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., ...

it is very important for managers, investors and financial policy-makers to detect and analyze factors affecting financial markets to obtain optimal decision and reduce risks. the importance of market analysis and attempt to improve its behavior understanding, has led analysts to use the experiences of other professionals in the fields such as social sciences and mathematics to examine the inte...

We study the expected value of the length Ln of the minimum spanning tree of the complete graph Kn when each edge e is given an independent uniform [0, 1] edge weight. We sharpen the result of Frieze [6] that limn→∞ E(Ln) = ζ(3) and show that E(Ln) = ζ(3) + c1 n + c2+o(1) n4/3 where c1, c2 are explicitly defined constants.

We show that any tree whose maximum degree is at most 10 can be drawn in 3-space such that it is the minimum spanning tree of its vertices.