Regular versus Irregular Problems and Algorithms

Viewing a parallel execution as a set of tasks that execute on a set of processors, a main problem is to nd a schedule of the tasks that provides an eecient execution. This usually leads to divide algorithms into two classes: static and dynamic algorithms, depending on whether the schedule depends on the indata or not. To improve this rough classiication we study, on some key applications of the Stratag eme project 21, 22], the diierent ways schedules can be obtained and the associated overheads. This leads us to propose a classiication based on regularity criteria i.e. measures of how much an algorithm is regular (or irregular). For a given algorithm, this expresses more the quality of the schedules that can be found (irregular versus regular) as opposed to the way the schedules are obtained (dynamic versus static). These studies reveal some paradigms of parallel programming for irregular algorithms. Thus, in a second part we study a parallel programming model that takes into account these paradigms to free the user from task scheduling. An implementation, PAC++, is presented.