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1987]. \Analytic Variations on the Common Subexpression Problem
 Proceedings of the 17th Annual International Colloquium on Automata, Languages, and Programming (ICALP
, 1990
"... Abstract. Any tree can be represented in a max/ma//y compact form as a directed acyclic graph where common subtrees are factored and shared, being represented only once. Such a compaction can be effected in linear time. It is used to save storage in implementations of functional programming language ..."
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Cited by 11 (3 self)
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Abstract. Any tree can be represented in a max/ma//y compact form as a directed acyclic graph where common subtrees are factored and shared, being represented only once. Such a compaction can be effected in linear time. It is used to save storage in implementations of functional programming languages, as well as in symbolic manipulation and computer a/gebra systems. In compiling, the compaction problem is known as the "common subexpression problem " and it plays a central r61e in register allocation, code generation and optimisation. We establish here that, under a variety of probabilistic models, a tree of size n has a compacted form of expected size asymptotically n C.ogWi ' where the constant C is explicitly related to the type of trees to be compacted and to the statistical model reflecting tree usage. In particular the savings in storage approach 100 % on average for large structures, which overperforms the commonly used form of sharing that is restmcted to leaves (atoms). Introduction. A tree can be compacted by representing occurrences of repeated subtrees only once. In that case, several pointers will point to the representation of any common subtree,
Lazy Multiplication of Formal Power Series
, 1997
"... For most fast algorithms to manipulate formal power series, a fast multiplication algorithm is essential. If one desires to compute all coefficients of a product of two power series up to a given order, then several efficient algorithms are available, such as fast Fourier multiplication. However, on ..."
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Cited by 6 (4 self)
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For most fast algorithms to manipulate formal power series, a fast multiplication algorithm is essential. If one desires to compute all coefficients of a product of two power series up to a given order, then several efficient algorithms are available, such as fast Fourier multiplication. However, one often needs a lazy multiplication algorithm, for instance when the product computation is part of the computation of the coefficients of an implicitly defined power series. In this paper, we describe two lazy multiplication algorithms, which are faster than the naive method. In particular, we give an algorithm of time complexity O(n log n).
Discrete Mathematics for Combinatorial Chemistry
, 1998
"... The aim is a description of discrete mathematics used in a project devoted to the implementation of a software package for the simulation of combinatorial chemistry. ..."
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Cited by 2 (1 self)
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The aim is a description of discrete mathematics used in a project devoted to the implementation of a software package for the simulation of combinatorial chemistry.
A Note On Counting Connected Graph Covering Projections
, 1998
"... . During the last decade, a lot of progress has been made in the enumerative branch of topological graph theory. Enumeration formulas were developed for a large class of graph covering projections. The purpose of this paper is to count graph covering projections of graphs such that the corresponding ..."
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. During the last decade, a lot of progress has been made in the enumerative branch of topological graph theory. Enumeration formulas were developed for a large class of graph covering projections. The purpose of this paper is to count graph covering projections of graphs such that the corresponding covering space is a connected graph. The main tool of the enumeration is Polya's theorem. Key words. graph covering, enumeration, Polya's theorem AMS subject classifications. 05C10, 05C30, 57M10 PII. S0895480195293873 1. Introduction. In this paper, we consider simple undirected graphs. As usual, the vertex set and the edge set of the graph G are denoted by V (G) and E(G), respectively. An rtoone graph epimorphism p : H # G which sends the neighbors of each vertex x # V (H) bijectively to the neighbors of p(x) # V (G) is called an rfold covering projection of G. The graph H is the covering graph, and the graph G is the base graph of p. Topologically speaking, p is a local hom...
Mathematics for Combinatorial Chemistry
"... Some of the mathematical methods will be described which are implemented in the software package MOLCOMB 1 that allows to simulate combinatorial chemistry by generating combinatorial libraries and to do screening according to geometric substructures. 1 Combinatorial Chemistry To begin with, we c ..."
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Some of the mathematical methods will be described which are implemented in the software package MOLCOMB 1 that allows to simulate combinatorial chemistry by generating combinatorial libraries and to do screening according to geometric substructures. 1 Combinatorial Chemistry To begin with, we consider the examples described in the prominent papers [1] and [2] on combinatorial chemistry. The authors introduce particular combinatorial libraries obtained by starting from the central molecules Cl Cl Cl Cl O O O O O Cl Cl Cl Cl O O O O Cl Cl O Cl O O i.e. they start from cubane, xanthene, benzene triacid chlorine as central molecules to which they attach amino acids according to the reaction scheme that describes the reaction between the active sites 1 MOLCOMB is the outcome of a research project supported by the federal ministery for technology, under contract 03 KE7BA 14 C 3 2 1 Cl O of the central molecule and the active parts of the aminoacids in question: C O 1 2 3 4 5 C...