Process Partitioning through Graph Compaction

Abstract

This paper is concerned with process partitioning that arises in practice in preprocessing of programs for the MIMD parallel machines without shared memory. The graph compaction combinatorial optimization problem is defined and proposed as a model of process partitioning. This problem is proved to be NP-complete. An efficient divide-and-conquer heuristic is given for the solution of the graph compaction problem. By a theoretical analysis based on a random graph model, it is shown that our heuristic produces nearly optimal solutions for an overwhelmingly large proportion of the problem instances of interest. It is shown experimentally that the heuristic compares favorably to heuristics based on commonly used design techniques (neighborhood search, simulated annealing) for random as well as for practical inputs. Since the proposed heuristic has drastically lower running times (seconds vs hours for partitioning about 1000 processes), the experimental results suggest that the algorithm-design approach on which it is based has an advantage over the mentioned approaches when, as in the case of parallel program compilation, good real-time response is desired.