Years and Authors of Summarized Original Work
1993; Kao, Reif, Tate
Problem Definition
This problem deals with finding a point at an unknown position on one of a set of w rays which extend from a common point (the origin). In this problem there is a searcher, who starts at the origin, and follows a sequence of commands such as “explore to distance d on ray i.” The searcher detects immediately when the target point is crossed, but there is no other information provided from the search environment. The goal of the searcher is to minimize the distance traveled.
There are several different ways this problem has been formulated in the literature, including one called the “cow-path problem” that involves a cow searching for a pasture down a set of paths. When w = 2, this problem is to search for a point on the line, which has also been described as a robot searching for a door in an infinite wall or a shipwreck survivor searching for a stream after washing ashore on a beach.
Notation
The...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Recommended Reading
Baeza-Yates RA, Culberson JC, Rawlins GJE (1993) Searching in the plane. Inf Comput 16:234–252
Berman P, Blum A, Fiat A, Karloff H, Rosén A, Saks M (1996) Randomized robot navigation algorithms. In: Proceedings of the seventh annual ACM-SIAM symposium on discrete algorithms (SODA), pp 75–84
Blum A, Raghavan P, Schieber B (1991) Navigating in unfamiliar geometric terrain. In: Proceedings 23rd ACM symposium on theory of computing (STOC), pp 494–504
Fiat A, Rabani Y, Ravid Y (1990) Competitive k-server algorithms. In: Proceedings 31st IEEE symposium on foundations of computer science (FOCS), pp 454–463
Hipke C, Icking C, Klein R, Langetepe E (1999) How to find a point on a line within a fixed distance. Discret Appl Math 93:67–73
Kamphans T, Langetepe E (2005) Optimal competitive online ray search with an error-prone robot. In: 4th international workshop on experimental and efficient algorithms, pp 593–596
Kao M-Y, Littman ML (1997) Algorithms for informed cows. In: AAAI-97 workshop on on-line search, pp 55–61
Kao M-Y, Ma Y, Sipser M, Yin Y (1994) Optimal constructions of hybrid algorithms. In: Proceedings 5th ACM-SIAM symposium on discrete algorithms (SODA), pp 372–381
Kao M-Y, Reif JH, Tate SR (1996) Searching in an unknown environment: An optimal randomized algorithm for the cow-path problem. Inf Comput 133:63–80
López-Ortiz A, Schuierer S (2001) The ultimate strategy to search on m rays? Theor Comput Sci 261:267–295
Pearl J (1984) Heuristics: intelligent search strategies for computer problem solving. Addison-Wesley, Reading
Schuierer S (2003) A lower bound for randomized searching on m rays. In: Computer science in perspective, pp 264–277
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media New York
About this entry
Cite this entry
Tate, S. (2016). Randomized Searching on Rays or the Line. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_328
Download citation
DOI: https://doi.org/10.1007/978-1-4939-2864-4_328
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2863-7
Online ISBN: 978-1-4939-2864-4
eBook Packages: Computer ScienceReference Module Computer Science and Engineering