TY - GEN

T1 - Competitive algorithms for layered graph traversal

AU - Fiat, Amos

AU - Foster, Dean P.

AU - Karloff, Howard

AU - Rabani, Yuval

AU - Ravid, Yiftach

AU - Viswanathan, Sundar

PY - 1991/12

Y1 - 1991/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0026406464&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0026406464

SN - 0818624450

T3 - Annual Symposium on Foundations of Computer Science (Proceedings)

SP - 288

EP - 297

BT - Annual Symposium on Foundations of Computer Science (Proceedings)

PB - Publ by IEEE

T2 - Proceedings of the 32nd Annual Symposium on Foundations of Computer Science

Y2 - 1 October 1991 through 4 October 1991

ER -