Placing your Coins on a Shelf
نویسندگان
چکیده
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. We prove that the problem of minimizing the distance between the leftmost point and the rightmost point of any disk is NP-hard. On the positive side, we show how to approximate this problem within a factor of 4/3 in O(n logn) time, and provide an O(n logn)-time exact algorithm for a special case, in particular when the ratio between the largest and smallest radius is at most four.
منابع مشابه
Giving Your Knowledge Half a Chance
1000 fair causally isolated coins will be independently flipped tomorrow morning and you know this fact. I argue that the probability, conditional on your knowledge, that any coin will land tails is almost 1 if that coin in fact lands tails, and almost 0 if it in fact lands heads. I also show that the coin flips are not probabilistically independent given your knowledge. These results are uncom...
متن کاملBlet: A Mathematical Puzzle
Blet is a puzzle. One starts with an even number of coins, laid out in a circle. At first, the coins are laid out with heads and tails alternating (HTHTHT. . .HT). Each turn, you are allowed to take three consecutive coins that show tails-heads-tails and flip them over, getting heads-tails-heads. This increases the total number of heads by one. You may do the opposite, flipping a heads-tails-he...
متن کاملAt the threshold of knowledge
We explore consequences of the view that to know a proposition your rational credence in the proposition must exceed a certain threshold. In other words, to know something you must have evidence that makes rational a high credence in it. We relate such a threshold view to Dorr et al.’s (Philosophical Studies 170(2):277–287, 2014) argument against the principle they call FAIR COINS: ‘‘If you kno...
متن کاملThe Reasons for and Stages of Correcting and Arabicizing the Islamic Coins with an Emphasis on the Abd al-Malik ibn Marwan's Era
With the expansion of territories, great amounts of Persian, Coptic, and Greek coins entered the Islamic countries. These coins were different in terms of weight, purity, images, and carvings. Some of the Khalifs and Muslim rulers made efforts to Arabicize and organize these coins. The peak of these actions was during the rule of Abd al-Malik ibn Marwan (65-86 A.H./684-705 AD). At this time, so...
متن کاملSupporting Information Retrieval via Matchmaking
The massive increase in information available via electronic networks is placing severe burdens on traditional methods of information sharing and retrieval. Matchmaking proposes an intelligent facilitation agent that accepts machine-readable requests and advertisements from information consumers and providers, and determines potential information sharing paths. Matchmaking permits large nmnbers...
متن کامل