Generating all distributions of objects to bins

Authors:
Muhammad Abdullah Adnan;Md. Saidur Rahman
Affiliations:
Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh;Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh
Venue:
International Journal of Computer Mathematics
Year:
2009

Citing 9
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Abstract

In this paper, we give an elegant algorithm to generate all distributions of n identical objects to m bins without repetition. The best known previous algorithm, due to Klingsberg, generates each distribution in constant time in average sense. Using a new technique of efficient tree traversal, in this paper we improve the time complexity to constant time (in ordinary sense). By modifying our algorithm, we can generate the distributions in anti-lexicographic order. Overall space complexity of our algorithm is O(mlgn), where m is the number of bins and n is the number of objects.