Holger Petersen's scientific contributions

Publication (1)

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We consider how to assign labels to any undirected graph with n nodes such that, given the labels of two nodes and no other information regarding the graph, it is possible to determine the distance between the two nodes. The challenge in such a distance labeling scheme is primarily to minimize the maximum label lenght and secondarily to minimize th...


... The secondary goal is to optimize the query time, that is the time necessary to compute δ G (u, v) given the labels of u and v. Distance labeling for general unweighted undirected graphs on n nodes was first considered by Graham and Pollak [19], who obtained labels consisting of O(n) bits. The decoding time was subsequently improved to O(log log n) by Gavoille et al. [16], then to O(log * n) by Weimann and Peleg [32], and finally Alstrup et al. [6] obtained O(1) decoding time with labels of length log 3 2 n+o(n). 1 It is known that some labels must consist of at least n 2 bits [29,22]. Better schemes for distance labeling are known for restricted classes of graphs. ...