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

We address a generalization of the classical 1- and 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 that the problem of optimal scheduling of sparse instances can be solved in polynomial time.

[1]  Marek Kubale,et al.  Edge-chromatic sum of trees and bounded cyclicity graphs , 2000, Inf. Process. Lett..

[2]  Jacek Blazewicz,et al.  Scheduling Multiprocessor Tasks on Three Dedicated Processors , 1992, Inf. Process. Lett..

[3]  Lucio Bianco,et al.  Preemptive multiprocessor task scheduling with release times and time windows , 1997, Ann. Oper. Res..

[4]  Takao Nishizeki,et al.  Algorithm for the Cost Edge-Coloring of Trees , 2001, J. Comb. Optim..

[5]  Edward G. Coffman,et al.  Scheduling File Transfers , 1985, SIAM J. Comput..

[6]  Ming-Yang Kao,et al.  All-Cavity Maximum Matchings , 1997, ISAAC.

[7]  Henryk Krawczyk,et al.  An Approximation Algorithm for Diagnostic Test Scheduling in Multicomputer Systems , 1985, IEEE Transactions on Computers.

[8]  Jacek Blazewicz,et al.  Scheduling multiprocessor tasks on parallel processors with limited availability , 2003, Eur. J. Oper. Res..

[9]  Jacek Blazewicz,et al.  Scheduling multiprocessor tasks of three dedicated processors information processing letters 41 (5) (1992) 275–280 , 1994 .

[10]  Marek Kubale,et al.  Preemptive versus nonpreemptive scheduling of biprocessor tasks on dedicated processors , 1996 .

[11]  Mohamed Haouari,et al.  Optimal parallel machines scheduling with availability constraints , 2005, Discret. Appl. Math..

[12]  Marek Kubale,et al.  Complexity results on open shop scheduling to minimize total cost of operations , 2002, Int. J. Comput. Syst. Signals.

[13]  Uday S. Karmarkar,et al.  Simultaneous Resource Scheduling to Minimize Weighted Flow Times , 1989, Oper. Res..

[14]  Daniel P. Siewiorek,et al.  Parallel processing: the Cm* experience , 1986 .

[15]  Maciej Drozdowski,et al.  Scheduling multiprocessor tasks -- An overview , 1996 .

[16]  Errol L. Lloyd,et al.  Concurrent Task Systems , 1981, Oper. Res..

[17]  Marek Kubale,et al.  The Complexity of Scheduling Independent Two-Processor Tasks on Dedicated Processors , 1987, Information Processing Letters.