Enumerating Floorplans with Aligned Columns
A floorplan is a partition of an axis-aligned rectangle into a set of smaller rectangles. Given an axis-aligned rectangle R and a set P of points in R we wish to partition R into a set S of rectangles so that each point in P is on a boundary of a rectangle in S. We call such a partition of R a floor...
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| Published in | IEICE Transactions on Information and Systems Vol. E108.D; no. 3; pp. 181 - 185 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Tokyo
The Institute of Electronics, Information and Communication Engineers
01.03.2025
Japan Science and Technology Agency |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0916-8532 1745-1361 1745-1361 |
| DOI | 10.1587/transinf.2024FCP0001 |
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| Abstract | A floorplan is a partition of an axis-aligned rectangle into a set of smaller rectangles. Given an axis-aligned rectangle R and a set P of points in R we wish to partition R into a set S of rectangles so that each point in P is on a boundary of a rectangle in S. We call such a partition of R a floorplan covering P. Intuitively P is the locations of columns and a floorplan covering P is a floorplan in which no column is in the proper inside of a room and each column is on a wall. In this paper we design an algorithm to generate all floorplans covering P when P is the set of given grid points. The algorithm generates each floorplan in O(|P|) time. |
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| AbstractList | A floorplan is a partition of an axis-aligned rectangle into a set of smaller rectangles. Given an axis-aligned rectangle R and a set P of points in R we wish to partition R into a set S of rectangles so that each point in P is on a boundary of a rectangle in S. We call such a partition of R a floorplan covering P. Intuitively P is the locations of columns and a floorplan covering P is a floorplan in which no column is in the proper inside of a room and each column is on a wall. In this paper we design an algorithm to generate all floorplans covering P when P is the set of given grid points. The algorithm generates each floorplan in O(|P|) time. |
| ArticleNumber | 2024FCP0001 |
| Author | NAKANO, Shin-ichi |
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| Cites_doi | 10.1016/j.jcta.2005.10.003 10.1007/s004539900067 10.1007/3-540-45678-3_10 10.1142/S0129054123420078 10.1007/978-3-319-71150-8_3 10.1007/978-3-540-30559-0_3 10.1587/transfun.E101.A.1392 10.1016/0166-218X(95)00026-N 10.1002/scj.10563 10.1007/978-3-030-59267-7_5 |
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| References | [3] D. Avis, “Generating rooted triangulations without repetitions,” Algorithmica, vol.16, pp.618-632, 1996. 10.1007/s004539900067 [13] K. Yamanaka, M.S. Rahman, and S.-i. Nakano, “Enumerating floorplans with columns,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci., vol.E101-A, no.9, pp.1392-1397, 2018. 10.1587/transfun.e101.a.1392 [4] D. Avis and K. Fukuda, “Reverse search for enumeration,” Discrete Applied Mathematics, vol.65, no.1-3, pp.21-46, 1996. 10.1016/0166-218x(95)00026-n [9] S.-I. Nakano, “Family trees for enumeration,” International Journal of Foundations of Computer Science, vol.34, no.7, pp.715-736, 2023. 10.1142/s0129054123420078 [1] E. Ackerman, G. Barequet, and R.Y. Pinter, “On the number of rectangulations,” Proc. of SODA 2004, pp.729-738, 2004. [6] S.-i. Nakano, “Enumerating floorplans with n rooms,” Proc. of ISAAC 2001, LNCS, vol.2223, pp.107-115, 2001. 10.1007/3-540-45678-3_10 [7] S. Nakano, “Enumerating Floorplans with n Rooms,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E85-A, pp.1746-1750, 2002. [8] S.-i Nakano and T. Uno, “Constant time generation of trees with specified diameter,” Proc. of WG04, LNCS, vol.3353, pp.33-45, 2004. 