Matches in SemOpenAlex for { <https://semopenalex.org/work/W3155414097> ?p ?o ?g. }
Showing items 1 to 85 of
85
with 100 items per page.
- W3155414097 startingPage "16" @default.
- W3155414097 abstract "We provide a tight result for a fundamental problem arising from packing squares into a circular container: The critical density of packing squares into a disk is δ = 8/(5π)≈ 0.509. This implies that any set of (not necessarily equal) squares of total area A ≤ 8/5 can always be packed into a disk with radius 1; in contrast, for any e > 0 there are sets of squares of total area 8/5+e that cannot be packed, even if squares may be rotated. This settles the last (and arguably, most elusive) case of packing circular or square objects into a circular or square container: The critical densities for squares in a square (1/2), circles in a square (π/(3+2√2) ≈ 0.539) and circles in a circle (1/2) have already been established, making use of recursive subdivisions of a square container into pieces bounded by straight lines, or the ability to use recursive arguments based on similarity of objects and container; neither of these approaches can be applied when packing squares into a circular container. Our proof uses a careful manual analysis, complemented by a computer-assisted part that is based on interval arithmetic. Beyond the basic mathematical importance, our result is also useful as a blackbox lemma for the analysis of recursive packing algorithms. At the same time, our approach showcases the power of a general framework for computer-assisted proofs, based on interval arithmetic." @default.
- W3155414097 created "2021-04-26" @default.
- W3155414097 creator A5015542807 @default.
- W3155414097 creator A5049868079 @default.
- W3155414097 creator A5055048082 @default.
- W3155414097 creator A5076288432 @default.
- W3155414097 creator A5080464077 @default.
- W3155414097 creator A5090048794 @default.
- W3155414097 date "2021-06-07" @default.
- W3155414097 modified "2023-09-28" @default.
- W3155414097 title "Packing Squares into a Disk with Optimal Worst-Case Density" @default.
- W3155414097 doi "https://doi.org/10.4230/lipics.socg.2021.36" @default.
- W3155414097 hasPublicationYear "2021" @default.
- W3155414097 type Work @default.
- W3155414097 sameAs 3155414097 @default.
- W3155414097 citedByCount "0" @default.
- W3155414097 crossrefType "proceedings-article" @default.
- W3155414097 hasAuthorship W3155414097A5015542807 @default.
- W3155414097 hasAuthorship W3155414097A5049868079 @default.
- W3155414097 hasAuthorship W3155414097A5055048082 @default.
- W3155414097 hasAuthorship W3155414097A5076288432 @default.
- W3155414097 hasAuthorship W3155414097A5080464077 @default.
- W3155414097 hasAuthorship W3155414097A5090048794 @default.
- W3155414097 hasConcept C108710211 @default.
- W3155414097 hasConcept C11413529 @default.
- W3155414097 hasConcept C114614502 @default.
- W3155414097 hasConcept C123115066 @default.
- W3155414097 hasConcept C127413603 @default.
- W3155414097 hasConcept C130253271 @default.
- W3155414097 hasConcept C134306372 @default.
- W3155414097 hasConcept C135692309 @default.
- W3155414097 hasConcept C177264268 @default.
- W3155414097 hasConcept C183893376 @default.
- W3155414097 hasConcept C199360897 @default.
- W3155414097 hasConcept C2524010 @default.
- W3155414097 hasConcept C2781018962 @default.
- W3155414097 hasConcept C33923547 @default.
- W3155414097 hasConcept C34388435 @default.
- W3155414097 hasConcept C41008148 @default.
- W3155414097 hasConcept C78519656 @default.
- W3155414097 hasConceptScore W3155414097C108710211 @default.
- W3155414097 hasConceptScore W3155414097C11413529 @default.
- W3155414097 hasConceptScore W3155414097C114614502 @default.
- W3155414097 hasConceptScore W3155414097C123115066 @default.
- W3155414097 hasConceptScore W3155414097C127413603 @default.
- W3155414097 hasConceptScore W3155414097C130253271 @default.
- W3155414097 hasConceptScore W3155414097C134306372 @default.
- W3155414097 hasConceptScore W3155414097C135692309 @default.
- W3155414097 hasConceptScore W3155414097C177264268 @default.
- W3155414097 hasConceptScore W3155414097C183893376 @default.
- W3155414097 hasConceptScore W3155414097C199360897 @default.
- W3155414097 hasConceptScore W3155414097C2524010 @default.
- W3155414097 hasConceptScore W3155414097C2781018962 @default.
- W3155414097 hasConceptScore W3155414097C33923547 @default.
- W3155414097 hasConceptScore W3155414097C34388435 @default.
- W3155414097 hasConceptScore W3155414097C41008148 @default.
- W3155414097 hasConceptScore W3155414097C78519656 @default.
- W3155414097 hasLocation W31554140971 @default.
- W3155414097 hasOpenAccess W3155414097 @default.
- W3155414097 hasPrimaryLocation W31554140971 @default.
- W3155414097 hasRelatedWork W2000902553 @default.
- W3155414097 hasRelatedWork W2041237399 @default.
- W3155414097 hasRelatedWork W2069254977 @default.
- W3155414097 hasRelatedWork W2131547375 @default.
- W3155414097 hasRelatedWork W2168190509 @default.
- W3155414097 hasRelatedWork W2280720710 @default.
- W3155414097 hasRelatedWork W2470030486 @default.
- W3155414097 hasRelatedWork W2511629645 @default.
- W3155414097 hasRelatedWork W2588034099 @default.
- W3155414097 hasRelatedWork W2595429479 @default.
- W3155414097 hasRelatedWork W2779188873 @default.
- W3155414097 hasRelatedWork W2895117976 @default.
- W3155414097 hasRelatedWork W2905098239 @default.
- W3155414097 hasRelatedWork W2962917430 @default.
- W3155414097 hasRelatedWork W2973464667 @default.
- W3155414097 hasRelatedWork W3138481520 @default.
- W3155414097 hasRelatedWork W596534195 @default.
- W3155414097 hasRelatedWork W62054538 @default.
- W3155414097 hasRelatedWork W89929351 @default.
- W3155414097 hasRelatedWork W2566263782 @default.
- W3155414097 isParatext "false" @default.
- W3155414097 isRetracted "false" @default.
- W3155414097 magId "3155414097" @default.
- W3155414097 workType "article" @default.