Three-dimensional torus is a common topology of network interconnects of multicomputers due to its simplicity and high scalability. A parallel job submitted to a three-dimensional toroidal machine typically requires an isolated, contiguous, rectangular partition connected as a mesh or a torus. Such partitioning leads to fragmentation and thus reduces resource utilization of the machines. In particular, toroidal partitions often require allocation of additional communication links to close the torus. If the links are treated as dedicated resources (due to the partition isolation requirement) this may prevent allocation of other partitions that could, otherwise, use those links. Overall, on toroidal machines, the likelihood of successful allocation of a new partition decreases as the number of toroidal partitions increases. This paper presents a novel "multi-toroidal" interconnect topology that is able to accommodate multiple adjacent meshed and toroidal partitions at the same...