Statistics Papers

Document Type

Journal Article

Date of this Version

1998

Publication Source

SIAM Journal on Computing

Volume

28

Issue

2

Start Page

447

Last Page

462

DOI

10.1137/S0097539795279943

Abstract

A layered graph is a connected graph whose vertices are partitioned into sets L0=s, L1, L2,..., and whose edges, which have nonnegative integral weights, run between consecutive layers. Its width is {|Li|}. In the on-line 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.

We give upper and lower bounds on the competitive ratio of layered graph traversal algorithms. We give a deterministic on-line algorithm which is O(9w)-competitive on width-w graphs and prove that for no w can a deterministic on-line algorithm have a competitive ratio better than 2w-2 on width-w graphs. We prove that for all w, w/2 is a lower bound on the competitive ratio of any randomized on-line layered graph traversal algorithm. For traversing layered graphs consisting of w disjoint paths tied together at a common source, we give a randomized on-line algorithm with a competitive ratio of O(log w) and prove that this is optimal up to a constant factor.

Copyright/Permission Statement

Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Keywords

competitive analysis, layered graphs, search strategies

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Date Posted: 27 November 2017

This document has been peer reviewed.