Using Multi-valued Decision Diagrams to Solve the Expected Hop Count Problem

The Expected Hop Count (EHC) of a computer communication network has so far been computed for network models that consider only device or link failure, but not both. We introduce an Augmented Ordered Multi-valued Decision Diagram (OMDD-A) to obtain the EHC of a network in which both devices and links may fail. The OMDD-A approach can compute the EHC of a 2´100 grid network with 299 paths, which is unsolvable using existing techniques. We show that OMDD-A generates significantly fewer nodes than the corresponding ordered binary decision diagram, leading to large reductions in processing time.