHMICA no. 63, pages 26 - 38,
ISSN: 0178-4617
Language:: English
Publication year:: 2012
Bibliographic description:: Kosowski A., Navarra A.: Graph Decomposition for Memoryless Periodic Exploration // ALGORITHMICA. -Vol. 63, nr. Iss. 1-2 (2012), s.26-38
DOI:: Digital Object Identifier (open in new tab) 10.1007/s00453-011-9518-1
Verified by:: Gdańsk University of Technology