Parallel generation of t-ary trees in A-order

We present a cost-optimal and adaptive parallel algorithm for generating t-ary trees in A-order. The generation is based on an encoding using integer sequences (z-sequences) due to Zaks [(1980), Lexicographic generation of ordered tree. Theor. Comput. Sci., 10, 63-82]. Our algorithm is the first introduced parallel generation algorithm, which generates t-ary trees in A-order in the literature. The used computational model is CREW SM SIMD multi-processors. This algorithm is designed based on a novel sequential generation algorithm that is also discussed. Ranking and unranking algorithms for z-sequences are also presented.