### 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 ≤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.

Original language | English (US) |
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Title of host publication | Stabilization, Safety, and Security of Distributed Systems - 20th International Symposium, SSS 2018, Proceedings |

Editors | Taisuke Izumi, Petr Kuznetsov |

Publisher | Springer Verlag |

Pages | 126-138 |

Number of pages | 13 |

ISBN (Print) | 9783030032319 |

DOIs | |

State | Published - Jan 1 2018 |

Externally published | Yes |

Event | 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2018 - Tokyo, Japan Duration: Nov 4 2018 → Nov 7 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11201 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2018 |
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Country | Japan |

City | Tokyo |

Period | 11/4/18 → 11/7/18 |

### Keywords

- 2d space
- Increasing speeds
- Line
- Search problem

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Stabilization, Safety, and Security of Distributed Systems - 20th International Symposium, SSS 2018, Proceedings*(pp. 126-138). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11201 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-03232-6_9