### Abstract

A novel combinatorial optimization algorithm called 2-stage discrete optimization method (2DOM) is proposed for the largest common subgraph problem (LCSP) in this paper. Given two graphs G = (V_{1}, E_{1}) and H = (V_{2}. E_{2}), the goal of LCSP is to find a subgraph G′ = (V′_{1}, E′_{1}) of G and a subgraph H′ = (V′_{2},E′_{2}) of H such that G′ and H′ are not only isomorphic to each other but also their number of edges is maximized. The two graphs G′ and H′ are isomorphic when |V′_{1}| = |V′_{2}| and |E′_{1}| = |E′_{2}|, and there exists one-to-one vertex correspondence f : V′_{1} → V′_{2} such that {u, v} ∈ E′_{1} if and only if {f(u),/(w)} ∈ E′_{2}. LCSP is known to be NP-complete in general. The 2DOM consists of a construction stage and a refinement stage to achieve the high solution quality and the short computation time for large size difficult combinatorial optimization problems. The construction stage creates a feasible initial solution with considerable quality, based on a greedy heuristic method. The refinement stage improves it keeping the feasibility, based on a random discrete descent method. The performance is evaluated by solving two types of randomly generated 1200 LCSP instances with a maximum of 500 vertices for G and 1000 vertices for H. The simulation result shows the superiority of 2DOM to the simulated annealing in terms of the solution quality and the computation time.

Original language | English |
---|---|

Pages (from-to) | 1145-1153 |

Number of pages | 9 |

Journal | IEICE Transactions on Information and Systems |

Volume | E82-D |

Issue number | 8 |

Publication status | Published - 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Common subgraph
- Discrete descent method
- Greedy method
- Isomorphic
- NP-complete
- Simulated annealing

### ASJC Scopus subject areas

- Information Systems
- Computer Graphics and Computer-Aided Design
- Software

### Cite this

*IEICE Transactions on Information and Systems*,

*E82-D*(8), 1145-1153.

**A two-stage discrete optimization method for largest common subgraph problems.** / Funabiki, Nobuo; Kitamichi, Junji.

Research output: Contribution to journal › Article

*IEICE Transactions on Information and Systems*, vol. E82-D, no. 8, pp. 1145-1153.

}

TY - JOUR

T1 - A two-stage discrete optimization method for largest common subgraph problems

AU - Funabiki, Nobuo

AU - Kitamichi, Junji

PY - 1999

Y1 - 1999

N2 - A novel combinatorial optimization algorithm called 2-stage discrete optimization method (2DOM) is proposed for the largest common subgraph problem (LCSP) in this paper. Given two graphs G = (V1, E1) and H = (V2. E2), the goal of LCSP is to find a subgraph G′ = (V′1, E′1) of G and a subgraph H′ = (V′2,E′2) of H such that G′ and H′ are not only isomorphic to each other but also their number of edges is maximized. The two graphs G′ and H′ are isomorphic when |V′1| = |V′2| and |E′1| = |E′2|, and there exists one-to-one vertex correspondence f : V′1 → V′2 such that {u, v} ∈ E′1 if and only if {f(u),/(w)} ∈ E′2. LCSP is known to be NP-complete in general. The 2DOM consists of a construction stage and a refinement stage to achieve the high solution quality and the short computation time for large size difficult combinatorial optimization problems. The construction stage creates a feasible initial solution with considerable quality, based on a greedy heuristic method. The refinement stage improves it keeping the feasibility, based on a random discrete descent method. The performance is evaluated by solving two types of randomly generated 1200 LCSP instances with a maximum of 500 vertices for G and 1000 vertices for H. The simulation result shows the superiority of 2DOM to the simulated annealing in terms of the solution quality and the computation time.

AB - A novel combinatorial optimization algorithm called 2-stage discrete optimization method (2DOM) is proposed for the largest common subgraph problem (LCSP) in this paper. Given two graphs G = (V1, E1) and H = (V2. E2), the goal of LCSP is to find a subgraph G′ = (V′1, E′1) of G and a subgraph H′ = (V′2,E′2) of H such that G′ and H′ are not only isomorphic to each other but also their number of edges is maximized. The two graphs G′ and H′ are isomorphic when |V′1| = |V′2| and |E′1| = |E′2|, and there exists one-to-one vertex correspondence f : V′1 → V′2 such that {u, v} ∈ E′1 if and only if {f(u),/(w)} ∈ E′2. LCSP is known to be NP-complete in general. The 2DOM consists of a construction stage and a refinement stage to achieve the high solution quality and the short computation time for large size difficult combinatorial optimization problems. The construction stage creates a feasible initial solution with considerable quality, based on a greedy heuristic method. The refinement stage improves it keeping the feasibility, based on a random discrete descent method. The performance is evaluated by solving two types of randomly generated 1200 LCSP instances with a maximum of 500 vertices for G and 1000 vertices for H. The simulation result shows the superiority of 2DOM to the simulated annealing in terms of the solution quality and the computation time.

KW - Common subgraph

KW - Discrete descent method

KW - Greedy method

KW - Isomorphic

KW - NP-complete

KW - Simulated annealing

UR - http://www.scopus.com/inward/record.url?scp=0032597935&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032597935&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032597935

VL - E82-D

SP - 1145

EP - 1153

JO - IEICE Transactions on Information and Systems

JF - IEICE Transactions on Information and Systems

SN - 0916-8532

IS - 8

ER -