Results 1 
3 of
3
Scheduling and Packing Malleable and Parallel Tasks with Precedence Constraints of Bounded Width
 JOURNAL OF COMBINATORIAL OPTIMIZATION
, 2010
"... We study the problems of nonpreemptively scheduling and packing malleable and parallel tasks with precedence constraints to minimize the makespan. In the scheduling variant, we allow the free choice of processors; in packing, each task must be assigned to a contiguous subset. Malleable tasks can b ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We study the problems of nonpreemptively scheduling and packing malleable and parallel tasks with precedence constraints to minimize the makespan. In the scheduling variant, we allow the free choice of processors; in packing, each task must be assigned to a contiguous subset. Malleable tasks can be processed on different numbers of processors with varying processing times, while parallel tasks require a fixed number of processors. For precedence constraints of bounded width, we resolve the complexity status of the problem with any number of processors and any width bound. We present an FPTAS based on Dilworth’s decomposition theorem for the NPhard problem variants, and exact efficient algorithms for all remaining special cases. For our positive results, we do not require the otherwise common monotonous penalty assumption on the processing times of malleable tasks, whereas our hardness results hold even when assuming this restriction. We complement our results by showing that these problems are all strongly NPhard under precedence constraints which form a tree.
Supervisor at Nada was Örjan Ekeberg
"... In this paper, we use two different evolutionary algorithms, the genetic algorithm and the differential evolution, to optimize project schedules created in Microsoft Project 2003. Project management is crucial for every company. To create a good schedule might be quite hard. It has been shown, that ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper, we use two different evolutionary algorithms, the genetic algorithm and the differential evolution, to optimize project schedules created in Microsoft Project 2003. Project management is crucial for every company. To create a good schedule might be quite hard. It has been shown, that optimize a project schedule is a NPhard problem. Evolutionary algorithms are often used to conquer NPhard problems. We have chosen two of many to solve the optimization problem. The best one is used for optimizing a large schedule with over 100 tasks. The tests on both small and large schedules show that genetic algorithms are more suitable for schedule optimization than differential evolution. The study shows that they are better on both speed and quality of the optimization. We also investigate the possibilities to import and export data from MS Project. One of them, XML, is not fully supported in Microsoft Project 2003. It is better and more reliable in everyday professional activities to
Hardness of Vertex Deletion and Project Scheduling
 THEORY OF COMPUTING, SPECIAL ISSUE: APPROXRANDOM 2012
, 2013
"... Assuming the Unique Games Conjecture, we show strong inapproximability results for two natural vertexdeletion problems on directed graphs: for any integer k ≥ 2 and arbitrary small ε> 0, the Feedback Vertex Set problem and the DAG Vertex Deletion problem are inapproximable within a factor k − ..."
Abstract
 Add to MetaCart
(Show Context)
Assuming the Unique Games Conjecture, we show strong inapproximability results for two natural vertexdeletion problems on directed graphs: for any integer k ≥ 2 and arbitrary small ε> 0, the Feedback Vertex Set problem and the DAG Vertex Deletion problem are inapproximable within a factor k − ε even on graphs where the vertices can be almost partitioned into k solutions. This gives a more structured and yet simpler UGhardness result for the Feedback Vertex Set problem than the previous hardness result (albeit using the “It Ain’t Over Till It’s Over ” Theorem). In comparison with the classical Feedback Vertex Set problem, the DAG Vertex Deletion problem has received little attention. Although we think it is a natural and interesting problem, the main motivation for our inapproximability result stems from its relationship with the classical Discrete Time–Cost Tradeoff Problem. More specifically, our results imply that the deadline version is UGhard to approximate within any constant. This explains the difficulty in obtaining good approximation algorithms for that problem and further motivates previous alternative approaches such as bicriteria approximations.