# Local Maps: New Insights into Mobile Agent Algorithms

* Corresponding author
2 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe
Abstract : In this paper, we study the complexity of computing with mobile agents having small local knowledge. In particular, we show that the number of mobile agents and the amount of local information given initially to agents can significantly influence the time complexity of resolving a distributed problem. Our results are based on a generic scheme allowing to transform a message passing algorithm, running on an $n$-node graph $G$, into a mobile agent one. By generic, we mean that the scheme is independent of both the message passing algorithm and the graph $G$. Our scheme, coupled with a well-chosen clustered representation of the graph, induces $\widetilde{O}(1) ratio between the time complexity of the obtained mobile agent algorithm and the time complexity of the original message passing counterpart, while using$\widetilde{O}(n)$mobile agents. If only$k$agents are allowed ($k$is an integer parameter), then we show that the time ratio is$O(n/\sqrt{k})$. As a consequence, we show that any global labeling function of$G$can be computed by exactly$n$mobile agents knowing their$n^{\epsilon}$-neighborhood in$\widetilde{O}(D)$time,$D$is the diameter of the graph and$\epsilon$is an arbitrary small constant. We apply our generic results for the fundamental problem of computing a leader (resp. a BFS tree) under the additional restriction of$\widetilde{O}(1)$(resp.$\widetilde{O}(n)$) memory bits per agent, and obtain$\widetilde{O}(D)\$ time algorithms.
Document type :
Reports

Cited literature [49 references]

https://hal.inria.fr/inria-00271624
Contributor : Bilel Derbel <>
Submitted on : Monday, April 21, 2008 - 12:01:39 PM
Last modification on : Tuesday, May 12, 2020 - 5:26:07 PM
Document(s) archivé(s) le : Friday, November 25, 2016 - 9:56:39 PM

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RR-6511.pdf
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• HAL Id : inria-00271624, version 3

### Citation

Bilel Derbel. Local Maps: New Insights into Mobile Agent Algorithms. [Research Report] RR-6511, INRIA. 2008, pp.23. ⟨inria-00271624v3⟩

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