Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks

Erratum to "Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks"

Minimizing the makespan for a UET bipartite graph on a single processor with an integer precedence delay

We consider a set of tasks of unit execution times and a bipartite precedence delays graph with a positive precedence delay d : an arc (i; j) of this graph means that j can be executed at least d time units after the completion time of i. The problem is to sequence the tasks in order to minimize the makespan. Firstly, we prove that the associated decision problem is NP-complete. Then, we provid...

On the hardness of approximating the UET-UCT scheduling problem with hierarchical communications

We consider the unit execution time unit communication time (UET-UCT) schedulingmodelwith hierarchical communications [1], and we study the impact of the hierarchical communications hypothesis on the hardness of approximation. We prove that there is no polynomial time approximation algorithm with performance guarantee smaller than 5/4 (unless P = NP). This result is an extension of the result o...

Inapproximability Results for Wavelength Assignment in WDM Optical Networks

We address the issue of inapproximability of the wavelength assignment problem in wavelength division multiplexing (WDM) optical networks. We prove that in an n-node WDM optical network with m lightpaths and maximum load L, if NP = ZPP, for any constant δ > 0, no polynomial time algorithm can achieve approximation ratio n1/2−δ or m1−δ , where NP is the class of problems which can be solved by n...

Chromatic Scheduling of 1- and 2-Processor UET Tasks on Dedicated Machines with Availability Constraints

We address a generalization of the classical 1and 2-processor UET scheduling problem on dedicated machines. In our chromatic model of scheduling machines have non-simultaneous availability times and tasks have arbitrary release times and due dates. Also, the versatility of our approach makes it possible to generalize all known classical criteria of optimality. Under these constraints we show th...