A Community-Division Based Algorithm for Finding Relations Among Linear Constraints

  • Minghao Liu
  • Feifei MaEmail author
  • Jun YanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11062)


Linear constraints are widely used in the modeling of many practical problems, and the solving technologies have important applications in satisfiability modulo theories, program analysis and verification. The efficiency of solving procedure could be improved by taking advantages of the relations among constraints. Traditional methods find relations through search, which do not take advantage of the structural characteristics and cost too much time. In this paper, a heuristic based on community division is proposed for finding relations among linear constraints. Firstly it builds a relation graph, which maps each constraint to a node. Then a division tool is employed to divide the nodes into several communities. At last, it tries to find relations among constraints in the same community through search. Experimental results show that the algorithm can effectively process large set of constraints, reduce time cost and find relations with higher quality.


Linear constraint Relation finding Community division Constraint programming 



This work is supported by National Natural Science Foundation of China (Grant No. 61672505), the National Key Basic Research (973) Program of China (Grant No. 2014CB340701), and Key Research Program of Frontier Sciences, CAS (Grant No. QYZDJ-SSW-JSC036). Feifei Ma is also supported by the Youth Innovation Promotion Association, CAS.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Computer Science, Institute of SoftwareChinese Academy of SciencesBeijingChina
  2. 2.Laboratory of Parallel Software and Computational Science, Institute of SoftwareChinese Academy of SciencesBeijingChina
  3. 3.Technology Center of Software Engineering, Institute of SoftwareChinese Academy of SciencesBeijingChina
  4. 4.University of Chinese Academy of SciencesBeijingChina

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