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Placing your Coins on a Shelf [article]

Helmut Alt, Kevin Buchin, Steven Chaplick, Otfried Cheong, Philipp Kindermann, Christian Knauer, Fabian Stehn
2017 arXiv   pre-print
We consider the problem of packing a family of disks "on a shelf", that is, such that each disk touches the x-axis from above and such that no two disks overlap.  ...  On the positive side, we show how to approximate this problem within a factor of 4/3 in O(n n) time, and provide an O(n n)-time exact algorithm for a special case, in particular when the ratio between  ...  We also thank all participants at the Korean Workshop on Computational Geometry in Würzburg 2016.  ... 
arXiv:1707.01239v1 fatcat:e6vzfcvq7bck7owwjbczful7e4

Placing your Coins on a Shelf

Helmut Alt, Kevin Buchin, Steven Chaplick, Otfried Cheong, Philipp Kindermann, Christian Knauer, Fabian Stehn, Marc Herbstritt
2017 International Symposium on Algorithms and Computation  
We consider the problem of packing a family of disks "on a shelf," that is, such that each disk touches the x-axis from above and such that no two disks overlap.  ...  On the positive side, we show how to approximate this problem within a factor of 4 /3 in O(n log n) time, and provide an O(n log n)-time exact algorithm for a special case, in particular when the ratio  ...  We also thank all participants at the Korean Workshop on Computational Geometry in Würzburg 2016.  ... 
doi:10.4230/lipics.isaac.2017.4 dblp:conf/isaac/AltBCCKKS17 fatcat:f4wxv55ihvbqloufblxxvhjgou

Placing your Coins on a Shelf *

Helmut Alt, Kevin Buchin, Steven Chaplick, Otfried Cheong, Philipp Kindermann, Christian Knauer, Fabian Stehn
unpublished
We consider the problem of packing a family of disks "on a shelf," that is, such that each disk touches the x-axis from above and such that no two disks overlap.  ...  On the positive side, we show how to approximate this problem within a factor of 4 /3 in O(n log n) time, and provide an O(n log n)-time exact algorithm for a special case, in particular when the ratio  ...  We also thank all participants at the Korean Workshop on Computational Geometry in Würzburg 2016.  ... 
fatcat:rtdf4elfmne2lkyjlugwpzafvi

Page 262 of Our Young Folks. an Illustrated Magazine for Boys and Girls Vol. 1, Issue 4 [page]

1865 Our Young Folks. an Illustrated Magazine for Boys and Girls  
A coin is borrowed from one of the audience, with a request that the per- son who lends it will place some mark on it, so as to identify it.  ...  Get behind your table, lay the back of your left hand on it, toss the lemon in the air with your right, and as it falls catch it, throw it quickly on to the shelf of the table, and cover your left with  ... 

Page 528 of Overland Monthly and Out West Magazine Vol. 44, Issue 5 [page]

1904 Overland Monthly and Out West Magazine  
On the opposite side of the room, from a rack, you select a glass of a size to correspond with the character of your indulgence; this you invert on an electric device placed upon a shelf, and with your  ...  turn after having made your selection and inserted your coin.  ... 

Page 620 of Munsey's Magazine Vol. 65, Issue 4 [page]

1919 Munsey's Magazine  
I have just remembered something which I should have observed in the first place if I had been really wide awake. The envelope— you know the one I mean—was sealed with a Chinese coin, known as cas/:.  ...  He found himself staring at the shelf immediately above that upon which the coin had lain.  ... 

Page 135 of The Cornhill Magazine Vol. 62, Issue 368 [page]

1927 The Cornhill Magazine  
She asked you to pull up in your wicked way of life, and your voice grew so savage that she backed away. Then she spun round like a top, and crashed her head against the mantel-shelf.’  ...  You'd do almost anything for the jingle of coin, and I tapped your pockets.’ ‘You did. I'll bear that out, Jasper.’ “When I caught you, a month later, the good game began.  ... 

