In this paper a new parallel algorithm is presented for generation of t--ary trees. Computations run in an associative processor model.

In this paper an O(n) parallel algorithm is presented for fast unranking t--ary trees with n internal nodes in Zaks' representation.

This article surveys parallel generation algorithms for listing all combinatorial objects of certain type. The algorithms are designed for a very simple model, linear array of processors. The methods are divided into three groups: division of instances into groups, shared instances and combined methods.

A hardware-oriented algorithm for generating permutations is presented that takes as a theoretic base an iterative decomposition of the symmetric group Sn into cosets. It generates permutations in a new order. Simple ranking and unranking algorithms are given. The construction of a permutation generator is proposed which contains a cellular permutation network as a main component. The application of the permutation generator for solving a class of combinatorial problems on parallel computers is suggested.

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. Key words: ASC SIMD, t-ary trees, t-sequence, parallel enumeration, parallel generation;