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Fast collaborative graph exploration

Abstrakt

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=Dn^(1+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=Dn^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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Kategoria:
Publikacja w czasopiśmie
Typ:
artykuł w czasopiśmie wyróżnionym w JCR
Opublikowano w:
INFORMATION AND COMPUTATION nr 243, strony 37 - 49,
ISSN: 0890-5401
Język:
angielski
Rok wydania:
2015
Opis bibliograficzny:
Dereniowski D., Disser Y., Kosowski A., Pająk D., Uznański P.: Fast collaborative graph exploration // INFORMATION AND COMPUTATION. -Vol. 243, (2015), s.37-49
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1016/j.ic.2014.12.005
Weryfikacja:
Politechnika Gdańska

wyświetlono 149 razy

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