Generalized Canadian traveller problems

Chung-Shou Liao () and Yamming Huang ()
Additional contact information
Chung-Shou Liao: National Tsing Hua University
Yamming Huang: National Tsing Hua University

Journal of Combinatorial Optimization, 2015, vol. 29, issue 4, No 2, 712 pages

Abstract: Abstract This study investigates a generalization of the Canadian Traveller Problem (CTP), which finds real applications in dynamic navigation systems used to avoid traffic congestion. Given a road network $$G=(V,E)$$ G = ( V , E ) in which there is a source $$s$$ s and a destination $$t$$ t in $$V$$ V , every edge $$e$$ e in $$E$$ E is associated with two possible distances: original $$d(e)$$ d ( e ) and jam $$d^+(e)$$ d + ( e ) . A traveller only finds out which one of the two distances of an edge upon reaching an end vertex incident to the edge. The objective is to derive an adaptive strategy for travelling from $$s$$ s to $$t$$ t so that the competitive ratio, which compares the distance traversed with that of the static $$s,t$$ s , t -shortest path in hindsight, is minimized. This problem was initiated by Papadimitriou and Yannakakis. They proved that it is PSPACE-complete to obtain an algorithm with a bounded competitive ratio. In this paper, we propose tight lower bounds of the problem when the number of ”traffic jams” is a given constant $$k$$ k ; and we introduce a deterministic algorithm with a $$\mathrm{min}\{ r, 2k+1\}$$ min { r , 2 k + 1 } -ratio, which meets the proposed lower bound, where $$r$$ r is the worst-case performance ratio. We also consider the Recoverable CTP, where each blocked edge is associated with a recovery time to reopen. Finally, we discuss the uniform jam cost model, i.e., for every edge $$e$$ e , $$d^+(e) = d(e) + c$$ d + ( e ) = d ( e ) + c , for a constant $$c$$ c .

Keywords: Canadian traveller problem; Competitive ratio; Online algorithm (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-013-9614-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:29:y:2015:i:4:d:10.1007_s10878-013-9614-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-013-9614-z

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().