We present a probabilistic algorithm that, given a connected graph G (represented by adjacency lists) of average degree d, with edge weights in the set {1, . . . , w}, and given a ...
Abstract. We consider the problem of maintaining a minimum spanning tree within a graph with dynamically changing edge weights. An online algorithm is confronted with an input sequ...
We consider the problem of finding a sparse set of edges containing the minimum spanning tree (MST) of a random subgraph of G with high probability. The two random models that we ...
We analyze the convergence of the spectrum of large random graphs to the spectrum of a limit infinite graph. We apply these results to graphs converging locally to trees and deri...
We study the merging process when Kruskal's algorithm is run with random graphs as inputs. Our aim is to analyze this process when the underlying graph is the complete graph ...