Resource Cut, a New Bounding Procedure to Algorithms for Enumerating Tree-Like Chemical Graphs

Area of Science:

• Computational Chemistry
• Graph Theory
• Drug Design

Background:

• Enumerating chemical compounds is crucial for structure elucidation and drug design.
• Chemical graphs and feature vectors (path frequencies) are used to represent compounds.
• Existing branch-and-bound algorithms face challenges in efficiently enumerating these structures.

Purpose of the Study:

• To propose a novel bounding procedure, Resource Cut, to accelerate the enumeration of tree-like chemical graphs.
• To improve the efficiency of generating unique vertex-colored trees representing chemical compounds.
• To address the issue of constructing non-extendable trees during the enumeration process.

Main Methods:

• Modeling tree-like chemical graphs as vertex-colored trees, where colors represent chemical elements.
• Developing and applying a branch-and-bound algorithm enhanced with the Resource Cut bounding procedure.
• Deriving a mathematical condition to identify and prune unextendable tree structures.

Main Results:

• The Resource Cut procedure significantly reduces the search space during graph enumeration.
• The method enables the exact counting of chemical graphs up to 17 vertices (excluding hydrogen).
• Successfully identified and discarded non-unique or unextendable tree constructions.

Conclusions:

• Resource Cut is an effective method for speeding up the enumeration of chemical graphs.
• This advancement aids in the accurate characterization of chemical compound structures.
• The findings contribute to more efficient computational approaches in drug discovery and materials science.