Best-Of-Two-Worlds Analysis of Online Search

Authors Spyros Angelopoulos , Christoph Dürr , Shendan Jin

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Spyros Angelopoulos
  • Sorbonne Université, CNRS, Laboratoire d'informatique de Paris 6, LIP6, F-75252 Paris, France
Christoph Dürr
  • Sorbonne Université, CNRS, Laboratoire d'informatique de Paris 6, LIP6, F-75252 Paris, France
Shendan Jin
  • Sorbonne Université, CNRS, Laboratoire d'informatique de Paris 6, LIP6, F-75252 Paris, France


We are thankful to Elmar Langetepe for discussions on the literature of online search, as well as to Pascal Schweitzer for comments on an early draft of this paper.

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Spyros Angelopoulos, Christoph Dürr, and Shendan Jin. Best-Of-Two-Worlds Analysis of Online Search. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


In search problems, a mobile searcher seeks to locate a target that hides in some unknown position of the environment. Such problems are typically considered to be of an on-line nature, in that the input is unknown to the searcher, and the performance of a search strategy is usually analyzed by means of the standard framework of the competitive ratio, which compares the cost incurred by the searcher to an optimal strategy that knows the location of the target. However, one can argue that even for simple search problems, competitive analysis fails to distinguish between strategies which, intuitively, should have different performance in practice. Motivated by the above, in this work we introduce and study measures supplementary to competitive analysis in the context of search problems. In particular, we focus on the well-known problem of linear search, informally known as the cow-path problem, for which there is an infinite number of strategies that achieve an optimal competitive ratio equal to 9. We propose a measure that reflects the rate at which the line is being explored by the searcher, and which can be seen as an extension of the bijective ratio over an uncountable set of requests. Using this measure we show that a natural strategy that explores the line aggressively is optimal among all 9-competitive strategies. This provides, in particular, a strict separation from the competitively optimal doubling strategy, which is much more conservative in terms of exploration. We also provide evidence that this aggressiveness is requisite for optimality, by showing that any optimal strategy must mimic the aggressive strategy in its first few explorations.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Online computation
  • search problems
  • linear search
  • performance measures


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