Visualisations of abstract data are believed to assist the searcher by providing an overview of the semantic structure of a document collection whereby semantically similar items tend to cluster in space. Cribbin and Chen (2001) found that similarity data represented using minimum spanning tree (MST) graphs provided greater levels of support to users when conducting a range of information seeki...

Wireless sensor networks have recently attracted lots of research effort due to its wide range of applications. These networks must operate for months or years. However, the sensors are powered by battery, which may not be possible to be recharged after they are deployed. Thus, energy-aware network management is extremely important. In this paper, we study the following problem: Given a set of ...

Microarrays technology allows us to measure the expression level of hundreds of thousands of genes simultaneously. The microarrays data analysis process involves various heavy computational tasks such as clustering. The clustering can be defined as partitioning a dataset into groups where objects in the same group are similar in somehow. CLUMP (clustering through MST in parallel) is one of the ...

We analyze a new general representation for the Minimum Weight Steiner Tree (MST) problem which translates the topological connectivity constraint into a set of local conditions which can be analyzed by the so called cavity equations techniques. For the limit case of the Spanning tree we prove that the fixed point of the algorithm arising from the cavity equations leads to the global optimum. 1...

We discuss a new approach to constructing the rectilinear Steiner tree (RST) of a given set of points in the plane, starting from a minimum spanning tree (MST). The main idea in our approach is to find layouts for the edges of the MST, so as to maximize the overlaps between the layouts, thus minimizing,the cost (i.e., wire length) of the resulting rectilinear Steiner tree. We describe two algor...

It is difficult to apply traditional Minimum spanning tree(MST) algorithms to a large dataset since the time complexity of the algorithms is quadratic. In this paper, we present a fast approximate MST framework on the complete graph of N points, and any exact MST algorithm can be incorporated into the framework and speeded up. The proposed framework employs a divide-and-conquer scheme to produc...

Continuing the program begun by the authors in a previous paper, we develop an exact low-density expansion for the random minimum spanning tree (MST) on a finite graph and use it to develop a continuum perturbation expansion for the MST on critical percolation clusters in space dimension d . The perturbation expansion is proved to be renormalizable in d=6 dimensions. We consider the fractal dim...

In this paper, we consider the use of multiple mobile software agents to perform different tasks in wireless sensor networks (WSNs). To this regard, determining the number of mobile agents in the WSN remains an open issue in solving multi-agent itinerary planning (MIP) problem. We propose a novel scheme entitled MST-MIP based on minimum spanning tree, where each branch stemmed from the sink cor...

This paper studies the topological properties of dynamics industry indices network at Moroccan stock exchange by using theory. The Minimum Spanning Tree (MST) was constructed from metric distances which had been calculated for different pairs industrial indices. MST were analysed over period 2013 to 2020 sliding window technique. studied divided into pre-pandemic Covid-19 and pandemic period. C...

Clustering is the process of partitioning the data set into subsets called clusters, so that the data in each subset share some properties in common. Clustering is an important tool to explore the hidden structures of modern large Databases. Because of the huge variety of the problems and data distributions, different classical clustering algorithms, such as hierarchical, partitional, density-b...