10.1007/978-3-540-30559-0_3 [12] K. Yamanaka and S.-i. Nakano, “Floorplans with walls,” Proc. of TAMC 2020, LNCS, vol.12337, pp.50-59, 2020. 10.1007/978-3-030-59267-7_5 [2] E. Ackerman, G. Barequet, and R.Y. Pinter, “On the number of rectangulations of a planar point set,” Journal of Combinatorial Theory, Series A, vol.113, no.6, pp.1072-1091, 2006. 10.1016/j.jcta.2005.10.003 [5] A.I. Merino and T. Mütze, “Efficient Generation of Rectangulations via permutation languages,” Proc. of SoCG 2021, vol.189, pp.54:1-54:18, 2021. 10.4230/LIPIcs.SoCG.2021.54 [10] M. Takagi and S.-i. Nakano, “Listing all rectangular drawings with certain properties,” Systems and Computers in Japan, vol.35, no.4, pp.1-8, 2004. 10.1002/scj.10563 [11] K. Yamanaka, M.S. Rahman and S.-I. Nakano, “Floorplans with columns,” Proc. of COCOA 2017, LNCS, vol.10627, pp.33-40, 2017. 10.1007/978-3-319-71150-8_3 11 12 13 1 2 3 4 5 6 7 8 9 10 |
| References_xml | – reference: [1] E. Ackerman, G. Barequet, and R.Y. Pinter, “On the number of rectangulations,” Proc. of SODA 2004, pp.729-738, 2004. – reference: [2] E. Ackerman, G. Barequet, and R.Y. Pinter, “On the number of rectangulations of a planar point set,” Journal of Combinatorial Theory, Series A, vol.113, no.6, pp.1072-1091, 2006. 10.1016/j.jcta.2005.10.003 – reference: [8] S.-i Nakano and T. Uno, “Constant time generation of trees with specified diameter,” Proc. of WG04, LNCS, vol.3353, pp.33-45, 2004. 10.1007/978-3-540-30559-0_3 – reference: [10] M. Takagi and S.-i. Nakano, “Listing all rectangular drawings with certain properties,” Systems and Computers in Japan, vol.35, no.4, pp.1-8, 2004. 10.1002/scj.10563 – reference: [12] K. Yamanaka and S.-i. Nakano, “Floorplans with walls,” Proc. of TAMC 2020, LNCS, vol.12337, pp.50-59, 2020. 10.1007/978-3-030-59267-7_5 – reference: [3] D. Avis, “Generating rooted triangulations without repetitions,” Algorithmica, vol.16, pp.618-632, 1996. 10.1007/s004539900067 – reference: [9] S.-I. Nakano, “Family trees for enumeration,” International Journal of Foundations of Computer Science, vol.34, no.7, pp.715-736, 2023. 10.1142/s0129054123420078 – reference: [13] K. Yamanaka, M.S. Rahman, and S.-i. Nakano, “Enumerating floorplans with columns,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci., vol.E101-A, no.9, pp.1392-1397, 2018. 10.1587/transfun.e101.a.1392 – reference: [5] A.I. Merino and T. Mütze, “Efficient Generation of Rectangulations via permutation languages,” Proc. of SoCG 2021, vol.189, pp.54:1-54:18, 2021. 10.4230/LIPIcs.SoCG.2021.54 – reference: [4] D. Avis and K. Fukuda, “Reverse search for enumeration,” Discrete Applied Mathematics, vol.65, no.1-3, pp.21-46, 1996. 10.1016/0166-218x(95)00026-n – reference: [11] K. Yamanaka, M.S. Rahman and S.-I. Nakano, “Floorplans with columns,” Proc. of COCOA 2017, LNCS, vol.10627, pp.33-40, 2017. 10.1007/978-3-319-71150-8_3 – reference: [6] S.-i. Nakano, “Enumerating floorplans with n rooms,” Proc. of ISAAC 2001, LNCS, vol.2223, pp.107-115, 2001. 10.1007/3-540-45678-3_10 – reference: [7] S. Nakano, “Enumerating Floorplans with n Rooms,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E85-A, pp.1746-1750, 2002. – ident: 5 – ident: 1 – ident: 2 doi: 10.1016/j.jcta.2005.10.003 – ident: 3 doi: 10.1007/s004539900067 – ident: 6 doi: 10.1007/3-540-45678-3_10 – ident: 9 doi: 10.1142/S0129054123420078 – ident: 11 doi: 10.1007/978-3-319-71150-8_3 – ident: 8 doi: 10.1007/978-3-540-30559-0_3 – ident: 13 doi: 10.1587/transfun.E101.A.1392 – ident: 4 doi: 10.1016/0166-218X(95)00026-N – ident: 7 – ident: 10 doi: 10.1002/scj.10563 – ident: 12 doi: 10.1007/978-3-030-59267-7_5 |
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| SubjectTerms | algorithm Algorithms enumeration floorplan Floorplans |
| Title | Enumerating Floorplans with Aligned Columns |
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