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Even–Paz Protocol
The Even–Paz algorithm is an computationally-efficient algorithm for fair cake-cutting. It involves a certain heterogeneous 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. History 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). Description The algorithm uses a divide-and-conquer strategy, it is possible to achieve a proportional division in time O(n\log n). * Each partner is asked to draw a line dividing the cake into a right and left part such that he believes the ratio is \lfloor n/2\rfloor :\lceil n/2\rceil. The cuts are required to be non-intersecting; a simple way to guarantee this is to allow only horizontal l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Cake-cutting
Fair cake-cutting is a kind of fair division problem. The problem involves a ''heterogeneous'' resource, such as a cake with different toppings, that is assumed to be ''divisible'' – it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who have different preferences over different parts of the cake, i.e., some people prefer the chocolate toppings, some prefer the cherries, some just want as large a piece as possible. The division should be ''unanimously'' fair – each person should receive a piece believed to be a fair share. The "cake" is only a metaphor; procedures for fair cake-cutting can be used to divide various kinds of resources, such as land estates, advertisement space or broadcast time. The prototypical procedure for fair cake-cutting is divide and choose, which is mentioned in the book of Book of Genesis, Genesis to resolve Abraham and Lot's conflict. This procedure solves the fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportional Division
A proportional division is a kind of fair division in which a resource is divided among ''n'' partners with subjective valuations, giving each partner at least 1/''n'' of the resource by his/her own subjective valuation. Proportionality was the first fairness criterion studied in the literature; hence it is sometimes called "simple fair division". It was first conceived by Steinhaus. Example Consider a land asset that has to be divided among 3 heirs: Alice and Bob who think that it's worth 3 million dollars, and George who thinks that it's worth $4.5M. In a proportional division, Alice receives a land-plot that she believes to be worth at least $1M, Bob receives a land-plot that ''he'' believes to be worth at least $1M (even though Alice may think it is worth less), and George receives a land-plot that he believes to be worth at least $1.5M. Existence A proportional division does not always exist. For example, if the resource contains several indivisible items and the number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Last Diminisher
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. For example, if Alice values the entire cake as $100 and there are 5 partners then Alice can receive a piece that she values as at least $20, regardless of what the other partners think or do. History During World War II, the Polish-Jewish mathematician Hugo Steinhaus, who was hiding from the Nazis, occupied himself with the question of how to divide resources fairly. Inspired by the divide and choose procedure for dividing a cake between two brothers, he asked his students, Stefan Banach and Bronisław Knaster, to find a proced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shimon Even
Shimon Even (; June 15, 1935 – May 1, 2004) was an Israeli computer science researcher. His main topics of interest included algorithms, graph theory and cryptography. He was a member of the Computer Science Department at the Technion since 1974. Shimon Even was the PhD advisor of Oded Goldreich, a prominent cryptographer. Books * ''Algorithmic Combinatorics'', Macmillan, 1973. * ''Graph Algorithms'', Computer Science Press, 1979. . See also * Oblivious transfer In cryptography, an oblivious transfer (OT) protocol is a type of protocol in which a sender transfers one of potentially many pieces of information to a receiver, but remains oblivious as to what piece (if any) has been transferred. The first fo ... External links Memorial pageProf. Even's "genealogy" (PDF)* 1935 births 2004 deaths Modern cryptographers Graph theorists Israeli computer scientists Israeli cryptographers Harvard University alumni Even Shimon Burials at Yarkon Cemetery {{Israel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Azaria Paz
Azaria () or Azarya is a moshav in central Israel. Located in the Shephelah around five kilometres south-east of Ramle, it falls under the jurisdiction of Gezer Regional Council. In it had a population of . Etymology Its name is symbolic, though there is a theory that it was named after Azariah of Judah. The symbolic meaning is an acronym from the Hebrew religious sentence 'עולי זאכו ראו ישועת ה (''Oleh zakho ra'u yeshuat HaShem'', lit. "Immigrants of Zakho (village in Kurdistan) saw the salvation of the Lord").Carta's Official Guide to Israel and Complete Gazetteer to all Sites in the Holy Land. (3rd edition 1993) Jerusalem, Carta, p.91, (English) History The moshav was established on the land of the depopulated Palestinian village of Al-Barriyya on 30 October 1949 by 25 families from Jerusalem Jerusalem is a city in the Southern Levant, on a plateau in the Judaean Mountains between the Mediterranean Sea, Mediterranean and the Dead Sea. It i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ranking
A ranking is a relationship between a set of items, often recorded in a list, such that, for any two items, the first is either "ranked higher than", "ranked lower than", or "ranked equal to" the second. In mathematics, this is known as a weak order or total preorder of objects. It is not necessarily a total order of objects because two different objects can have the same ranking. The rankings themselves are totally ordered. For example, materials are totally preordered by hardness, while degrees of hardness are totally ordered. If two items are the same in rank it is considered a tie. By reducing detailed measures to a sequence of ordinal numbers, rankings make it possible to evaluate complex information according to certain criteria. Thus, for example, an Internet search engine may rank the pages it finds according to an estimation of their relevance, making it possible for the user quickly to select the pages they are likely to want to see. Analysis of data obtained by ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Division Protocols
A fair (archaic: faire or fayre) is a gathering of people for a variety of entertainment or commercial activities. Fairs are typically temporary with scheduled times lasting from an afternoon to several weeks. Fairs showcase a wide range of goods, products, and services, and often include competitions, exhibitions, and educational activities. Fairs can be thematic, focusing on specific industries or interests. Types Variations of fairs include: * Art fairs, including art exhibitions and arts festivals * Book Fairs in communities and schools provide an opportunity for readers, writers, publishers to come together and celebrate literature. * County fair (US) or county show (UK), a public agricultural show exhibiting the equipment, animals, sports and recreation associated with agriculture and animal husbandry. * Festival, an event ordinarily coordinated with a theme e.g. music, art, season, tradition, history, ethnicity, religion, or a national holiday. * Health fair, an even ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
