I don't mean to diminish LA. I'm not a diminisher.
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The last diminisher procedure has been improved later in many ways. For details, see proportional division.
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Repeat with the remaining cake and players, the last player gets the remainder of the cake. Similar to the last diminisher procedure, it can be used to cut the cake into contiguous parts for each player.
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"The Diminisher" is the alter-ego of Chicago musician David McDonnell (born 1976), who was a founding member of the trio Bablicon, bass player Griffin Rodriguez informally assigned the moniker in reference to McDonnell's liberal use of the so-called diminished chord in Bablicon songs. When Bablicon informally dissolved in 2001, he began or joined a number of experimental jazz/rock projects, such as Michael Columbia and Icy Demons, and continued composing in Chicago. In 2006, McDonnell released a solo album on the label Unsound Records, titled Imaginary Volcano, under the name of The Diminisher.
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See also the last diminisher. A newer method is reported in Scientific American. It was developed by Aziz and Mackenzie. While faster in principle than the earlier method, it is still potentially very slow: O(n2n+3), where n is the number of divisions desired.
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The first published algorithm for proportional division of a cake was the last diminisher algorithm, published in 1948. Its run-time complexity was O(n^2). in 1984, Shimon Even and Azaria Paz published their improved algorithm, whose run-time complexity is only O(n log n).
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Hence, after each iteration the number of intervals per partners is still equal to the number of partners, and the process can proceed until every partner receives an interval.This selection procedure is similar to the Interval scheduling#Greedy polynomial solution) This protocol requires each partner to answer n queries so the query complexity is O(n2), similarly to Last Diminisher.
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The last diminisher procedure is a procedure for fair cake-cutting. It involves a certain heterogenous and divisible resource, such as a birthday cake, and n partners with different preferences over different parts of the cake. It allows the n people to achieve a proportional division, i.e., divide the cake among them such that each person receives a piece with a value of at least 1/n of the total value according to his own subjective valuation.
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In addition to the usual constraint that all pieces must be connected, in some cases there are additional constraints. In particular, when the cake to divide is a disputed territory lying among several countries, it may be required that the piece allocated to each country is adjacent to its current location. A proportional division with this property always exists and can be found by combining the Last Diminisher protocol with geometric tricks involving conformal mappings. See Hill–Beck land division problem.
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When there are 3 or more partners, the division obtained by the last-diminisher protocol is not always envy-free. For example, suppose the first partner Alice receives a piece (which she values as 1/3 of the total). Then, the other two partners Bob and Charlie divide the remainder in such a way that is fair in their opinion, but in Alice's opinion Bob's share is worth 2/3 while Charlie's share is worth 0. Then Alice envies Bob.
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A simple solution is to allow re-entrance. I.e, a partner that won a piece by being the last diminisher, does not have to leave the game, but may rather stay and participate in further steps. If he wins again, he must release his current piece and it is returned to the cake. In order to make sure that the protocol terminates, we select a certain constant \epsilon and add a rule that allows each partner to re-enter at most 1/\epsilon times.
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If you want that, call Mr. Ford," who is a "bulldozer" while Smitherman is an "axe" and a "diminisher."" Pantalone was also the only candidate who rejected contracting out more services now done by city employees. However, several pundits suggested that Pantalone had largely misread the electorate, as a Nanos Research poll showed that a combined 83% of decided voters supported mayoral candidates who advocated sweeping changes. Pantalone never managed to break the 20% threshold in opinion polls and he consistently polled in third place in the mid to low teens behind Smitherman and Ford.
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The algorithm simplifies in the degenerate case that all partners have the same preference function because the partner that optimally first cuts a slice will also be its last diminisher. Equivalently, each partner 1, 2, ..., n−1 in turn cuts a slice from the remaining cake. Then in reverse order, each partner n, n−1, ..., 1 in turn selects a slice that has not yet been claimed. The first partner who cut a slice other than of value 1/n would be envious of another partner who ended up with more than they did.
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God's Caliph, 68, 107 Tabari records Yazid's nickname "the Diminisher (Naqis)", given because he reduced military annuities by 10%,Philip Khuri Hitti, 478 whereas his predecessor had promised a raise. According to Islamic popular tradition, recorded in an apocalyptic style, Yazid would go himself into the marketplace.David Cook, Studies in Muslim Apocalyptic, 350: appendix I, III, 12 a The city of Homs refused allegiance to Yazid, and there were several other dissident movements against him.1234 Chronicle apud Hoyland, 661 Another cousin, Marwan ibn Muhammad ibn Marwan, governor of Armenia, had initially supported Walid and on Walid's death entered Iraq to avenge him.
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Bronisław Knaster (22 May 1893 – 3 November 1980) was a Polish mathematician; from 1939 a university professor in Lwów and from 1945 in Wrocław.. He is known for his work in point-set topology and in particular for his discoveries in 1922 of the hereditarily indecomposable continuum or pseudo-arc and of the Knaster continuum, or buckethandle continuum.. Together with his teacher Hugo Steinhaus and his colleague Stefan Banach, he also developed the last diminisher procedure for fair cake cutting. Knaster received his Ph.D. degree from University of Warsaw in 1925, under the supervision of Stefan Mazurkiewicz.
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It was devised by a group of Polish mathematicians, Hugo Steinhaus, Bronisław Knaster and Stefan Banach, who used to meet in the Scottish Café in Lvov (then in Poland). A proportional (fair division) division for any number of players called 'last- diminisher' was devised in 1944. This was attributed to Banach and Knaster by Steinhaus when he made the problem public for the first time at a meeting of the Econometric Society in Washington D.C. on 17 September 1947. At that meeting he also proposed the problem of finding the smallest number of cuts necessary for such divisions.
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Bablicon was an Elephant 6-related free-jazz band consisting of members of Neutral Milk Hotel and The Gerbils. The band was formed in 1996 when Dave McDonnell (credited as The Diminisher), Jeremy Barnes (as "Marta Tennae"), and Griffin Rodriguez ("Blue Hawaii") teamed up to write and improvise music. Their almost-entirely-improvised album In A Different City was recorded in Chicago during this time, and later released in 1999. In a unique twist, the band had an audience paint vinyl LP covers while they performed, which were later collected as "painticons" and distributed as the actual album covers for the LP version of the album.
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