Parallel Data Structures for Symbolic Computation

Symbolic applications often require dynamic irregular data structures, such as linked lists, unbalanced trees, and graphs, and they exhibit unpredictable computational patterns that lead to asynchronous communication and load imbalance when parallelized. In this paper we describe several symbolic applications and their parallelizations. The main problem in parallelization of each application was to replace the primary data structures with parallel versions that allow for high throughput, low latency access. In each case there are two problems to be solved: load balancing the parallel computation and sharing information about the solution as it is being constructed. The rst problem is typically solved using a scheduling data structure, a stack, queue, or priority queue in sequential programs. The diiculty in parallelizing these structure is the trade-oo between locality and load balancing: aggressive load balancing can lead to poor locality. The second problem of storing the solution depends much more on the type of solution, but range from simple scalar values to sets or tables. These structures use partitioning, full replication, or dynamic caching in their parallelizations. In sequential programming environments, common data structures are often provided through reusable libraries. We have built a parallel analog to these libraries, called Multipol. Multipol support irregular and asynchronous applications, including symbolic applications, discrete event simulation, and adaptive algorithms. The performance issues in Multipol include masking remote latency, elimination of communication, load balance, performance portability across machines, and local node performance.