This paper discusses the compile time task scheduling of parallel program running on cluster of SMP workstations. Firstly, the problem is stated formally and transformed into a graph partition problem and proved to be NP-Complete. A heuristic algorithm MMP-Solver is then proposed to solve the problem. Experiment result shows that the task scheduling can reduce communication overhead of parallel applications greatly and MMP-Solver outperforms the existing algorithms.
As far as we know, the testing problem of legal firing sequence is NP-complete for general Petri net, the related results of this problem on the polynomial-time solvability are limited only to some special net classes, such as persistent Petri nets, conflict-free Petri nets and state machine Petri nets. In this paper, the language properties of synchronous composition net are discussed. Based on these results, the testing algorithm polynomial-time complexity for legal firing sequence is proposed. Therefore, net classification of polynomial-time solvability for testing legal firing sequence is extended.
