Parallel Interval Order Recognition and Construction of Interval Representations

Parallel algorithms for recognizing and representing interval orders are proposed for differ. ent models of parallel random access machines (PRAM). The algorithms accept as input a transitively~losed directed graph with N nodes and M edges. They run in time O0og N) with O(N + M~ processors and O{N + M} space and in co , tam time with O(N z) proces~rs and O{N ~) space depending on the data structure and the PRAM model used. Optimal probabiliP tic algorithms for PRAM are also presented as well as algorithms for dis!ributed.memory machines.