Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
A. Fiat , Dept. of Comput. Sci., Tel-Aviv Univ., Israel
A layered graph is a connected, weighted graph whose vertices are partitioned into sets L/sub 0/=(s), L/sub 1/, L/sub 2/, . . ., and whose edges run between consecutive layers. Its width is max( mod L/sub i/ mod ). 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/sup -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.
deterministic online algorithm, competitive algorithms, upper bounds, layered graph traversal, weighted graph, searcher, target vertex, lower bounds
H. Karloff, S. Viswanathan, A. Fiat, Y. Ravid, Y. Rabani and D. Foster, "Competitive algorithms for layered graph traversal,"  Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 288-297.