Cycle avoidance in 2D/3D bidirectional graphs using shortest-path dynamic programming network

An ordinary-differential-equation (ODE) simulation model has recently been proposed for an N-node dynamic programming (DP) network, which solves the transitive closure and shortest path problems on an architecturally equivalent N-node 2D/3D grid stack. For large-scale randomly generated bidirectional network, where N is large and the inter-grid paths may take either direction, cycles commonly occur leading to a high percentage of nodes with unbound path lengths. The detection of such cycle nodes can be readily found using a shortest-path DP network. In this work we address several issues on the cycle avoidance problem, by first defining the 〈H〉-index and 〈V〉-index and hence its product 〈HV〉 as the two-dimensional turn ability. A regression model was then proposed and obtained empirically to relate the cycle-node ratio, which is the percentage of cycle nodes over N, with 〈HV〉 for several random networks of sizes N = 10×10×2, 10×10×5, 10×10×8. By reducing 〈HV〉 from 0.8 to 0.2, the cycle-node ratio can be reduced from close to 60% to 20% and indicates a significant avoidance of cycle nodes.