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Competitive Search in the Line and the Star with Predictions

Author Spyros Angelopoulos

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Author Details

Spyros Angelopoulos
  • CNRS and LIP6, Sorbonne University, Paris, France

Funding

This work was partially funded by the grant ANR-19-CE48-0016 from the French National Research Agency (ANR).

Acknowledgements

I am thankful to Shahin Kamali for several helpful discussions.

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Spyros Angelopoulos. Competitive Search in the Line and the Star with Predictions. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.MFCS.2023.12

Abstract

We study the classic problem of searching for a hidden target in the line and the m-ray star, in a setting in which the searcher has some prediction on the hider’s position. We first focus on the main metric for comparing search strategies under predictions; namely, we give positive and negative results on the consistency-robustness tradeoff, where the performance of the strategy is evaluated at extreme situations in which the prediction is either error-free, or adversarially generated, respectively. For the line, we show tight bounds concerning this tradeoff, under the untrusted advice model, in which the prediction is in the form of a k-bit string which encodes the responses to k binary queries. For the star, we give tight, and near-tight tradeoffs in the positional and the directional models, in which the prediction is related to the position of the target within the star, and to the ray on which the target hides, respectively. Last, for all three prediction models, we show how to generalize our study to a setting in which the performance of the strategy is evaluated as a function of the searcher’s desired tolerance to prediction errors, both in terms of positive and inapproximability results.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Theory and algorithms for application domains
Keywords
  • Search problems
  • line and star search
  • competitive ratio
  • predictions
  • consistency and robustness

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