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In this paper we give an algorithm to generate all distributions of distinguishable objects to bins without repetition. Our algorithm generates each distribution in constant time. To the best of our knowledge, our algorithm is the first algorithm which generates each solution in O(1) time in the ordinary sense. As a byproduct of our algorithm, we obtain a new algorithm to enumerate all multiset partitions when the number of partitions is fixed and the partitions are numbered. In this case, the algorithm generates each multiset partitions in constant time (in the ordinary sense). Finally, we extend the algorithm to the case when the bins have priorities associated with them. Overall space complexity of the algorithm is O(mklgn), where there are m bins and the objects fall into k different classes. In a companion paper, the generation of all distributions of identical objects to bins is also considered. [ABSTRACT FROM AUTHOR]

The aim of this paper is to exploit the algorithms of paper Experimental Math. 8 (1999) in order to produce a new algebraic method for computing efficiently absolute Lagrange resolvent, a fundamental tool in constructive algebraic Galois theory. This article is composed of two parts.The main idea of the first part is to break up the calculation of absolute resolvent into smaller computations. Since a multi-resolvent is a factor of a resolvent, the whole resolvent may be computed by means of several multi-resolvents.The idea of the second part is that an irreducible polynomial over Z might be reducible over Z /pZ for certain integer p. So the first part can be applied and then, the Chinese remainder theorem allows to lift up the resolvent over Z. [Copyright &y& Elsevier]

In this paper, the maximal abelian dimension is computationally obtained for an arbitrary finite-dimensional Lie algebra, defined by its nonzero brackets. More concretely, we describe and implement an algorithm which computes such a dimension by running it in the symbolic computation package MAPLE. Finally, we also show a computational study related to this implementation, regarding both the computing time and the memory used. [ABSTRACT FROM AUTHOR]

Abstract: The coefficient of fragmentability of a class of graphs measures the proportion of vertices that need to be removed from the graphs in the class in order to leave behind bounded sized components. We have previously given bounds on this parameter for the class of graphs satisfying a given constant bound on maximum degree. In this paper, we give fragmentability bounds for some classes of graphs of bounded average degree, as well as classes of given thickness, the class of -colourable graphs, and the class of n-dimensional cubes. In order to establish the fragmentability results for bounded average degree, we prove that the proportion of vertices that must be removed from a graph of average degree at most in order to leave behind a planar subgraph (in fact, a series-parallel subgraph) is at most , provided or the graph is connected and . The proof yields an algorithm for finding large induced planar subgraphs and (under certain conditions) a lower bound on the size of the induced planar subgraph it finds. This bound is similar in form to the one we found for a previous algorithm we developed for that problem, but applies to a larger class of graphs. [Copyright &y& Elsevier]

In past studies, the digital straight-line segment is defined as a figure approximating the straight-line segment in the continuous space, by grid points in the discrete space. Because of this definition, the properties of the segment vary depending on the approximation process, which prevented the development of a general discussion. For this problem, the authors introduced a topology into the discrete space, and defined the digital straight-line segment using only the topology. As a result, the digital straight-line segment can be defined generally for various spaces and topologies, and the properties of the segment can be analyzed. In this paper, the properties of the digital straight-line segment are analyzed based on the 5-neighborhood concept. As the first step, the assertion that characterizes the digital straight-line segment, as well as five equivalent assertions are presented. Then, it is shown that by using those assertions, the corresponding segment generation algorithm can easily be obtained, and the figure generated by the segment generation algorithm which is known in the CG technology is the same as the proposed digital straight-line segment. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(6): 16–26, 1998 [ABSTRACT FROM AUTHOR]

This paper discusses the problems of finding one of the largest similar substructures in tree Tb to tree Ta, where both Ta and Tb are rooted and ordered trees (RO-trees) or unrooted and cyclically ordered trees (CO-trees). A maximal closest common ancestor mapping and a largest similar substructure in Tb to Ta based on this mapping are defined and two algorithms are proposed for finding one of the largest similar substructures for RO-trees and that for CO-trees. The time and space complexities of the algorithm for RO-trees are OT(NaNb) and OS(NaNb), respectively; and those of the algorithm for CO-trees are OT(mambNaNb) and OS((ma + mb)NaNb), respectively, where ma(mb) and Na(Nb) are the largest degree of a vertex and the number of vertices of Ta(Tb), respectively. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(2): 92–104, 1997 [ABSTRACT FROM AUTHOR]