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...
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 ...
In the b-degree constrained Euclidean minimum spanning tree problem (bMST) we are given n points in [0;1]d and a degree constraint b 2. The aim is to nd a minimum weight spannin...
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 ...