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International Conference on Current Trends in Theory and Practice of Informatics

SOFSEM 2019: SOFSEM 2019: Theory and Practice of Computer Science pp 392–405Cite as

Minimizing the Cost of Team Exploration

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11376))

Abstract

A group of mobile agents is given a task to explore an edge-weighted graph G, i.e., every vertex of G has to be visited by at least one agent. There is no centralized unit to coordinate their actions, but they can freely communicate with each other. The goal is to construct a deterministic strategy which allows agents to complete their task optimally. In this paper we are interested in a cost-optimal strategy, where the cost is understood as the total distance traversed by agents coupled with the cost of invoking them. Two graph classes are analyzed, rings and trees, in the off-line and on-line setting, i.e., when a structure of a graph is known and not known to agents in advance. We present algorithms that compute the optimal solutions for a given ring and tree of order n, in O(n) time units. For rings in the on-line setting, we give the 2-competitive algorithm and prove the lower bound of 3/2 for the competitive ratio for any on-line strategy. For every strategy for trees in the on-line setting, we prove the competitive ratio to be no less than 2, which can be achieved by the DFS algorithm.

Research partially supported by National Science Centre (Poland) grant number 2015/17/B/ST6/01887.

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Notes

  1. 1.

    After finishing the exploration, agents do not have to come back to the homebase.

  2. 2.

    One may notice, that in order to reduce the number of time units of the algorithm, agents moves, when possible, should be perform simultaneously.

  3. 3.

    There exist cost-optimal strategies that can use more than \(\varLambda _v.k\) agents. Indeed, if \(d(v,\varLambda _v.u_l) = d(r,v) + q\) reusing the agent and calling a new one generates equal cost.

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Authors and Affiliations

  1. Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, Gdańsk, Poland

    Dorota Osula

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  1. Dorota Osula
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Correspondence to Dorota Osula .

Editor information

Editors and Affiliations

  1. University of Genoa, Genoa, Italy

    Barbara Catania

  2. Comenius University, Bratislava, Slovakia

    Rastislav Královič

  3. Poznań University of Technology, Poznań, Poland

    Jerzy Nawrocki

  4. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

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Osula, D. (2019). Minimizing the Cost of Team Exploration. In: Catania, B., Královič, R., Nawrocki, J., Pighizzini, G. (eds) SOFSEM 2019: Theory and Practice of Computer Science. SOFSEM 2019. Lecture Notes in Computer Science(), vol 11376. Springer, Cham. https://doi.org/10.1007/978-3-030-10801-4_31

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  • DOI: https://doi.org/10.1007/978-3-030-10801-4_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10800-7

  • Online ISBN: 978-3-030-10801-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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