Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a(0) + a(1)x(1) + ... + a(n)x(n) subject to certain constraints to solve the problem of minimizing a rational function of the form (a(0) + a(1)x(1) + ... + a(n)x(n))/(b(0) + b(1)x(1) + ... + b(n)x(n)) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo`s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo`s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an alpha-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an alpha-approximation (1 1/alpha-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.

Application execution management on the InteGrade opportunistic grid middleware

The InteGrade project is a multi-university effort to build a novel grid computing middleware based on the opportunistic use of resources belonging to user workstations. The InteGrade middleware currently enables the execution of sequential, bag-of-tasks, and parallel applications that follow the BSP or the MPI programming models. This article presents the lessons learned over the last five years of the InteGrade development and describes the solutions achieved concerning the support for robust application execution. The contributions cover the related fields of application scheduling, execution management, and fault tolerance. We present our solutions, describing their implementation principles and evaluation through the analysis of several experimental results. (C) 2010 Elsevier Inc. All rights reserved.