Abstract
In the classical search problem on the line or in higher dimension one is asked to find the shortest (and often the fastest) route to be adopted by a robot R from the starting point s towards the target point t located at unknown location and distance D. It is usually assumed that robot R moves with a fixed unit speed 1. It is well known that one can adopt a “zig-zag” strategy based on the exponential expansion, which allows to reach the target located on the line in time \(\le 9D,\) and this bound is tight. The problem was also studied in two dimensions where the competitive factor is known to be O(D).
In this paper we study an alteration of the search problem in which robot R starts moving with the initial speed 1. However, during search it can encounter a point or a sequence of points enabling faster and faster movement. The main goal is to adopt the route which allows R to reach the target t as quickly as possible. We study two variants of the considered search problem: (1) with the global knowledge and (2) with the local knowledge. In variant (1) robot R knows a priori the location of all intermediate points as well as their expulsion speeds. In this variant we study the complexity of computing optimal search trajectories. In variant (2) the relevant information about points in P is acquired by R gradually, i.e., while moving along the adopted trajectory. Here the focus is on the competitive factor of the solution, i.e., the ratio between the solutions computed in variants (2) and (1). We also consider two types of search spaces with points distributed on the line and subsequently with points distributed in two-dimensional space.
This work was initiated while the first author visited Kyushu University. The work is partly supported by JST PRESTO Grant Number JPMJPR16E4 and Networks Sciences and Technologies (NeST) EEECS School initiative, University of Liverpool.
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Acknowledgements
The authors would like to thank Jurek Czyzowicz for early discussions on the studied problem and the anonymous reviewers for a number of corrections and suggestions which helped us to improve the presentation.
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Gąsieniec, L., Kijima, S., Min, J. (2018). Searching with Increasing Speeds. In: Izumi, T., Kuznetsov, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2018. Lecture Notes in Computer Science(), vol 11201. Springer, Cham. https://doi.org/10.1007/978-3-030-03232-6_9
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