Parallel solutions of indexed recurrence equations

Y. Ben-Asher, G. Haber
Proceedings 11th International Parallel Processing Symposium  
A new type of recurrence equations called "indexed recurrences" (IR) is defined, in which the common notion of X i = opX i ; X i ,1 i = 1 : : : nis generalized to X gi = opX fi ; X h i f;g;h : f1: : : n g 7 ! f 1 : : : m g . This enables us to model sequential loops of the form for i = 1 to n do begin X gi := opX fi ;X h i ; as IR equations. Thus, a parallel algorithm that solves a set of IR equations is in fact a way to transform sequential loops into parallel ones. Note that the circuit
more » ... t the circuit evaluation problem (CVP) can also be expressed as a set of IR equations. Therefore an efficient parallel solution to the general IR problem is not likely to be found, as such solution would also solve the CVP, showing that P NC. In this paper we introduce parallel algorithms for two variants of the IR equations problem: An Olog n greedy algorithm for solving IR equations where gi is distinct and hi = gi using On processors. An Olog 2 n algorithm with no restriction on f;gor h, using up to On 2 processors. However, we show that for general IR, op must be commutative so that a parallel computation can be used.
doi:10.1109/ipps.1997.580935 dblp:conf/ipps/HaberB97 fatcat:oz3ux6yfdzc5hf2vgts5xhwhc4