Efficient Covering of Thin Convex Domains Using Congruent Discs
We present efficient strategies for covering classes of thin domains in the plane using unit discs. We start with efficient covering of narrow domains using a single row of covering discs. We then move to efficient covering of general rectangles by discs centered at the lattice points of an irregula...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/23/3056 |
| _version_ | 1797507462277890048 |
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| author | Shai Gul Reuven Cohen |
| author_facet | Shai Gul Reuven Cohen |
| author_sort | Shai Gul |
| collection | DOAJ |
| description | We present efficient strategies for covering classes of thin domains in the plane using unit discs. We start with efficient covering of narrow domains using a single row of covering discs. We then move to efficient covering of general rectangles by discs centered at the lattice points of an irregular hexagonal lattice. This optimization uses a lattice that leads to a covering using a small number of discs. We compare the bounds on the covering using the presented strategies to the bounds obtained from the standard honeycomb covering, which is asymptotically optimal for fat domains, and show the improvement for thin domains. |
| first_indexed | 2024-03-10T04:48:50Z |
| format | Article |
| id | doaj.art-e042cd15acce4180b3c3676f3d7d3972 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T04:48:50Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e042cd15acce4180b3c3676f3d7d39722023-11-23T02:45:22ZengMDPI AGMathematics2227-73902021-11-01923305610.3390/math9233056Efficient Covering of Thin Convex Domains Using Congruent DiscsShai Gul0Reuven Cohen1Department of Applied Mathematics, Holon Institute of Technology, Holon 5810201, IsraelDepartment of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, IsraelWe present efficient strategies for covering classes of thin domains in the plane using unit discs. We start with efficient covering of narrow domains using a single row of covering discs. We then move to efficient covering of general rectangles by discs centered at the lattice points of an irregular hexagonal lattice. This optimization uses a lattice that leads to a covering using a small number of discs. We compare the bounds on the covering using the presented strategies to the bounds obtained from the standard honeycomb covering, which is asymptotically optimal for fat domains, and show the improvement for thin domains.https://www.mdpi.com/2227-7390/9/23/3056coveringthin domainsoptimal placement |
| spellingShingle | Shai Gul Reuven Cohen Efficient Covering of Thin Convex Domains Using Congruent Discs Mathematics covering thin domains optimal placement |
| title | Efficient Covering of Thin Convex Domains Using Congruent Discs |
| title_full | Efficient Covering of Thin Convex Domains Using Congruent Discs |
| title_fullStr | Efficient Covering of Thin Convex Domains Using Congruent Discs |
| title_full_unstemmed | Efficient Covering of Thin Convex Domains Using Congruent Discs |
| title_short | Efficient Covering of Thin Convex Domains Using Congruent Discs |
| title_sort | efficient covering of thin convex domains using congruent discs |
| topic | covering thin domains optimal placement |
| url | https://www.mdpi.com/2227-7390/9/23/3056 |
| work_keys_str_mv | AT shaigul efficientcoveringofthinconvexdomainsusingcongruentdiscs AT reuvencohen efficientcoveringofthinconvexdomainsusingcongruentdiscs |