Single-Row Transformation of Complete Graphs

A complete graph is a fully-connected graph where every node is adjacent to all other nodes in the graph. Very often, many applications in science and engineering are reducible to this type of graph. Hence, a simplified form of a complete graph contributes in providing the solutions to these problems. In this paper, we present a technique for transforming a complete graph into a single-row routing problem. Single-row routing is a classical technique in the VLSI design that is known to be NP-complete. We solved this problem earlier using a method called ESSR, and, the same technique is applied to the present work to transform a complete graph into its single-row routing representation. A parallel computing model is proposed which contributes in making the problem modular and scalable. We also discuss the application of this work on the channel assignment problem in the wireless cellular telephone networks.     

Enhanced Simulated Annealing Technique for the Single-Row Routing Problem

This paper presents ESSR (Enhanced Simulated annealing for Single-row Routing) model for solving the single-row routing problem. The main objective in this problem is to produce a realization that minimizes both the street congestion and the number of doglegs. Simulated annealing (SA) is a stochastic, hill-climbing and gradient-descent technique based on the statistical properties of particles undergoing thermal annealing. By performing slow cooling, the nets in the single-row routing problem align themselves according to a configuration with the lowest energy. The model has been known to produce reasonably good solutions for many NP-complete optimization problems, such as the single-row routing problem. In ESSR, our strategy is to minimize both the street congestion and the number of interstreet crossings (doglegs) by expressing a single energy function as their collective properties. This objective is achieved by representing the energy as the absolute sum of the heights of the net segments. To speed up convergence, we pivot the street congestion value while having the energy drops directly proportional to the number of doglegs. This action has the effect of minimizing the number of doglegs as the energy stabilizes. Our simulation work on ESSR produces optimal results in most cases for both the street congestion and the number of doglegs. Our experimental results compare well against results obtained from our earlier model (SRR-7) and two other methods reported in the literature.     

An iterative multistep formula for solving initial value problems

The iterative multistep method (IMS) introduced by Hyman (1978) for solving initial value problems in ordinary differential equations has the advantage of being able to offer a higher degree of accuracy than the Runge-Kutta formulas by continuing the iteration process. In this article, another IMS formula is developed based on the geometric means predictor-corrector formulas introduced by Sanugi and Evans (1989). A numerical example is provided that shows that this formula can be used as a competitive alternative to Hyman's IMS formula.     

The development of spectral indices for early detection of Ganoderma disease in oil palm seedlings

Field spectroscopy is a rapid and non-destructive analytical technique that may be used for assessing plant stress and disease. The objective of this study was to develop spectral indices for detection of Ganoderma disease in oil palm seedlings. The reflectance spectra of oil palm seedlings from three levels of Ganoderma disease severity were acquired using a spectroradiometer. Denoizing and data transformation using first derivative analysis was conducted on the original reflectance spectra. Then, comparative statistical analysis was used to select significant wavelength from transformed data. Wavelength pairs of spectral indices were selected using optimum index factor. The spectral indices were produced using the wavelength ratios and a modified simple ratio method. The relationship analysis between spectral indices and total leaf chlorophyll (TLC) was conducted using regression technique. The results suggested that six spectral indices are suitable for the early detection of Ganoderma disease in oil palm seedlings. Final results after regression with TLC showed that Ratio 3 is the best spectral index for the early detection of Ganoderma infection in oil palm seedlings. For future works, this can be used for the development of robust spectral indices for Ganoderma disease detection in young and mature oil palm using airborne hyperspectral imaging.     

A new fourth order Runge-Kutta formula for y′ = Ay with stepsize control

A new fourth order Runge-Kutta method for solving linear initial value problems of the form y′ = Ay is derived which provides as estimate of the truncation error without any extra function evaluations. The idea follows from the fact that two numerical solutions of similar order can be obtained by using the arithmetic mean (AM) and the geometric mean (GM) averaging of the functional values. The numerical results given confirm that this new method is suitable to be used as an error control strategy.