We show how to approximate in NC the problem of Scheduling Unrelated Parallel Machines, for a xed number of machines. We develop a (2 + ")-approximate parallel algorithm for the problem. Our approach shows how to relate the linear program obtained by relaxing the integer programming formulation of the problem with a linear program formulation that is positive and in the packing/covering form. T...

Jachymski [ Proc. Amer. Math. Soc., 136 (2008), 1359-1373] gave modified version of a Banach fixed point theorem on a metric space endowed with a graph. In the present paper, (G, Φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. Also, Hardy-Rogers G-contraction have been introduced and some fixed point theorems have been proved. S...

An automatic scaling C program translator is developed for the eecient execution of application programs in xed-point digital signal processors. The program for range estimation is automatically generated by inserting codes which collect the statistics of each signal during the simulation. With the range information, the number of shifts needed for the scaling is determined and the oating-point...

In this thesis, we present algorithmic solutions to shortest path queries on polyhedral surfaces and in polygonal domains. The research problems addressed in this thesis and shortest path problems in general are fundamental problems in geographic information systems (GIS) and computational geometry. We present novel algorithms that answer approximate shortest path queries between any pair of po...

Resumen Background: Likelihood-based methods can work poorly when the residuals are not normally distributed and the variances across clusters are heterogeneous. Method: The performance of two estimation methods, the non-parametric residual bootstrap (RB) and the restricted maximum likelihood (REML) for fi tting multilevel models are compared through simulation studies in terms of bias, coverag...

Two xed-point optimization utility programs, the range estimator and the xed-point simulator, are developed for scaling and wordlength determination of digital signal processing algorithms written in C or C++ language. By exploiting the operator overloading characteristics of C++ language, range estimation and xed-point simulation can be conducted just by modifying the variable declaration of t...

We say a functional equation () is stable if any function g satisfying the equation () approximatelyis near to true solution of (). Using xed point methods, we investigate approximately higherternary derivations in Banach ternary algebras via the Cauchy functional equationf(1x + 2y + 3z) = 1f(x) + 2f(y) + 3f(z) :

In this paper, we prove that an implicit iterative process with er-rors converges strongly to a common xed point for a nite family of generalizedasymptotically quasi-nonexpansive mappings on unbounded sets in a uniformlyconvex Banach space. Our results unify, improve and generalize the correspond-ing results of Ud-din and Khan [4], Sun [21], Wittman [23], Xu and Ori [26] andmany others.

A xed-point C compiler is developed for convenient and efcient programming of TMS320C50 xed-point digital signal processor. This compiler supports the `fix' data type that can have an individual integer word-length according to the range of a variable. It can add or subtract two data having di erent integer word-lengths by automatically inserting shift operations. The accuracy of xed-point mult...

In this paper we present a new xed point theorem applicable for a countable system of recursive equations over a wellfounded domain. Wellfoundedness is an essential feature of many computer science applications as it guarantees termination of the corresponding xed point computation algorithms. Besides being a natural restriction, it marks a new area of application, where not even monotonicity i...