Competitive algorithms for layered graph traversal

Amos Fiat*, Dean P. Foster, Howard Karloff, Yuval Rabani, Yiftach Ravid, Sundar Viswanathan

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

27 Scopus citations


A layered graph is a connected, weighted graph whose vertices are partitioned into sets L0 = {s}, L1, L2, ..., and whose edges run between consecutive layers. Its width is max{|Li|}. In the online layered graph traversal problem, a searcher starts at s in a layered graph of unknown width and tries to reach a target vertex t; however, the vertices in layer i and the edges between layers i - 1 and i are only revealed when the searcher reaches layer i-1. The authors give upper and lower bounds on the competitive ratio of layered graph traversal algorithms. They give a deterministic online algorithm that is O(9w)-competitive on width-w graphs and prove that for no w can a deterministic online algorithm have a competitive ratio better than 2w-2 on width-w graphs. They prove that for all w, w/2 is a lower bound on the competitive ratio of any randomized online layered graph traversal algorithm. For traversing layered graphs consisting of w disjoint paths tied together at a common source, they give a randomized online algorithm with a competitive ratio of O(log w) and prove that this is optimal up to a constant factor.

Original languageAmerican English
Title of host publicationAnnual Symposium on Foundations of Computer Science (Proceedings)
PublisherPubl by IEEE
Number of pages10
ISBN (Print)0818624450
StatePublished - Dec 1991
Externally publishedYes
EventProceedings of the 32nd Annual Symposium on Foundations of Computer Science - San Juan, PR, USA
Duration: 1 Oct 19914 Oct 1991

Publication series

NameAnnual Symposium on Foundations of Computer Science (Proceedings)
ISSN (Print)0272-5428


ConferenceProceedings of the 32nd Annual Symposium on Foundations of Computer Science
CitySan Juan, PR, USA


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