We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m=n p, where p...
We describe dynamic data structures for half-space range reporting and for maintaining the minima of a decomposable function. Using these data structures, we obtain efficient dyna...
Given a 2-node connected, undirected graph G = (V, E), with n nodes and m edges with real weights, and given a minimum spanning tree (MST) T = (V, ET ) of G, we study the problem o...
Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so tha...
Consider a connected r-regular n-vertex graph G with random independent edge lengths, each uniformly distributed on [0, 1]. Let mst(G) be the expected length of a minimum spanning...