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Abstract
We study the following scenario of online graph exploration. A team of k agents is initially located at a distinguished vertex r of an undirected graph. At every time step, each agent can traverse an edge of the graph. All vertices have unique identifiers, and upon entering a vertex, an agent obtains the list of identifiers of all its neighbors. We ask how many time steps are required to complete exploration, i.e., to make sure that every vertex has been visited by some agent. We consider two communication models: one in which all agents have global knowledge of the state of the exploration, and one in which agents may only exchange information when simultaneously located at the same vertex. As our main result, we provide the first strategy which performs exploration of a graph with n vertices at a distance of at most D from r in time O(D), using a team of agents of polynomial size k = D n^{1 + ε} < n^{2 + ε} , for any ε > 0. Our strategy works in the local communication model, without knowledge of global parameters such as n or D. We also obtain almost-tight bounds on the asymptotic relation between exploration time and team size, for large k. For any constant c > 1, we show that in the global communication model, a team of k = D n^c agents can always complete exploration in D(1+1/(c−1)+o(1)) time steps, whereas at least D(1+1/c−o(1)) steps are sometimes required. In the local communication model, D(1+2/(c−1)+o(1)) steps always suffice to complete exploration, and at least D(1+2/c−o(1)) steps are sometimes required. This shows a clear separation between the global and local communication models.
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Authors (5)
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Yann Disser
- .. ..
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Adrian Kosowski
- Inria Bordeaux Sud-Quest ..
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Dominik Pająk
- . .
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Przemysław Uznański
- Inria Bordeaux Sud-Quest ...
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Keywords
Details
- Category:
- Conference activity
- Type:
- materiały konferencyjne indeksowane w Web of Science
- Published in:
-
LECTURE NOTES IN COMPUTER SCIENCE
no. 7966,
pages 520 - 532,
ISSN: 0302-9743 - Title of issue:
- 40th International Colloquium on Automata, Languages and Programming (ICALP) strony 520 - 532
- Language:
- English
- Publication year:
- 2013
- Bibliographic description:
- Dereniowski D., Disser Y., Kosowski A., Pająk ., Uznański P..: Fast Collaborative Graph Exploration, W: 40th International Colloquium on Automata, Languages and Programming (ICALP), 2013, ,.
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/978-3-642-39212-2_46
- Verified by:
- Gdańsk University of Technology
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