Fog of Search Resolver for Minimum Remaining Values Strategic Colouring of Graph

  • Saajid AbuluaihEmail author
  • Azlinah MohamedEmail author
  • Muthukkaruppan AnnamalaiEmail author
  • Hiroyuki IidaEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 937)


Minimum Remaining Values (MRV) is a popular strategy used along with Backtracking algorithm to solve Constraint Satisfaction Problems such as the Graph Colouring Problem. A common issue with MRV is getting stuck on search plateaus when two or more variables have the same minimum remaining values. MRV breaks the tie by arbitrarily selecting one of them, which might turn out to be not the best choice to expand the search. The paper relates the cause of search plateaus in MRV to ‘Fog of Search’ (FoS), and consequently proposes improvements to MRV to resolve the situation. The improved MRV+ generates a secondary heuristics value called the Contribution Number, and employs it to resolve a FoS. The usefulness of the FoS resolver is illustrated on Sudoku puzzles, a good instance of Graph Colouring Problem. An extensive experiment involving ten thousand Sudoku puzzles classified under two difficulty categories (based on the Number of clues and the Distribution of the clues) and five difficulty levels (ranging from Extremely Easy to Evil puzzles) were conducted. The results show that the FoS resolver that implements MRV+ is able to limit the FoS situations to a minimal, and consequently drastically reduce the number of recursive calls and backtracking moves that are normally ensued in MRV.


Fog of Search Search plateau Constraint satisfaction problem Graph colouring problem Minimum remaining values Contribution number Sudoku puzzles 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Faculty of Computer and Mathematical SciencesUniversiti Teknologi MARAShah AlamMalaysia
  2. 2.Faculty of Computer and Mathematical Sciences, Advanced Analytic Engineering Center (AAEC)Universiti Teknologi MARAShah AlamMalaysia
  3. 3.School of Information ScienceJapan Advanced Institute of Science and Technology (JAIST)IshikawaJapan

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