Counting Candy Crush configurations.
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| Title: | Counting Candy Crush configurations. |
|---|---|
| Authors: | Hamilton, Adam1 (AUTHOR) adam.h.hamilton@adelaide.edu.au, Nguyen, Giang T.1 (AUTHOR) giang.nguyen@adelaide.edu.au, Roughan, Matthew1 (AUTHOR) matthew.roughan@adelaide.edu.au |
| Source: | Discrete Applied Mathematics. May2021, Vol. 295, p47-56. 10p. |
| Subjects: | Candy, Polynomial approximation, Polynomial time algorithms, Counting, Hypergraphs |
| Abstract: | 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 with 7 available colours there are approximately 4. 3 × 1 0 61 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 149435871 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Counting Candy Crush configurations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hamilton%2C+Adam%22">Hamilton, Adam</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> adam.h.hamilton@adelaide.edu.au</i><br /><searchLink fieldCode="AR" term="%22Nguyen%2C+Giang+T%2E%22">Nguyen, Giang T.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> giang.nguyen@adelaide.edu.au</i><br /><searchLink fieldCode="AR" term="%22Roughan%2C+Matthew%22">Roughan, Matthew</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> matthew.roughan@adelaide.edu.au</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. May2021, Vol. 295, p47-56. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Candy%22">Candy</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomial+approximation%22">Polynomial approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomial+time+algorithms%22">Polynomial time algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Counting%22">Counting</searchLink><br /><searchLink fieldCode="DE" term="%22Hypergraphs%22">Hypergraphs</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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 with 7 available colours there are approximately 4. 3 × 1 0 61 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.dam.2021.02.013 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 47 Subjects: – SubjectFull: Candy Type: general – SubjectFull: Polynomial approximation Type: general – SubjectFull: Polynomial time algorithms Type: general – SubjectFull: Counting Type: general – SubjectFull: Hypergraphs Type: general Titles: – TitleFull: Counting Candy Crush configurations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hamilton, Adam – PersonEntity: Name: NameFull: Nguyen, Giang T. – PersonEntity: Name: NameFull: Roughan, Matthew IsPartOfRelationships: – BibEntity: Dates: – D: 31 M: 05 Text: May2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 0166218X Numbering: – Type: volume Value: 295 Titles: – TitleFull: Discrete Applied Mathematics Type: main |
| ResultId | 1 |
