Trade-Offs in Non-Reversing Diameter
نویسندگان
چکیده
Consider a tree T with a number of extra edges (the bridges) added. We consider the notion of diameter, that is obtained by admitting only paths p with the property that for every bridge b in path p, no edge that is on the unique path (in T) between the endpoints of b is also in p or on the unique path between the two endpoints of any other bridge in p. (Such a path is called non-reversing.) We investigate the trade-oo between the number of added bridges and the resulting diameter. Upper and lower bounds of the same order are obtained for all diameters of constant size. For the special case where T is a chain we also obtain matching upper and lower bounds for diameters of size (N) + O(1) or of size f(N) where f(N) grows faster than (N). Some applications are given. 1 The Problem Let an undirected tree T = (V; E) be given. The diameter of this tree is to be reduced by the addition of as few edges as possible, where a modiied deenition of the distance is given below. Calling the set of additional edges (the bridges) B, let
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عنوان ژورنال:
- Nord. J. Comput.
دوره 1 شماره
صفحات -
تاریخ انتشار 1994