It is known that an indirect network with a small host-to-host Average Shortest Path Length (h-ASPL) improves overall system performance in a parallel computer system . As a means to discuss such indirect networks in graph theory, the Order/Radix Problem (ORP) has been proposed. ORP involves finding a graph with a minimum h-ASPL that satisfies a given number of hosts and radix. A graph in ORP represents an indirect network and has two types of vertices: host and switch. We propose an optimization algorithm to generate graphs with a sufficiently small h-ASPL. The primary features of the proposed algorithm are the symmetry of the graph and the bias of the hosts adjacent to each switch. These features reduce the computational time to calculate the h-ASPL and improve the search performance of the algorithm. The performance of the proposed algorithm is evaluated using problems presented by Graph Golf, an international ORP competition. Our results show that the proposed algorithm can generate graphs with a smaller h-ASPL than the existing algorithm. To evaluate the performance of the graphs generated by the proposed algorithm, we use the parallel simulation framework SimGrid and the parallel benchmark collection NAS Parallel Benchmarks. Our results also show that the graphs generated by the proposed algorithm have higher performance than those generated by the existing algorithm.

The purpose of this paper is to point out a new connection between information theory and dynamical systems. In the information theory side, we consider rate distortion theory, which studies lossy data compression of stochastic processes under distortion constraints. In the dynamical systems side, we consider mean dimension theory, which studies how many parameters per iterate we need to describe a dynamical system. The main results are new variational principles connecting rate distortion function to metric mean dimension.