A robust method for searching the smallest set of smallest rings with a path-included distance matrix

Abstract

The perception of rings in graphs is widely used in many fields of science and engineering. Algorithms developed in the chemistry community, called smallest set of smallest rings (SSSR), applicable only for simple graphs or chemical structures. In contrast, algorithms developed by the computer science community, called minimum cycle basis (MCB) are identical to SSSR yet exhibit greater robustness. MCB-based algorithms can correctly reveal all rings in any complex graph. However, they are slow when applied to large complex graphs due to the inherent limitations of the algorithms used. Here, we suggest a heuristic method called RP-Path. This method is a robust, simple, and fast search method with O ( n 3 ) runtime algorithm that correctly identifies the SSSR of all of the test case of complex graphs by using approach different from the MCB-based method. Both the robustness and improvement in speed are achieved by using a path-included distance matrix and describing the characteristic features of rings in the matrix. This method is accurate and faster than any other methods and may find many application in various fields of science and engineering that use complicated graphs with thousands of nodes.

SmilesDrawer: Parsing and Drawing SMILES-Encoded Molecular Structures Using Client-Side JavaScript

“…Smallest set of smallest ring discovery is implemented applying a robust algorithm based on path-included distance matrices . Once atoms have been positioned, overlaps are resolved by rotating rotatable bonds where the resulting positions yield a lower overlap score.…”

“…Smallest set of smallest ring discovery is implemented applying a robust algorithm based on path-included distance matrices. 30 , where l is the optimal bond length.…”

Magnetically Induced Current Density Spatial Domains

“…This complex information is provided by the SCGs. For each SCG an algorithm has been adapted from a recently developed method for the search of the smallest set of smallest rings (SSSR), 52 which provides all the circuits connecting the saddle nodes. With respect to the SSSR, our algorithm exploits also the versus of each connection, which helps greatly to accomplish the task.…”

Machine Learning Predicts Degree of Aromaticity from Structural Fingerprints

“…This method, however, does not consider the individual rings within fused systems and an additional step was added to dissect fused aromatic systems. This was based on the smallest set of smallest rings (SSSR) approach, 34 a methodology for determining the most efficient set of possible rings in a molecule that algorithmically returns a set of ringsidentified by sets of atoms and bonds within the larger structure comparable to that identified by an expert chemist. Therefore, the aromaticity is calculated for each of the rings in the SSSR 34 of the fused aromatic system and for the envelope ring if it is not present in the SSSR.…”