Parallelization of Graph Mining using Backtrack Search Algorithm

This paper describes parallel implementations of a highly complex graph mining problem to extract Common Itemset connected subGraphs (CIGs) from a graph whose vertices are labeled by their own sets of items, or itemsets in short. The problem is to extract all connected subgraphs in a given graph, each of which satisfies that the cardinality of its common itemset, i.e., the intersection of the itemsets of all of its vertices, is not less than a given threshold. Our implementations are to parallelize this mining problem for both shared and distributed memory environments. This kind of graph mining can be applied to the analysis of social and biological networks. An efficient sequential backtrack search algorithm named COPINE has already been proposed for this problem. COPINE avoids unnecessary searches using a pruning mechanism that depends on the knowledge acquired during the leftand depth-first traversal of its search tree. In a parallel search where a unique set of subtrees is assigned to each worker as its task, the branches in the subtrees must be pruned as well for efficiently reducing the search space, but not excessively by a blind consultation of the knowledge acquired by another worker. To avoid such excessive pruning, we found a restriction imposed on the workers when referring to the knowledge acquired by other workers. In consideration of this restriction, we designed a parallel extension of COPINE. Because the search trees in COPINE have an irregular structure, dynamic load balancing should be applied in parallelized implementations. Applications with these properties are often implemented by task-parallel languages, by which we can dynamically spawn tasks to be automatically assigned to workers as parallel threads and/or processes. We implemented the parallel COPINE algorithm using the task-parallel language Tascell, which offers high performance in various backtrack search algorithms. The parallel COPINE algorithm requires workers to share the acquired knowledge for the pruning mechanism. For shared memory environments, we implemented a sharing method in which a single table controlled by locks is shared among all workers. This method enables workers to refer to the knowledge acquired by another worker immediately. In addition, we proposed a task creation strategy whereby useful pruning knowledge can be acquired as early as possible in a parallel search. On the implementation of this algorithm in distributed memory environments, we should consider the cost of internode communication. The sharing method shown above is impractical in distributed memory environments because internode communication is required every time a worker acquires new knowledge. Therefore, we also implemented a sharing method in which each computing node manages its own table and sends table updates to other nodes periodically. Furthermore, the conventional work-stealing strategy in Tascell, which aims to minimize the number of internode work-steals, could cause a load imbalance by increasing the number of intranode work-steals for small tasks. We solved this problem by implementing new workstealing strategies in Tascell to enable workers to obtain larger tasks.