2019/08/27 by Adam Hamilton, Hamilton, Adam, Giang T. Nguyen +3
Computer Science · Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.DM #math.CO
paper · pdf · doi:10.48550/arxiv.1908.09996
19 pages, 3 figures
arxiv created 2019/08/27 · arxiv updated 2019/08/28
A k-stable c-coloured Candy Crush grid is a weak proper c-colouring of a particular type of k-uniform hypergraph. In this paper we introduce a fully polynomial randomised approximation scheme (FPRAS) which counts the number of k-stable c-coloured Candy Crush grids of a given size (m, n) for certain values of c and k. We implemented this algorithm on Matlab, and found that in a Candy Crush grid with7 available colours there are approximately 4.3*1061 3-stable colourings. (Note that, typical Candy Crush games are played with 6 colours and our FPRAS is not guaranteed to work in expected polynomial time with k= 3 and c= 6.) We also discuss the applicability of this FPRAS to the problem of counting the number of weak c-colourings of other, more general hypergraphs.