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![Fig. 4, Some edges of a balanced edge-cut K=[S,S]. Edges from Y to X...](profile/William-Kocay/publication/254397943/figure/fig2/AS:651112730345480@1532248780779/Some-edges-of-a-balanced-edge-cut-KS-S-Edges-from-Y-to-X-are-not-shown_Q320.jpg)
The Balanced Network Search (BNS) is an algorithm which finds a maximum balanced flow in a balanced network N. This algorithm is a way of using network flows to solve a number of standard problems, including maximum matchings, the factor problem, maximum capacitated b-matchings, etc., in general graphs. The value of a maximum balanced flow equals t...
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Citations
... The normalization and the stereochemical perception stages rely heavily on testing whether a bond order can be changed due to the presence of an alternating bond circuit, as well as the possibility of a hydrogen atom, charge, or radical center to migrate along a path of alternating bonds. This testing is based on a matching algorithm described in detail in ref. [35]. ...
This paper documents the design, layout and algorithms of the IUPAC International Chemical Identifier, InChI.
... The tautomer information can be obtained from various algorithms [9]. The InChI system calculates the mobile hydrogen using an intrinsic tautomer detection algorithm based on balanced network searches (BNS) [10]. However, the accuracy of the tautomer detection algorithms is still controversial, so instead of using a tautomer detection algorithm, yaInChI uses tautomer information from the input file. ...
A modified InChI (International Chemical Identifier) string scheme, yaInChI (yet another InChI), is suggested as a method for including the structural information of a given molecule, making it straightforward and more easily readable. The yaInChI theme is applicable for checking the structural identity with higher sensitivity and generating three-dimensional (3-D) structures from the one-dimensional (1-D) string with less ambiguity than the general InChI method. The modifications to yaInChI provide non-rotatable single bonds, stereochemistry of organometallic compounds, allene and cumulene, and parity of atoms with a lone pair. Additionally, yaInChI better preserves the original information of the given input file (SDF) using the protonation information, hydrogen count +1, and original bond type, which are not considered or restrictively considered in InChI and SMILES. When yaInChI is used to perform a duplication check on a 3D chemical structure database, Ligand.Info, it shows more discriminating power than InChI. The structural information provided by yaInChI is in a compact format, making it a promising solution for handling large chemical structure databases.
... The normalization and the stereochemical part heavily relies on testing whether a bond order can be changed due to presence of an alternating bond circuit or possibility of a hydrogen atom, charge, or radical center to migrate along a path of alternating bond. This testing is based on matching algorithm described in details in [4]. ...
We discuss a wide range of matching problems in terms of a network flow model. More than this, we start up a matching theory which is very intuitive and independent from the original graph context. This first paper contains a standardized theory for the performance analysis of augmentation algorithms in a wide area of matching problems. Several optimality criteria are given which do not use cuts or barriers. As an application of our theory, the known cardinality matching algorithms of Edmonds, Kameda and Munro, and Micali and Vazirani, and the algorithm of Kocay and Stone for capacitated matching problems can be studied in their effects. From our theory a c-capacitated b-matching algorithm can be derived that behaves like the Dinic algorithm for the maximum flow problem. It will turn out that techniques for the maximum flow problem can be applied to matching problems much more explicitly than done before. A comprehensive duality theory depending on the network flow model used here will follow. Explicit algorithms for nonweighted problems will be presented in subsequent papers. © 1999 John Wiley & Sons, Inc. Networks 33: 1–28, 1999
In previous papers, we discussed the fundamental theory of matching problems and algorithms in terms of a network flow model. In this paper, we present explicit augmentation procedures which apply to the wide range of capacitated matching problems and which are highly efficient for k-factor problems and the f-factor problem. © 1999 John Wiley & Sons, Inc. Networks 33: 29–41, 1999
