In this paper we consider a spanning tree problem of uncertain network, which is a natural uncertain variation of the deterministic minimum spanning tree problem. By means of uncertainty theory, we propose three types of minimum spanning tree models for uncertain network, i.e., expected minimum spanning tree, α-minimum spanning tree, and distribution minimum spanning tree. Generally, we can the...

In a sequence of recent results (PODC 2015 and PODC 2016), the running time of the fastest algorithm for the minimum spanning tree (MST) problem in the Congested Clique model was first improved to O(log log logn) from O(log logn) (Hegeman et al., PODC 2015) and then to O(log∗ n) (Ghaffari and Parter, PODC 2016). All of these algorithms use Θ(n2) messages independent of the number of edges in th...

We study the problem of finding a minimum spanning tree on the complete graph on n points in E' , with the weight of an edge between any two points being the distance between the two points under some distance metric. A fast algorithm, which finds an approximate minimum spanning tree with wei h t a t most (1+c) times optimal in developed for the L,, q =2,3, ..., distance metrics. Moreover, if t...

I find a topological arrangement of assets traded in a phonographic market which has associated a meaningful economic taxonomy. I continue using the Minimal Spanning Tree and the Life-time Of Correlations between assets, but now outside the stock markets. This is the first attempt to use these methods on phonographic market where we have artists instead of stocks. The value of an artist is defi...

This first algorithm is quite simple. (Though this was probably known earlier, its proof can be found in Prof. Indyk’s 1999 paper “Sublinear Time Algorithms for Metric Space Problems”.) Let Dij denote the distance between a pair of points i and j, over m total points. The entries of Dij must satisfy the triangle inequality; additionally the matrix is symmetric. Note that the matrix size (i.e., ...