Page 531 of Monthly Chronicle of North Country Lore and Legend Vol. 2, Issue 22 [page]

1888 Monthly Chronicle of North Country Lore and Legend  
Pattison put his family Bible on the shelf, and the glit- tering sovereigns in his pocket; Mr.  ...  I haveno doubt you will find the coin engraved in works on Roman numismata. ieve me yours very truly, C. Roacu Smit.  ... 

Page 329 of Science Education Vol. 12, Issue 1 [page]

1927 Science Education  
Oh, yes, “A Speck of Dust!” Whew! It’s dusty. Look at the dust on your coat sleeve, shoes, on the rug, shelf, window- sill, on your radio cabinet. Inhale!  ...  A coin. A mirror. A pencil. A piece of white paper. A pinch of starch. I promise you a beautiful lesson. Be ready promptly at 7.00 o’clock next Monday evening. Let me see now.  ... 

Page 1184 of JAMA: The Journal of the American Medical Association Vol. 174, Issue 8 [page]

1960 JAMA: The Journal of the American Medical Association  
“Gimme,” said one, pointing to the top shelf, “a nickel, a nickel’s worth of those red cinnamon drops.”  ...  An elderly man had just opened a candy shop near a primary school and had as his first customers three small boys clutching coins in their fists.  ... 

Page 605 of Journal of Shoulder and Elbow Surgery Vol. 19, Issue 4 [page]

2010 Journal of Shoulder and Elbow Surgery  
Can you lift a full glass to the level of your shoulder? Can you place a coin on a shelf? Can you place your hand behind your head? Can you reach the small of your back to tuck in your shirt?  ...  Fenlin Tuberoplasty revisited Would your shoulder allow you to do your normal work? Can you wash the back of your opposite shoulder? Do you think you can toss a softball overhand twenty meters?  ... 

Page 882 of Ballou's Monthly Magazine Vol. 24, Issue 4 [page]

1866 Ballou's Monthly Magazine  
He obsenred, while drinking, that the dealer placed the money on a little shelf behind him, and Just abore his head; it was within reaching distsmee, too, from his stand beside the temporary counter.  ...  his efforts to chase it op appeared nnarailing—so many patches on his hnntlng-shlrt, it was impossible to And the one he had made a pocket to contain the precious coin, and at last he had giren it np.  ... 

Page 119 of Antiquary: A Medium of Intercommunication for Men of Letters, the Archaeologist, and the Reading Public Vol. 1, Issue [page]

1871 Antiquary: A Medium of Intercommunication for Men of Letters, the Archaeologist, and the Reading Public  
HENFREY. 15, Laton Place, Brighton. ADMISSION TO MEDAL ROOM, BRITISH MUSEUM. To the Editor of “* THE ANTIQUARY.” S1r,—Your correspondent “‘G. R.  ...  I am, sir, yours, &c., August 29, 1871. To the Editor of “THE ANTIQUARY,” S1Rr,—A gentleman in the country has kindly sent me a coin for my acceptance.  ... 

Page 313 of The Mirror, Monthly Magazine Vol. 2, Issue 20 [page]

1842 The Mirror, Monthly Magazine  
the look out for current coins as ‘we are for old ones.  ...  He next de- spatched one of the gang to a place two miles off, with orders to bring an individual whom he named, without a moment’s loss of time; and we retired into a cave where a dinner and wine was  ... 

Page 856 of The Cornhill Magazine Vol. 26, Issue 156 [page]

1909 The Cornhill Magazine  
he asked. a *Play-money,’ said the fool impassively. ‘Ye see, David,’ I’ve no more use for coins than for pebbles i’ a stream, so I saved” ’em up against your home-coming.  ...  Not for fingers, I reckaay David was puzzled as the other jingled the coins and place his money-box in the smith’s hands. ‘ What is all this, Billy??  ... 
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