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A Comment on “A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks”
Oct. 2011 (vol. 22 no. 10)
pp. 1775-1776
Freek Verbeek, Radboud University Nijmegen, Nijmegen
Julien Schmaltz, Open University of the Netherlands, Heerlen
The purpose of this comment is to show that Duato's condition for deadlock freedom is only sufficient and not necessary. We propose a fix to keep the condition necessary. The issue is subtle but essential: in a wormhole network worms necessarily do not intersect.

[1] J. Duato, "A New Theory of Deadlock-Free Adaptive Routing in Wormhole Networks," IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 12, pp. 1320-1331, 1993.
[2] J. Duato, "A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks," IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 10, pp. 1055-1067, Oct. 1995.
[3] S. Taktak, E. Encrenaz, and J.L. Desbarbieux, "A Polynomial Algorithm to Prove Deadlock-Freeness of Wormhole Networks," Proc. 18th Euromicro Int'l Conf. Parallel, Distributed, and Network-Based Computing (PDP), pp. 121-128, 2010.
[4] F. Verbeek and J. Schmaltz, "On Necessary and Sufficient Conditions for Deadlock-Free Routing in Wormhole Networks," IEEE Trans. Parallel and Distributed Systems, preprint, 3 Feb. 2011, doi: 10.1109/TPDS.2011.60.

Citation:
Freek Verbeek, Julien Schmaltz, "A Comment on “A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks”," IEEE Transactions on Parallel and Distributed Systems, vol. 22, no. 10, pp. 1775-1776, Oct. 2011, doi:10.1109/TPDS.2011.16
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