Let S be a set of n points in IRd and let t > 1 be a real number. A t-spanner for S is a graph having the points of S as its vertices such that for any pair p, q of points ther...
In this paper we present space-query trade-offs for external memory data structures that answer shortest path queries on planar directed graphs. For any S = Ω(N1+ ) and S = O(N2...
We obtain the following results related to dynamic versions of the shortest-paths problem: (i) Reductions that show that the incremental and decremental singlesource shortest-paths...
For each integer m 1, consider the graph Gm whose vertex set is the set N = {0, 1, 2, . . . } of natural numbers and whose edges are the pairs xy with y = x + m or y = x - m or y...
Given a graph G we consider the problem of preprocessing it so that given two vertices x,y and a set X of vertices, we can efficiently report the shortest path (or just its length...