Enumerating Stereoisomers of Tree Structured Molecules Using Dynamic Programming

Journal of Discrete Algorithms

2014

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An unranking algorithm for a finite set S is an algorithm that, given a number in {0, 1, . . . , |S| − 1}, returns an element of S that is associated with the number. We suppose that a number can be associated with any element in S so long as distinct elements are associated with different numbers. A ranking algorithm is the reverse of an unranking algorithm. In this paper, we present an unranking algorithm for the set of all m-element subsets of an n-element set. Our algorithm runs with O (m 3m+3 ) arithmetic operations, which is independent of n and hence is effective when n is large. We also show that it admits a ranking algorithm with the same running time.

Section: Introductionmentioning

confidence: 99%

“…A number of enumeration algorithms are known for C (n, m) (for examples, see [6,12,22]). They have many applications, including data mining [1,2], artificial intelligence [7,23], operations research [3,11,15,17,18,24], and bioinformatics [4,9,10]. However, there are several situations in which they are not useful.…”

Section: Introductionmentioning

confidence: 99%

Unranking of small combinations from large sets

Shimizu

Fukunaga²,

Journal of Discrete Algorithms

2014

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“…As an application of our result, we consider rooted outerplanar graphs with vertex and edge labelings. Recently computational enumeration of chemical compounds has been studied extensively [4], [7]- [9], [11], [12]. A chemical compound is modeled as a graph with vertex and edge labelings such that each vertex label represents a kind of atom, such as a carbon, nitrogen, and so on, and each edge label represents the multiplicity of a bond between two atoms.…”

Section: Introductionmentioning

confidence: 99%

Indexing All Rooted Subgraphs of a Rooted Graph

Imada

IEICE Trans. Inf. & Syst.

2012

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Let G be a connected graph in which we designate a vertex or a block (a biconnected component) as the center of G. For each cut-vertex v, let G v be the connected subgraph induced from G by v and the vertices that will be separated from the center by removal of v, where v is designated as the root of G v. We consider the set R of all such rooted subgraphs in G, and assign an integer, called an index, to each of the subgraphs so that two rooted subgraphs in R receive the same indices if and only if they are isomorphic under the constraint that their roots correspond each other. In this paper, assuming a procedure for computing a signature of each graph in a class G of biconnected graphs, we present a framework for computing indices to all rooted subgraphs of a graph G with a center which is composed of biconnected components from G. With this framework, we can find indices to all rooted subgraphs of a outerplanar graph with a center in linear time and space.

“…Our research group has been developing algorithms for enumerating chemical graphs that satisfy given various constraints [6], [8], [9]. The pioneering work for enumerating chemical graphs performed by Caley [2] was dedicated to enumerating structural isomers of alkanes, and a century later several studies based on computational methods followed [3].…”

Section: Introductionmentioning

confidence: 99%

Generation of Symmetric and Asymmetric Biconnected Rooted Outerplanar Graphs

Zhuang

IEICE Trans. Inf. & Syst.

2011

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Bingbing ZHUANG†a) , Nonmember and Hiroshi NAGAMOCHI †b) , Member SUMMARYIn a rooted graph, a vertex is designated as its root. An outerplanar graph is represented by a plane embedding such that all vertices appear along its outer boundary. Two different plane embeddings of a rooted outerplanar graphs are called symmetric copies. Given integers n ≥ 3 and g ≥ 3, we give an O(n)-space and O(1)-time delay algorithm that generates all biconnected rooted outerplanar graphs with exactly n vertices such that the size of each inner face is at most g without delivering two symmetric copies of the same graph.