Next Article in Journal
A General Principle of Isomorphism: Determining Inverses
Previous Article in Journal
Approximation of a Linear Autonomous Differential Equation with Small Delay
Open AccessArticle

A Symmetry-Breaking Node Equivalence for Pruning the Search Space in Backtracking Algorithms

Faculty of Computer and Information Science, University of Ljubljana, Večna pot 113, 1000 Ljubljana, Slovenia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(10), 1300; https://doi.org/10.3390/sym11101300
Received: 6 September 2019 / Revised: 10 October 2019 / Accepted: 13 October 2019 / Published: 15 October 2019
We introduce a new equivalence on graphs, defined by its symmetry-breaking capability. We first present a framework for various backtracking search algorithms, in which the equivalence is used to prune the search tree. Subsequently, we define the equivalence and an optimization problem with the goal of finding an equivalence partition with the highest pruning potential. We also position the optimization problem into the computational-complexity hierarchy. In particular, we show that the verifier lies between P and NP -complete problems. Striving for a practical usability of the approach, we devise a heuristic method for general graphs and optimal algorithms for trees and cycles. View Full-Text
Keywords: Graph equivalence; Symmetry breaking; Backtracking; Monomorphism search; Search tree pruning; Graph algorithm Graph equivalence; Symmetry breaking; Backtracking; Monomorphism search; Search tree pruning; Graph algorithm
Show Figures

Figure 1

MDPI and ACS Style

Čibej, U.; Fürst, L.; Mihelič, J. A Symmetry-Breaking Node Equivalence for Pruning the Search Space in Backtracking Algorithms. Symmetry 2019, 11, 1300.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop