1998
DOI: 10.1137/s0097539795279943
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Competitive Algorithms for Layered Graph Traversal

Abstract: A layered graph is a connected graph whose vertices are partitioned into sets L 0 =s, L 1 , L 2 ,..., and whose edges, which have nonnegative integral weights, run between consecutive layers. Its width is {|L i |}. 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 bound… Show more

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Cited by 26 publications
(43 citation statements)
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“…We consider the problem both for the measure of the number of rejected requests and for the measure of the number accepted requests. We observe that using known techniques [7,9,6] we can construct a combined randomized preemptive algorithm which is at most O(log k) worse with respect to the number of rejected requests of the best algorithm among the k. Using known results [2] we can also construct a combined randomized preemptive algorithm which is at most O(log k) worse with respect to the number of accepted requests of the best algorithm among the k. These two combined algorithms can be combined to one master algorithm using our main result to guarantee both rejection and acceptance competitiveness.…”
Section: Introductionmentioning
confidence: 90%
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“…We consider the problem both for the measure of the number of rejected requests and for the measure of the number accepted requests. We observe that using known techniques [7,9,6] we can construct a combined randomized preemptive algorithm which is at most O(log k) worse with respect to the number of rejected requests of the best algorithm among the k. Using known results [2] we can also construct a combined randomized preemptive algorithm which is at most O(log k) worse with respect to the number of accepted requests of the best algorithm among the k. These two combined algorithms can be combined to one master algorithm using our main result to guarantee both rejection and acceptance competitiveness.…”
Section: Introductionmentioning
confidence: 90%
“…Results of this form already exist in the literature [2,6,7,9] but our main point here is that (a) these known techniques can be applied in our abstract model, and (b) using our main result we can combine the two master algorithms that result into one combined algorithm which guarantees both rejection and acceptance competitiveness.…”
Section: Combining Admission Control Algorithmsmentioning
confidence: 96%
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“…Lower and upper bounds of 9 were given there and are one of the usual introductory examples at the courses on on-line algorithms. Some of the problems stated in this paper and other, closely related, were afterwards considered by many researchers [6,4,7]. We refer the reader to [3] for a more modern and general reflection on the subject, or [5] for a more classic approach to search problems.…”
Section: Introductionmentioning
confidence: 99%
“…For randomized algorithms with memory, the two problems are intertwined. Another related problem that is more general than the k-server problem and a special case of metrical task systems is the metrical service systems [50,51] which is equivalent to the layered graph traversal problem [52,53]. Also the CNN problem [54,55] is similar to the k-server problem, especially to the weighted version in which the servers have different speeds (or costs) [56].…”
mentioning
confidence: 99%