Parallel Enumeration of t–ary Trees in ASC SIMD Model

In this paper parallel algorithms are presented for enumeration and unranking of t–ary trees with n internal nodes. Generation algorithms are designed in the associative computing model ASC that belongs to a broad category of SIMD models. Tree sequences are generated in lexicographical order, with O(1) time per object, in a new representation, as combinations with repetitions with restricted growth. The resulting full t–ary trees in the form of z–sequences and x–sequences appear in lexicographical and decreasing lexicographical order, respectively. Sequential O(n) ranking and O(nt) unranking algorithms for t–ary trees with n internal nodes are also described on the basis of dynamic programming paradigm. Parallel implementations of ranking and unranking algorithms are discussed. O(n) parallel unranking algorithm is derived in the ASC SIMD model.