there have been several efforts in the literature to extract as much information as possible from the financial networks. most of the research has been concerned about the hierarchical structures, clustering, topology and also the behavior of the market network; but not a notable work on the network filtration exists. this paper proposes a stock market filtering model using the correlation - ba...

A tree T is defined as a graph without any cycles. If edges are weighted, then we can define the minimum spanning tree (MST) of a graph G. The MST is the tree with smallest total edge weight that connects every node in G. Note that G must be a connected graph for any spanning tree, let alone a minimum spanning tree, to exist. We denote this MST as T ∗, which will be a subgraph of G (i.e., the e...

The concept of the minimum spanning tree (MST) plays an important role in topological network design, because it models a cheapest connected network. In a tree, however, the failure of a vertex can disconnect the network. In order to tolerate such a failure, we generalize the MST to the concept of a cheapest biconnected network. For a set of points in the Euclidean plane, we show that it is NP-...

Let G be a set of disjoint bi-chromatic straight line segments and H be a set of red and blue points in the plane, no three points are collinear. We give tight upper bounds on the maximum degree of a node in the color conforming minimum weight spanning tree (MST) formed by G and H. We also consider bounds on the total length of the edges of 1) the planar MST and the unrestricted MST, 2) the gre...

Given a spanning tree T of some graph G, the problem of minimum spanning tree verification is to decide whether T = MST (G). A celebrated result of Komlós shows that this problem can be solved with a linear number of comparisons. Somewhat unexpectedly, MST verification turns out to be useful in actually computing minimum spanning trees from scratch. It is this application that has led some to w...

Let G =< V,E > be a connected graph with real-valued edge weights: w : E → R, having n vertices and m edges. A spanning tree in G is an acyclic subgraph of G that includes every vertex of G and is connected; every spanning tree has exactly n− 1 edges. A minimum spanning tree (MST) is a spanning tree of minimum weight which is defined to be the sum of the weights of all its edges. Our problem is...

Given points in Euclidean space of arbitrary dimension, we prove that there exists a spanning tree having no vertices of degree greater than 3 with weight at most 1.561 times the weight of the minimum spanning tree. We also prove that there is a set of points such that no spanning tree of maximal degree 3 exists that has this ratio be less than 1.447. Our central result is based on the proof of...

Given an undirected graph G = (V,E) and a function d : V → N , the Min-Degree Constrained Minimum Spanning Tree (md-MST) problem is to find a minimum cost spanning tree T of G where each node i ∈ V has minimum degree d(i) or is a leaf node. This problem is closely related with the well-known Degree Constrained Minimum Spanning Tree (d-MST) problem, where the degree constraint is an upper limit ...

Clustering is partitioning a set of observation into groups called clusters, where the observation in the same group has a common characteristic. One of the best known algorithms for solving the microarrays data clustering problem using minimum spanning tree (MST) is CLUMP algorithm (Clustering algorithm through MST in Parallel) which identifies a dense clusters in a noisy background. The MST c...