“…Both two-dimensional (2D) and three-dimensional (3D) meshes and tori have been utilized in recent experimental and commercial multicomputers. Most contiguous processor allocation strategies that are proposed in the previous studies are for 2D meshes (Chiu & Chen, 1999;Ababneh, 2006;Ababneh, 2009;Ababneh et al, 2010;Chuang & Tzeng, 1994;Zhu, 1992). In spite of the fact that the 2D mesh has been used in a various of parallel machines, such as the Cray XE6m (Cray, 2014b), the iWARP (Peterson et al, 1991) and the Touchstone Delta system (Intel, 1991), current multicomputers, such as the K-computer (Riken & Fujitsu, 2014), the Cray XE6 (Cray, 2014a) and the IBM BlueGene/L (Horn et al, 2014) use the 3D mesh or the 3D tori (Cray, 2014a;Horn et al, 2014;Riken & Fujitsu, 2014) as an interconnection network due to their characteristics such as lower diameter and lower average communication distance (Athas & Seitz, 1988).…”