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Weighted Group Search on a Line

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Algorithms for Sensor Systems (ALGOSENSORS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 12503))

Abstract

We introduce and study a new search-type problem on the line with 2 searchers. As in so-called evacuation search problems with multiple searchers, we require that all searchers reach a hidden item (the exit), placed in an unknown location on a line. The novelty of our problem, weighted group search on a line, pertains to the cost function of a search trajectory, which is defined as the weighted average (1 for the light searcher and \(w\ge 1\) for the heavy searcher) of the times that each searcher reaches the exit and stays there indefinitely. For that problem, and for every \(w\ge 1\), we design searchers’ trajectories (algorithms) that aim to perform well under the lens of (worst case) competitive analysis.

K. Georgiou—Research supported in part by NSERC Discovery grant.

J. Lucier—Research was part of an undergraduate thesis at Ryerson University, Dept. of Mathematics.

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Notes

  1. 1.

    This is referring to the relative multiplicative error, that is (heuristic-optimal)/optimal.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ryerson University, Toronto, Canada

    Konstantinos Georgiou & Jesse Lucier

Authors
  1. Konstantinos Georgiou
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  2. Jesse Lucier
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Correspondence to Konstantinos Georgiou .

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Editors and Affiliations

  1. Mathematics and Computer Science, University of Perugia, Perugia, Italy

    Cristina M. Pinotti

  2. Mathematics and Computer Science, University of Perugia, Perugia, Italy

    Alfredo Navarra

  3. Computer Science and Engineering, Indian Institute of Technology Delhi, New Delhi, India

    Amitabha Bagchi

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Georgiou, K., Lucier, J. (2020). Weighted Group Search on a Line. In: Pinotti, C.M., Navarra, A., Bagchi, A. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2020. Lecture Notes in Computer Science(), vol 12503. Springer, Cham. https://doi.org/10.1007/978-3-030-62401-9_9

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  • DOI: https://doi.org/10.1007/978-3-030-62401-9_9

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