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Listing combinatorial objects in parallel
"... 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 meth ..."
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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.
Ranking and Unranking of tary Trees Using the Right Distance Representation
"... In this paper, we introduce a concise representation, called rightdistance sequences (or RDsequences for short), to describe all tary trees with n internal nodes. A result reveals that there exists a close relationship between the representation and the wellformated integer sequences suggested b ..."
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In this paper, we introduce a concise representation, called rightdistance sequences (or RDsequences for short), to describe all tary trees with n internal nodes. A result reveals that there exists a close relationship between the representation and the wellformated integer sequences suggested by Zaks in 1980. Using recursion tree and its concomitant tables, a systematical way can help us to investigate the structural representation of tary trees. Consequently, we develop efficient algorithms for determining the rank of a given tary tree (i.e., ranking algorithm), and for converting a positive integer to its corresponding RDsequence (i.e., unranking algorithm). Both the ranking and unranking algorithms can be run in O(tn) time and without really building any auxiliary table. ∗ All correspondence should be addressed to Professor
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 ..."
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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, tary trees, tsequence, parallel enumeration, parallel generation;