scholarly journals The Subgraph Isomorphism Problem on a Class of Hyperedge Replacement Languages

2014 ◽  
pp. 192-206 ◽  
Author(s):  
H. N. de Ridder ◽  
N. de Ridder
Keyword(s):  
Isomorphism Problem ◽  
Subgraph Isomorphism ◽  
Hyperedge Replacement

scholarly journals Diamond Subgraphs in the Reduction Graph of a One-Rule String Rewriting System

2021 ◽  
Vol 178 (3) ◽  
pp. 173-185
Author(s):  
Arthur Adinayev ◽  
Itamar Stein
Keyword(s):  
Isomorphism Problem ◽  
Complete Characterization ◽  
Hasse Diagram ◽  
Subgraph Isomorphism ◽  
Rewriting Systems ◽  
Rewriting System ◽  
String Rewriting ◽  
Reduction Graph

In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice Mk (the unique lattice with k + 2 elements and one anti-chain of length k) and find the maximal k for which it is isomorphic to a subgraph of the reduction graph of a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such k is 2 and there are cases where there is no maximum. No other intermediate option is possible.

Investigation of incremental hybrid genetic algorithm with subgraph isomorphism problem

2019 ◽  
Vol 49 ◽  
pp. 75-86 ◽  
Author(s):  
HyukGeun Choi ◽  
Jinhyun Kim ◽  
Yourim Yoon ◽  
Byung-Ro Moon
Keyword(s):  
Genetic Algorithm ◽  
Hybrid Genetic Algorithm ◽  
Isomorphism Problem ◽  
Subgraph Isomorphism

scholarly journals A Convex Relaxation Bound for Subgraph Isomorphism

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Christian Schellewald
Keyword(s):  
Lower Bound ◽  
Structural Information ◽  
Convex Relaxation ◽  
Maximum Clique ◽  
Combinatorial Problem ◽  
Isomorphism Problem ◽  
Maximum Clique Problem ◽  
Subgraph Isomorphism ◽  
Semidefinite Programming Relaxation ◽  
Problem Instances

In this work a convex relaxation of a subgraph isomorphism problem is proposed, which leads to a new lower bound that can provide a proof that a subgraph isomorphism between two graphs can not be found. The bound is based on a semidefinite programming relaxation of a combinatorial optimisation formulation for subgraph isomorphism and is explained in detail. We consider subgraph isomorphism problem instances of simple graphs which means that only the structural information of the two graphs is exploited and other information that might be available (e.g., node positions) is ignored. The bound is based on the fact that a subgraph isomorphism always leads to zero as lowest possible optimal objective value in the combinatorial problem formulation. Therefore, for problem instances with a lower bound that is larger than zero this represents a proof that a subgraph isomorphism can not exist. But note that conversely, a negative lower bound does not imply that a subgraph isomorphism must be present and only indicates that a subgraph isomorphism can not be excluded. In addition, the relation of our approach and the reformulation of the largest common subgraph problem into a maximum clique problem is discussed.

Feature Based Search of 3D Databases

2016 ◽  
Author(s):  
Duncan Paterson ◽  
Johnathan Corney
Keyword(s):  
Model Comparison ◽  
Isomorphism Problem ◽  
Graph Representation ◽  
Subgraph Isomorphism ◽  
Target Feature ◽  
Adjacency Graph ◽  
Retrieval Systems ◽  
Experimental Implementation ◽  
3D Databases ◽  
Feature Based

This paper presents a novel algorithm “Twig Match” for feature based shape retrieval systems. The algorithm exploits recent advances in computational methods for subgraph isomorphism, in order to enable databases containing many thousands of components to be searched in less than a second. A face adjacency graph representation is created from a B-Rep model, allowing model comparison to be treated as a labelled subgraph isomorphism problem. This paper describes an experimental implementation which allows interactive specification of a target “feature”. By selectively including geometric filters, on faces and relations between neighbouring faces, the algorithm can ensure that matching topology is not incorrectly identified as matching geometry, while also offering users the ability to improve the precision of both query and results. Experimental results show that Twig Match accurately retrieves matching and similar sub-parts from collections at speeds suitable for interactive applications.

A Backtracking Algorithmic Toolbox for Solving the Subgraph Isomorphism Problem

2021 ◽  
pp. 208-246
Author(s):  
Jurij Mihelič ◽  
Uroš Čibej ◽  
Luka Fürst
Keyword(s):  
Independent Set ◽  
Isomorphism Problem ◽  
Lessons Learned ◽  
Subgraph Isomorphism ◽  
Graph Pattern Matching ◽  
Practical Applications ◽  
Graph Pattern ◽  
Complete Problems ◽  
Constraint Satisfaction Programming ◽  
Core Problem

The subgraph isomorphism problem asks whether a given graph is a subgraph of another graph. It is one of the most general NP-complete problems since many other problems (e.g., Hamiltonian cycle, clique, independent set, etc.) have a natural reduction to subgraph isomorphism. Furthermore, there is a variety of practical applications where graph pattern matching is the core problem. Developing efficient algorithms and solvers for this problem thus enables good solutions to a variety of different practical problems. In this chapter, the authors present and experimentally explore various algorithmic refinements and code optimizations for improving the performance of subgraph isomorphism solvers. In particular, they focus on algorithms that are based on the backtracking approach and constraint satisfaction programming. They gather experiences from many state-of-the-art algorithms as well as from their engagement in this field. Lessons learned from engineering such a solver can be utilized in many other fields where backtracking is a prominent approach for solving a particular problem.

Sign in / Sign up

Export Citation Format

Share Document