Access the full text.
Sign up today, get DeepDyve free for 14 days.
J. Czyzowicz, E. Kranakis, D. Krizanc, L. Narayanan, J. Opatrny (2016)
Search on a line with faulty robotsDistributed Computing
Marios Polycarpou, Yanli Yang, Kevin Passino (2001)
A cooperative search framework for distributed agentsProceeding of the 2001 IEEE International Symposium on Intelligent Control (ISIC '01) (Cat. No.01CH37206)
P. Bose, J. Carufel, Stephane Durocher (2013)
Revisiting the Problem of Searching on a Line
R. Bellman (1963)
An Optimal SearchSiam Review, 5
N Alon, C Avin, M Kouck, G Kozma, Z Lotker, MR Tuttle (2011)
Many random walks are faster than oneComb. Probab. Comput., 20
(1998)
and Y
A. Beck, D. Newman (1970)
Yet more on the linear search problemIsrael Journal of Mathematics, 8
A. Fiat, Y. Rabani, Yiftach Ravid (1990)
Competitive k-server algorithmsProceedings [1990] 31st Annual Symposium on Foundations of Computer Science
D. Bernstein, L. Finkelstein, S. Zilberstein (2003)
Contract Algorithms and Robots on Rays: Unifying Two Scheduling Problems
S. Schuierer (2003)
A Lower Bound for Randomized Searching on m Rays
E. Demaine, S. Fekete, S. Gal (2004)
Online searching with turn costTheor. Comput. Sci., 361
(2013)
Algorithms—ESA
R. Bellman (1956)
Review: E. A. Coddington and N. Levinson, Theory of differential equationsBulletin of the American Mathematical Society, 62
N. Alon, C. Avin, M. Koucký, G. Kozma, Zvi Lotker, M. Tuttle (2007)
Many random walks are faster than oneCombinatorics, Probability and Computing, 20
X. Zou (2020)
MinimizationAtmospheric Satellite Observations
Y. Azar, A. Broder, M. Manasse (1993)
On-line choice of on-line algorithms
W. Franck (1965)
On the optimal search problem
M. Kao, J. Reif, S. Tate (1996)
Searching in an unknown environment: an optimal randomized algorithm for the cow-path problemInf. Comput., 131
A. Beck (1964)
On the linear search problemIsrael Journal of Mathematics, 2
J. Czyzowicz, Konstantinos Georgiou, E. Kranakis, D. Krizanc, L. Narayanan, J. Opatrny, S. Shende (2016)
Search on a Line by Byzantine Robots
(1988)
( eds ) SWAT 88 . SWAT
J. Isbell (1957)
An optimal search patternNaval Research Logistics Quarterly, 4
O. Feinerman, Amos Korman, Zvi Lotker, Jean-Sébastien Sereni (2012)
Collaborative search on the plane without communicationArXiv, abs/1205.2170
Ricardo Baeza-Yates, J. Culberson, Gregory Rawlins (1988)
Searching with Uncertainty (Extended Abstract)
M. Goldberg (1981)
A Minimization ProblemSiam Review, 23
S. Alpern, S. Gal (2002)
The theory of search games and rendezvous, 55
Ricardo Baeza-Yates, J. Culberson, Gregory Rawlins (1993)
Searching in the PlaneInf. Comput., 106
A. Beck (1965)
More on the linear search problemIsrael Journal of Mathematics, 3
M. Kao, Yuan Ma, M. Sipser, Y. Yin (1994)
Optimal constructions of hybrid algorithmsArXiv, cs.DM/0101028
Suppose we are sending out k robots from 0 to search the real line at constant speed (with turns) to find a target at an unknown location; f of the robots are faulty, meaning that they fail to report the target although visiting its location (called crash type). The goal is to find the target in time at most λ|x|\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\lambda |x|$$\end{document}, if the target is located at x, |x|≥1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$|x| \ge 1$$\end{document}, for λ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\lambda $$\end{document} as small as possible. We show that this cannot be achieved for λ<2ρρ(ρ-1)ρ-1+1,ρ:=2(f+1)k,\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\begin{aligned}&\lambda < 2\frac{\rho ^\rho }{(\rho -1)^{\rho -1}}+1,~~ \rho := \frac{2(f+1)}{k}~, \end{aligned}$$\end{document}which is tight due to earlier work (see Czyzowitz et al. in Proc PODC’16, pp 405–414, 2016, where this problem was introduced). This also gives some better than previously known lower bounds for so-called Byzantine-type faulty robots that may actually wrongly report a target. In the second part of the paper we deal with the m-rays generalization of the problem, where the hidden target is to be detected on m rays all emanating at the same point. Using a generalization of our methods, along with a useful relaxation of the original problem, we establish a tight lower for this setting as well (as above, with ρ:=m(f+1)k\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\rho := \nicefrac {m(f+1)}{k}$$\end{document}). When specialized to the case f=0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$f=0$$\end{document}, this resolves the question on parallel search on m rays, posed by three groups of scientists some 15–30 years ago: by Baeza-Yates, Culberson, and Rawlins; by Kao, Ma, Sipser, and Yin; and by Bernstein, Finkelstein, and Zilberstein. The m-rays generalization is known to have connections to other, seemingly unrelated, problems, including hybrid algorithms for on-line problems, and so-called contract algorithms.
Distributed Computing – Springer Journals
Published: Aug 1, 2019
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.