Sparse Symmetric Positive Definite (SPD) Linear System Solvers (LSS) are routinely required in various Power System Analysis problems. In sparse LSS ordering of nodes is desired to reduce fill ins, which in turn reduce computations. Minimum Degree Algorithm (MDA) has established itself as a very competitive ordering algorithm, for reducing fill ins to quite often near minimum level. With the ac...

We study routing overhead in mobile ad-hoc networks employing geographic routing with no hierarchy. We first provide a new framework for quantifying routing overhead due to control messages generated to exchange location information. Second, we compute the minimum number of bits required on average to describe the locations of a node, borrowing tools from information theory. This result is then...

We consider a class of optimization problems called movement minimization on euclidean plane. Given a set of nodes on the plane, the aim is to achieve some specific property by minimum movement of the nodes. We consider two specific properties, namely the connectivity (Con) and realization of a given topology (Topol). By minimum movement, we mean either the sum of all movements (Sum) or the max...

In this paper, we propose a new minimum total communication distance (TCD) algorithm and an optimal TCD algorithm for broadcast in a 2-dimension mesh. The former generates a minimum TCD from a given source node, and the latter guarantees a minimum TCD among all the possible source nodes. These algorithms can be generalized to a d-dimensional mesh or torus. TCD can potentially be used as a measu...

One of the graph theoretic approaches of channel assignment for cellular networks is routing a pair of nodes arranged in a single-row axis called single-row routing problem. The network with nodes representing caller and receiver is to be transformed into a single-row network efficiently is proposed. The connected graph derived from the base network is presented using incidence matrix. The rows...

We study field-monitoring applications in which sensors are deployed in large numbers and the sensing process is expensive. In such applications, nodes should use the minimum possible sensing ranges to prolong the “coverage time” of the network. We investigate how to determine such minimum ranges in a distributed fashion when the nodes are location-unaware. We develop a distributed protocol (SR...

This paper introduces a K-Centers clustering protocol for heterogeneous wireless sensor networks. Energy consumption is an important issue for wireless sensor networks, and sensor nodes consume most of their energy with data delivery. The energy needed to transmit data is proportional to the distance between sensor nodes and either cluster heads or a base station. Clustering is an efficient tec...

We consider the minimum energy problem for a mobile ad hoc network, where any node in the network may communicate with any other via intermediate nodes. To provide quality of service, the network must be connected, even if one or more nodes drop out. This motivates the notion of k-connectivity. The minimum energy problem aims to optimise the total energy that all nodes spend for transmission. P...

The shortest paths problem on weighted directed graphs is one of the basic network optimization problems. Its importance is mainly due to its applications in various areas, such as communication and transportation. Given a source node s in a weighted directed graph G, with n nodes and m arcs, the single-source shortest path problem (SSSP, for short) from s is the problem of finding the minimum ...

A mobile ad hoc network (MANET) is a dynamic distributed system of wireless nodes that move independently of each other. MANET routing protocols are either proactive or reactive in nature. Proactive routing protocols determine and maintain routes between any pair of nodes irrespective of their requirement. The reactive on-demand routing protocols determine a route only when required. As the net...