title: Maximum common subgraph: some upper bound and lower bound results.
abstract: BACKGROUND
  Structure matching plays an important part in understanding the functional role of biological structures. Bioinformatics assists in this effort by reformulating this process into a problem of finding a maximum common subgraph between graphical representations of these structures. Among the many different variants of the maximum common subgraph problem, the maximum common induced subgraph of two graphs is of special interest.
  
  
  RESULTS
  Based on current research in the area of parameterized computation, we derive a new lower bound for the exact algorithms of the maximum common induced subgraph of two graphs which is the best currently known. Then we investigate the upper bound and design techniques for approaching this problem, specifically, reducing it to one of finding a maximum clique in the product graph of the two given graphs. Considering the upper bound result, the derived lower bound result is asymptotically tight.
  
  
  CONCLUSIONS
  Parameterized computation is a viable approach with great potential for investigating many applications within bioinformatics, such as the maximum common subgraph problem studied in this paper. With an improved hardness result and the proposed approaches in this paper, future research can be focused on further exploration of efficient approaches for different variants of this problem within the constraints imposed by real applications.
authors.affiliation: Department of Computer Science, Arkansas State University, State University, Arkansas 72467, USA. xzhuang@csm.astate.edu
authors.forename: Xiuzhen
authors.initials: X
authors.lastname: Huang
authors.forename: Jing
authors.initials: J
authors.lastname: Lai
authors.forename: Steven F
authors.initials: SF
authors.lastname: Jennings
mesh_terms: D000465:Algorithms; D001704:Biopolymers / Q000737:chemistry*; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D016415:Sequence Alignment / Q000379:methods*; D017421:Sequence Analysis / Q000379:methods*
chemical_list: D001704:Biopolymers