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Piera Barcaccia, Maurizio A. Bonuccelli, Miriam Di Ianni, "Complexity of Minimum Length Scheduling for Precedence Constrained Messages in Distributed Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 10, pp. 10901102, October, 2000.  
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@article{ 10.1109/71.888647, author = {Piera Barcaccia and Maurizio A. Bonuccelli and Miriam Di Ianni}, title = {Complexity of Minimum Length Scheduling for Precedence Constrained Messages in Distributed Systems}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {11}, number = {10}, issn = {10459219}, year = {2000}, pages = {10901102}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.888647}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Complexity of Minimum Length Scheduling for Precedence Constrained Messages in Distributed Systems IS  10 SN  10459219 SP1090 EP1102 EPD  10901102 A1  Piera Barcaccia, A1  Maurizio A. Bonuccelli, A1  Miriam Di Ianni, PY  2000 KW  Single hop distributed systems KW  scheduling KW  NPcompleteness KW  minimum schedule length KW  approximation algorithms. VL  11 JA  IEEE Transactions on Parallel and Distributed Systems ER   
Abstract—Switching networks are the core of many communication and multiprocessor systems. In these systems, a set of entities (communication equipment or processors) communicate through the switching network by exchanging messages. Simultaneous transmission or reception of two or more different messages through an input or output port results in the corruption of the messages (also called collision), which are useless and must be retransmitted later. This causes a performance degradation. Collisions can be avoided only by a proper scheduling of the messages. The same problem also arises in singlehop purely optical WDM systems, where simultaneous reception or transmission over the same wavelength channel results in a collision. In this paper, we study the problem of minimum length scheduling of a set of messages subject to precedence constraints. We show that the decision version of the problem is NPcomplete even in very restricted cases. This means that the optimization problem cannot be solved in polynomial time, unless P=NP. Since the problem cannot be optimally solved by fast algorithms, we then investigate the existence of polynomial time approximation algorithms, by first proving that approximation algorithms cannot exist with performance ratio bounded by
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