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<p><b>Abstract</b>—Recently, <it>wormhole</it> routers with <it>multidestination</it> capability have been proposed to support fast multicast in a multicomputer network. To avoid communication deadlock, existing results have proposed to construct a <it>Hamilton path</it>, <it>Euler path</it>, <it>trip</it>, or their variants in the network, perhaps with some degree of support of virtual channels [<ref type="bib" rid="bibT12821">1</ref>], [<ref type="bib" rid="bibT128214">14</ref>], [<ref type="bib" rid="bibT128215">15</ref>], [<ref type="bib" rid="bibT128218">18</ref>], [<ref type="bib" rid="bibT128223">23</ref>]. In this paper, we identify that a network which is itself Eulerian or is Eulerian after some links are removed, can enjoy the multidestination capability without support of virtual channels. From this definition, we then develop several techniques to achieve fault-tolerant multicast in a torus/mesh of any dimension with regular fault patterns (such as single node, block, L-shape, T-shape, <tmath>$+$</tmath>-shape, U-shape, and H-shape) and even irregular fault patterns. The result improves over existing results on the requirement of support of virtual channels and fault-tolerant capability. Simulation results on tori are presented.</p>
Euler path, fault tolerance, mesh, multicast, multicomputer network, torus, virtual channel, wormhole routing.

Y. Tseng, M. Yang and T. Juang, "Achieving Fault-Tolerant Multicast in Injured Wormhole-Routed Tori and Meshes Based on Euler Path Construction," in IEEE Transactions on Computers, vol. 48, no. , pp. 1282-1296, 1999.
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