We present a polynomial time approximation algorithm for unit time precedence constrained scheduling. Our algorithm guarantees schedules which are at most (

Scheduling the execution of parallel algorithms on parallel computers is a main issue in current research. Parallel computers can be used to solve scheduling problems very fast and we might be able to tackle new applications, where schedules must be obtained very quickly. Although the importance of parallel scheduling algorithms has been widely recognized, only few results have been obtained so...

In this paper computational results are presented with a very general, yet powerful backtracking procedure for solving the duration minimization and net present value maximization problems in a precedence and resource-constrained network. These networks are generally of the PERT/CPM variety, although it is not required that they be so. Among the advantages cited for our approach are low compute...

Given a set  of  points in the plane and a constant ,-center problem is to find two closed disks which each covers the whole , the diameter of the bigger one is minimized, and the distance of the two centers is at least . Constrained -center problem is the -center problem in which the centers are forced to lie on a given line . In this paper, we first introduce -center problem and its constrain...

The minimum storage-time sequencing problem generalizes many well known problems in Combinatorial Optimization, such as the directed linear arrangement and the problem of minimizing the weighted sum of completion times, subject to precedence constraints on a single processor. In this paper we propose a new lower bound, based on a Lagrangian relaxation, which can be computed very e cently. To im...

Due to the precedence constraints among vertices, the partitioning problem for dynamically reconfigurable FPGAs (DRFPGAs) is different from the traditional one. In this paper, we first derive logic formulations for the precedence-constrained partitioning problems, and then transform the formulations into integer linear programs (ILPs). The ILPs can handle the precedence constraints and minimize...

A systematic overview on the subject of assembly sequencing is presented. Sequencing lies at the core of assembly planning, and variants include finding a feasible sequence –respecting the precedence constraints between the assembly operations–, or determining an optimal one according to one or several operational criteria. The different ways of representing the space of feasible assembly seque...

Due to the precedence constraints among vertices, the partitioning problem for time-multiplexed field-programmable gate arrays (TMFPGAs) is different from the traditional one. In this paper, we first derive logic formulations for the precedence-constrained partitioning problems and then transform the formulations into integer linear programs (ILPs). The ILPs can handle the precedence constraint...

In 1966, Graham showed that a simple procedure called list scheduling yields a 2-approximation algorithm for the central problem of scheduling precedence constrained jobs on identical machines to minimize makespan. To date this has remained the best algorithm, and whether it can or cannot be improved has become a major open problem in scheduling theory. We address this problem by establishing a...