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On the randomized online strategies for the k-Canadian traveler problem

Authors
  • Shiri, Davood1
  • Salman, F. Sibel1
  • 1 Koc University, Industrial Engineering Department, Istanbul, Turkey , Istanbul (Turkey)
Type
Published Article
Journal
Journal of Combinatorial Optimization
Publisher
Springer-Verlag
Publication Date
Jan 11, 2019
Volume
38
Issue
1
Pages
254–267
Identifiers
DOI: 10.1007/s10878-019-00378-1
Source
Springer Nature
Keywords
License
Yellow

Abstract

We consider the online k-Canadian Traveler Problem (k-CTP) which is defined on an undirected graph with a given source node O and a destination node D. Non-negative edge costs are given. The traveling agent is initially at O. There are k blocked edges in the graph, but these edges are not known to the agent. A blocked edge is learned when the agent arrives at one of its end-nodes. The goal of the agent is to arrive at D with minimum total cost. We consider the k-CTP on graphs that consist of only node-disjoint O–D paths, where it was shown that there is no randomized online strategy with competitive ratio better than k+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k+1$$\end{document}. An optimal randomized online strategy was also given. However, we prove that the given strategy cannot be implemented in some cases. We also modify the given strategy such that it can be implemented in all cases and meets the lower bound of k+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k+1$$\end{document}.

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