In this paper we describe a minimum spanning tree problem with generalized degree constraints which arises in the design of wireless networks. The signal strength on the receiver side of a wireless link decreases with the distance between transmitter and receiver. In order to work properly, the interference on the receiving part of the link must be under a given threshold. In order to guarantee...

We propose a novel person verification system for real-time face identification. The main features of the system include accurate registration of face images using a robust form of correlation, a framework for global registration of a face database using a minimum spanning tree algorithm and a method for selecting a subset of features optimal for discrimination between clients and impostors. Th...

We associate an optimistic TU game with each minimum cost spanning tree problem. We define the worth of a coalition S as the cost of connecting agents in S to the source assuming that agents in N\S are already connected to the source, and agents in S can connect through agents in N\S. We study the Shapley value of this new game.

In this paper we analyzed cross-correlations in commodity markets investigating correlations of future contracts for commodities over the period 1998.09.01 2007.12.14. We constructed a minimal spanning tree based on the correlation matrix. The tree provides evidence for sector clusterization of investigated contracts. We also studied dynamic properties of correlations. It turned out that the ma...

We provide a characterization of the obligation rules in the context of minimum cost spanning tree games. We also explore the relation between obligation rules and random order values of the irreducible cost game it is shown that the later is a subset of the obligation rules. Moreover we provide a necessary and sufficient condition on obligation function such that the corresponding obligation r...

This paper presents a theorem that asserts that average edge length of the minimum spanning tree of a complete graph on n+ 1 vertices is less than or equal to the average edge length of all the n+ 1 minimum spanning trees of the induced graph on n vertices. The result is also in compliance with results given by Frieze and Steele.  1999 Elsevier Science B.V. All rights reserved.

Two applications of sparsification to parametric computing are given. The first is a fast algorithm for enumerating all distinct minimum spanning trees in a graph whose edge weights vary linearly with a parameter. The second is an asymptotically optimal algorithm for the minimum ratio spanning tree problem, as well as other search problems, on dense graphs.

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 tree. We show that mst(G) can be estimated quite accurately under two distinct circumstances. Firstly, if r is large and G has a modest edge expansion property then mst(G) ∼ r ζ(3), where ζ(3) = ∑∞ j=1 j −3 ∼ 1.202. Se...

A metric space has doubling dimension d if for every ρ > 0, every ball of radius ρ can be covered by at most 2d balls of radius ρ/2. This generalizes the Euclidean dimension, because the doubling dimension of Euclidean space Rd is proportional to d. The following results are shown, for any d ≥ 1 and any metric space of size n and doubling dimension d: First, the maximum number of diametral pair...

The d-Dim h-hops MST problem is defined as follows: Given a set S of points in the ddimensional Euclidean space and s ∈ S, find a minimum-cost spanning tree for S rooted at s with height at most h. We investigate the problem for any constants h and d > 0. We prove the first non trivial lower bound on the solution cost for almost all Euclidean instances (i.e. the lower-bound holds with hight pro...