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Edmonds–Pruhs Protocol
Edmonds–Pruhs protocol is a protocol for fair cake-cutting. Its goal is to create a partially proportional division of a heterogeneous resource among ''n'' people, such that each person receives a subset of the cake which that person values as at least 1/''an'' of the total, where a\geq 10 is some sufficiently large constant. It is a randomized algorithm whose running time is O(''n'') with probability close to 1. The protocol was developed by Jeff Edmonds and Kirk Pruhs, who later improved it in joint work with Jaisingh Solanki. Motivation A proportional division of a cake can be achieved using the recursive halving algorithm in time O(''n'' log ''n''). Several hardness results show that this run-time is optimal under a wide variety of assumptions. In particular, recursive halving is the fastest possible algorithm for achieving full proportionality when the pieces must be contiguous, and it is the fastest possible deterministic algorithm for achieving even partia ... [...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 that he or she believes 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 already in the book of Genesis. It solves the fair division problem for two people. The modern ... [...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] |
Randomized Algorithm
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables. One has to distinguish between algorithms that use the random input so that they always terminate with the correct answer, but where the expected running time is finite (Las Vegas algorithms, for example Quicksort), and algorithms which have a chance of producing an incorrect result (Monte Carlo algorithms, for example the Monte Carlo algorithm for the MFAS problem) or fail to produce a result either by signaling a failure or failing to terminate. In some cases, probabilistic algorithms are the only practical means of solving a problem. In common practice, randomized algor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jeff Edmonds
Jeff Edmonds is a Canadian and American mathematician and computer scientist specializing in computational complexity theory and machine learning. Academic career Edmonds received his Bachelors at Waterloo in 1987 and his Ph.D. in 1993 at University of Toronto. His thesis proved lower bounds on time-space tradeoffs. He did his post-doctorate work at the ICSI in Berkeley on secure data transmission over networks for multi-media applications. He joined Department of EECS at Lassonde School of Engineering York University in 1995. Research Edmonds' research interests include complexity theory, scheduling, proof systems, probability theory, combinatorics and machine learning. Personal life Edmonds is the son of another mathematician, Jack Edmonds. See also * Edmonds–Pruhs protocol Edmonds–Pruhs protocol is a protocol for fair cake-cutting. Its goal is to create a partially proportional division of a heterogeneous resource among ''n'' people, such that each person receives a sub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirk Pruhs
Kirk is a Scottish and former Northern English word meaning "church". It is often used specifically of the Church of Scotland. Many place names and personal names are also derived from it. Basic meaning and etymology As a common noun, ''kirk'' (meaning 'church') is found in Scots, Scottish English, Ulster-Scots and some English dialects, attested as a noun from the 14th century onwards, but as an element in placenames much earlier. Both words, ''kirk'' and ''church'', derive from the Koine Greek κυριακόν (δωμα) (kyriakon (dōma)) meaning ''Lord's (house)'', which was borrowed into the Germanic languages in late antiquity, possibly in the course of the Gothic missions. (Only a connection with the idiosyncrasies of Gothic explains how a Greek neuter noun became a Germanic feminine). Whereas ''church'' displays Old English palatalisation, ''kirk'' is a loanword from Old Norse and thus retains the original mainland Germanic consonants. Compare cognates: Icelandic & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balls Into Bins
The balls into bins (or balanced allocations) problem is a classic problem in probability theory that has many applications in computer science. The problem involves ''m'' balls and ''n'' boxes (or "bins"). Each time, a single ball is placed into one of the bins. After all balls are in the bins, we look at the number of balls in each bin; we call this number the ''load'' on the bin. The problem can be modelled using a Multinomial distribution, and may involve asking a question such as: What is the expected number of bins with a ball in them? Obviously, it is possible to make the load as small as ''m''/''n'' by putting each ball into the least loaded bin. The interesting case is when the bin is selected at random, or at least partially at random. A powerful balls-into-bins paradigm is the "power of two random choices" where each ball chooses two (or more) random bins and is placed in the lesser-loaded bin. This paradigm has found wide practical applications in shared-memory emulatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Load Balancing (computing)
In computing, load balancing is the process of distributing a set of tasks over a set of resources (computing units), with the aim of making their overall processing more efficient. Load balancing can optimize the response time and avoid unevenly overloading some compute nodes while other compute nodes are left idle. Load balancing is the subject of research in the field of parallel computers. Two main approaches exist: static algorithms, which do not take into account the state of the different machines, and dynamic algorithms, which are usually more general and more efficient but require exchanges of information between the different computing units, at the risk of a loss of efficiency. Problem overview A load-balancing algorithm always tries to answer a specific problem. Among other things, the nature of the tasks, the algorithmic complexity, the hardware architecture on which the algorithms will run as well as required error tolerance, must be taken into account. Therefore c ... [...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. Types Variations of fairs include: * Art fairs, including art exhibitions and arts festivals * County fair (USA) 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 event designed for outreach to provide basic preventive medicine and medical screening * Historical reenactments, including Renaissance fairs and Dickens fairs * Horse fair, an event where people buy and sell horses. * Job fair, event in which employers, recruiters, and schools give information to potential employees. * Regional or state fair, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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