Parallelization of Extracting Connected Subgraphs with Common Itemsets

抄録

This paper proposes a parallel algorithm to extract all connected subgraphs, each of which shares a common itemset whose size is not less than a given threshold, from a given graph in which each vertex is associated to an itemset. We also propose implementations of this algorithm using the task-parallel language Tascell. This kind of graph mining can be applied to analysis of social or biological networks. We have already proposed an efficient sequential search algorithm called COPINE for this problem. COPINE reduces the search space of a dynamically growing tree structure by pruning its branches corresponding to the following subgraphs; already visited, having itemsets smaller than the threshold, and having already-visited supergraphs with identical itemsets. For the third pruning, we use a table associating already-visited subgraphs and their itemsets. To avoid excess pruning in a parallel search where a unique set of subtrees (tasks) is assigned to each worker, we should put a certain restriction on a worker when it is referring to a table entry registered by another worker. We designed a parallel algorithm as an extension of COPINE by introducing this restriction. A problem of the implementation is how workers efficiently share the table entries so that a worker can safely use as many entries registered by other workers as possible. We implemented two sharing methods: (1) a victim worker makes a copy of its own table and passes it to a thief worker when the victim spawns a task by dividing its task and assigns it to the thief, and (2) a single table controlled by locks is shared among workers. We evaluated these implementations using a real protein network. As a result, the single table implementation achieved a speedup of approximately a factor four with 16 workers.