Abstract
Abstract We show that every permutation graph with n elements can be preprocessed in O ( n ) time, if two linear extensions of the corresponding poset are given, to produce an O ( n ) space data-structure supporting distance queries in constant time. The data-structure is localized and given as a distance labeling, that is each vertex receives a label of O (log n ) bits so that distance queries between any two vertices are answered by inspecting on their labels only. This result improves the previous scheme due to Katz, Katz and Peleg [M. Katz , N.A. Katz , and D. Peleg , Distance labeling schemes for well-separated graph classes , in 17 th Annual Symposium on Theoretical Aspects of Computer Science (STACS), H. Reichel and S. Tison, eds., vol. 1770 of Lecture Notes in Computer Science, Springer Verlag, Feb. 2000, pp. 516–528] in the STACS '00 by a log n factor.
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