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

Nobuo Funabiki, Junji Kitamichi

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1145-1153
Number of pages9
JournalIEICE Transactions on Information and Systems
Issue number8
Publication statusPublished - 1999
Externally publishedYes


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

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering
  • Artificial Intelligence


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