Centralized versus Distributed Efficient Route Computation with Multiply-Constrained Link Costs

Abstract

We quantify and compare the complexities of two computational algorithms, the Floyd-Warshall algorithm and a widest-remaining- path-first algorithm (WRaPFt), which we introduce here, that compute abstract node representations for autonomous systems in hierarchical networks. Both algorithms compute the traversing characteristics under bandwidth dependent link costs and give identical results. The techniques discussed here can be applied to any cost metrics that can be defined as elements of a semi-ring. We compare the execution time and the number of steps required to compute the efficient frontiers for the case of flow-controlled cost functions. For all node pairs, we found WRaPFt to be faster at lower connectivities and Floyd- Warshall to be faster at higher connectivities, the crossover point being roughly 0.5. Execution time for the WRaPFt algorithm is never more than 1.7 times the execution time of the Floyd-Warshall algorithm. Thus, WRaPFt can provide a speed-up factor of 1.7/ V in routing table update computation. Finally, we found that the execution time increases approximately proportional to the 4th power of V for both algorithms for fully connected random test networks.