A Graph-Theoretic Algorithm for Matching Chemical Structures.

Sussenguth, Edward H.

doi:10.1021/c160016a007

Cited by 157 publications

(78 citation statements)

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“…Second, a lot of effort has gone into the development of algorithms that can handle chemical graphs, as against graphs in general, very efficiently, with the elegant matching techniques described by Sussenguth (1965) and by Ullmann (1976) lying at the heart of current substructure searching systems.…”

Section: X23 Searching For Chemical Substructuresmentioning

confidence: 99%

Representation and Searching of Chemical Structure Information in Patents

Downs¹,

Holliday²,

Willett³

2017

Current Challenges in Patent Information Retrieval

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This chapter describes the techniques that are used to represent and to search for molecular structures in chemical patents. There are two types of structures: specific structures that describe individual molecules; and generic structures that describe sets of structurally related molecules. Methods for representing and searching specific structures have been well established for many years, and the techniques are also applicable, albeit with substantial modification, to the processing of generic structures.

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Section: X23 Searching For Chemical Substructuresmentioning

confidence: 99%

Representation and Searching of Chemical Structure Information in Patents

Downs¹,

Holliday²,

Willett³

2017

Current Challenges in Patent Information Retrieval

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“…Since loops and edges of two isomorphic graphs are in one-to-one correspondence and preserve adjacency, therefore, (2)(3)(4)(5)(6)(7)(8) Here [E.e] is the lopp elementary matrix which transforms the loops in graph 1 and graph 2. From Eq.…”

Section: Johnson and Towfigh [45] Applied The Number Synthesis Technimentioning

confidence: 99%

“…The number of linear graphs having 5 vertices and 6 edges (including fine and heavy edges) can be obtained from the coefficient 6 4 of x y of the cycle index of full-pair group, R 5 (x,y), and is equal to 6 [57]. Reje·ctedl (Rule l)…”

Section: Cam Kinematic Chainsmentioning

confidence: 99%

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Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains

Huang

Soni

1973

Journal of Engineering for Industry

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Using graph theory and Polya’s theory of counting, the present paper performs structural synthesis and analysis of planar and three-dimensional kinematic chains. The Section 2 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of planar kinematic chains with kinematic elements such as revolute pairs, cam pairs, springs, belt-pulley, piston-cylinder, and gears. The theory developed is applied to enumerate eight-link kinematic chains with these kinematic elements. The Section 3 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of multi-loop spatial kinematic chains with higher and lower kinematic pairs. The theory developed is applied to enumerate all possible two-loop kinematic chains with or without general constraints.

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“…Cycle bases have been used in the field of electrical networks since the time of Kirchoff [2]. Interest in minimum FCBs arises in a variety of application fields, such as electrical circuit testing [3], generating minimal perfect hash functions (used in compiler design) [4], planning cyclic timetables [5,6], coding of ring compounds [7] and planning complex syntheses in organic chemistry [8]. Many of the early results about the graph-theoretical structure of FCBs are due to a sequence of papers by Sys lo [9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Edge-swapping algorithms for the minimum fundamental cycle basis problem

et al. 2008

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We consider the problem of finding a fundamental cycle basis with minimum total cost in an undirected graph. This problem is NP-hard and has several interesting applications. Since fundamental cycle bases correspond to spanning trees, we propose a local search algorithm, a tabu search and variable neighborhood search in which edge swaps are iteratively applied to a current spanning tree. We also present a mixed integer programming formulation of the problem whose linear relaxation yields tighter lower bounds than other known formulations. Computational results obtained with our algorithms are compared with those from the best available constructive heuristic on several types of graphs. 1

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A Graph-Theoretic Algorithm for Matching Chemical Structures.

Cited by 157 publications

References 0 publications

Representation and Searching of Chemical Structure Information in Patents

Representation and Searching of Chemical Structure Information in Patents

Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains

Edge-swapping algorithms for the minimum fundamental cycle basis problem

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