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Mathematical Problems in Engineering
Volume 2015, Article ID 275019, 8 pages
http://dx.doi.org/10.1155/2015/275019
Research Article

Solving the Maximum Weighted Clique Problem Based on Parallel Biological Computing Model

1School of Information Sciences, Shanghai Ocean University, Shanghai 201306, China
2Guangxi Institute of Water Resources Research, Nanning 530023, China
3State Key Laboratory of Simulation and Regulation of River Basin Water Cycle, China Institute of Water Resources and Hydropower Research, Beijing 100048, China
4Department of Civil Engineering, Xi’an University of Architecture & Technology, Xi’an 710055, China

Received 2 July 2014; Revised 15 September 2014; Accepted 20 September 2014

Academic Editor: L. W. Zhang

Copyright © 2015 Zhaocai Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The maximum weighted clique (MWC) problem, as a typical NP-complete problem, is difficult to be solved by the electronic computer algorithm. The aim of the problem is to seek a vertex clique with maximal weight sum in a given undirected graph. It is an extremely important problem in the field of optimal engineering scheme and control with numerous practical applications. From the point of view of practice, we give a parallel biological algorithm to solve the MWC problem. For the maximum weighted clique problem with edges and vertices, we use fixed length DNA strands to represent different vertices and edges, fully conduct biochemical reaction, and find the solution to the MVC problem in certain length range with time complexity, comparing to the exponential time level by previous computer algorithms. We expand the applied scope of parallel biological computation and reduce computational complexity of practical engineering problems. Meanwhile, we provide a meaningful reference for solving other complex problems.