A Message-Passing Based Algorithm for k-Terminal Reliability

As the exact computation of the k-terminal reliability is an NP-Complete problem, runtime and memory requirements grow exponentially with the input size. Shared memory parallelization algorithms were developed for reducing runtime. However, even a relatively high amount of memory can already be exhausted within a short period of time. A message-passing based algorithm is proposed in order to circumvent the memory limitation of shared memory implementations. It is the first message-passing based algorithm for the k-terminal problem. The new algorithm is designed for the currently most efficient BDD-based method. New data structures such as the distributed BDD and a distributed hash table lead to good speedup results and load-balanced task distributions. Now the size of computable inputs are limited to the memory carried along by the available cores. The two-terminal reliability of a 17 node complete network was computed on 1024 cores of the SuperMUC within 7 minutes, using 1.28 Terabyte of memory and resulting in more than 6 billion BDD nodes.