Abstract
The presented research is devoted to the problem of developing new combinatorial generation algorithms for combinations. In this paper, we develop a modification of Ruskey’s algorithm for unranking m-combinations of an n-set in co-lexicographic order. The proposed modification is based on the use of approximations to make a preliminary search for the values of the internal parameter k of this algorithm. In contrast to the original algorithm, the obtained algorithm can be effectively applied when n is large and m is small because the running time of this algorithm depends only on m. Furthermore, this algorithm can be effectively used when n and m are both large but n−m is small, since we can consider unranking (n−m)-combinations of an n-set. The conducted computational experiments confirm the effectiveness of the developed modification.
Highlights
Introduction a Large Set in CoLexicographicCombinatorial algorithms are algorithms for investigating combinatorial structures.The development of combinatorial algorithms is one of the basic tasks in computer science [1,2]
Special attention is paid to the procedure for traversing all possible elements of a given combinatorial set
This paper focuses on unranking small m-combinations of a large n-set with using co-lexicographic order
Summary
The development of combinatorial algorithms is one of the basic tasks in computer science [1,2] Such algorithms provide efficient methods for processing information presented as a discrete structure. Special attention is paid to the procedure for traversing all possible elements of a given combinatorial set. This problem can be studied as enumerating (counting the total number of elements), listing (making and recording the complete list of all elements), and generating (constructing all the required elements and their sequential visiting) combinatorial objects [2]. Look at the generation of combinatorial objects in more detail since combinatorial generation algorithms are able to solve this problem [3]
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