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Movie Title Year Distributor Notes Rev Formats Adult Video News Awards 1992 1992 VCA Anal Brat 1993 Flame Video Anal DO Anal Files 8 1996 L.B.O. Entertainment DO Anal Vision 23 1994 L.B.O. Entertainment Anal DO Anal Vision 25 1994 L.B.O. Entertainment Anal O Army Brat 2 1989 Vivid 2 DO Barbara Dare: Dirtiest Of Dare 2004 Vivid O Barbara Dare: Up Close and Personal 2002 Vivid LezOnly DO Beach Blanket Brat 1989 Vivid O Biff Malibu's Totally Nasty Home Videos 38 1993 Anabolic Video Blonde Forces 2: Honeydrippers 1994 Coast To Coast DO Body English 1994 HIP Video Booty Camp 2001 Vivid LezOnly 1 DO Brat Force 1989 Vivid 1 DO Brat Pack 1990 Global Media DRO Bratgirl 1989 Vivid 1 DO Buffy Malibu's Nasty Girls 5 1993 Anabolic Video LezOnly 1 DRO Bustin Out My Best Anal 1995 Factory Home Video Anal 1 DRO Cherry Poppers 2 1994 Zane Entertainment Group Anal Bald 1 O Debi Diamond: Up Close and Personal 2002 Vivid DO
Double Take 1990 Coast To Coast Facial Hardcore Collection 7 1995 L.B.O. Entertainment O Jessie James 1995 Xibitions MastOnly Love in the Great Outdoors: Hyapatia Lee 1993 Vivid Nymphobrat 1989 Vivid Anal 1 DR Perfect Brat 1989 Vivid DO Pumping It Up 1992 Las Vegas Video Say Something Nasty 1990 Coast To Coast O Screw The Right Thing 1990 Vidway DO Sexual Fantasies 1989 MFM Home Video LezOnly Seymore Butts Meets the Cumback Brat 1993 Factory Home Video Anal DO Titillation 1993 Vivid Tonya And Nancy - The Real Story 1994 Executive Video Ultimate Barbara Dare 2002 Vivid D Victoria With An 'A' 1994 Pleasure Productions Bald Vivid Girls 1 2007 Vivid 1 DRO Vivid's Bloopers And Boners 1996 Vivid LezOnly 1 Who Framed Ginger Grant 1989 Coast To Coast Wild Goose Chase 1991 Evil Angel



problems on graphs. A graph exploration algorithm specifies rules for moving around a graph and is useful for such problems. This category also includes search algorithms, branch and bound enumeration and backtracking. Randomized algorithm Such algorithms make some choices randomly (or pseudo-randomly). They can be very useful in finding approximate solutions for problems where finding exact solutions can be impractical (see heuristic method below). For some of these problems, it is known that the fastest approximations must involve some randomness.[76] Whether randomized algorithms with polynomial time complexity can be the fastest algorithms for some problems is an open question known as the P versus NP problem. There are two large classes of such algorithms: Monte Carlo algorithms return a correct answer with high-probability. E.g. RP is the subclass of these that run in polynomial time. Las Vegas algorithms always return the correct answer, but their running time is only probabilistically bound, e.g. ZPP. Reduction of complexity This technique involves solving a difficult problem by transforming it into a better-known problem for which we have (hopefully) asymptotically optimal algorithms. The goal is to find a reducing algorithm whose complexity is not dominated by the resulting reduced algorithm's. For example, one selection algorithm for finding the median in an unsorted list involves first sorting the list (the expensive portion) and then pulling out the middle element in the sorted list (the cheap portion). This technique is also known as transform and conquer. Back tracking In this approach, multiple solutions are built incrementally and abandoned when it is determined that they cannot lead to a valid full solution. Optimization problems For optimization problems there is a more specific classification of algorithms; an algorithm for such problems may fall into one or more of the general categories described above as well as into one of the following: Linear programming When searching for optimal solutions to a linear function bound to linear equality and inequality constraints, the constraints of the problem can be used directly in producing the optimal solutions. There are algorithms that can solve any problem in this category, such as the popular simplex algorithm.[77] Problems that can be solved with linear programming include the maximum flow problem for directed graphs. If a problem additionally requires that one or more of the unknowns must be an integer then it is classified in integer programming. A linear programming algorithm can solve such a problem if it can be proved that all restrictions for integer values are superficial, i.e., the solutions satisfy these restrictions anyway. In the general case, a specialized algorithm or an algorithm that finds approximate solutions is used, depending on the difficulty of the problem. Dynamic programming When a problem shows optimal substructures—meaning the optimal solution to a problem can be constructed from optimal solutions to subproblems—and overlapping subproblems, meaning the same subproblems are used to solve many different problem instances, a quicker approach called dynamic programming avoids recomputing solutions that have already been computed. For example, Floyd–Warshall algorithm, the shortest path to a goal from a vertex in a weighted graph can be found by using the shortest path to the goal from all adjacent vertices. Dynamic programming and memoization go together. The main difference between dynamic programming and divide and conquer is that subproblems are more or less independent in divide and conquer, whereas subproblems overlap in dynamic programming. The difference between dynamic programming and straightforward recursion is in caching or memoization of recursive calls. When subproblems are independent and there is no repetition, memoization does not help; hence dynamic programming is not a solution for all complex problems. By using memoization or maintaining a table of subproblems already solved, dynamic programming reduces the exponential nature of many problems to polynomial complexity. The greedy method A greedy algorithm is similar to a dynamic programming algorithm in that it works by examining substructures, in this case not of the problem but of a given solution. Such algorithms start with some solution, which may be given or have been constructed in some way, and improve it by making small modifications. For some problems they can find the optimal solution while for others they stop at local optima, that is, at solutions that cannot be improved by the algorithm but are not optimum. The most popular use of greedy algorithms is for finding the minimal spanning tree where finding the optimal solution is possible with this method. Huffman Tree, Kruskal, Prim, Sollin are greedy algorithms that can solve this optimization problem. The heuristic method In optimization problems, heuristic algorithms can be used to find a solution close to the optimal solution in cases where finding the optimal solution is impractical. These algorithms work by getting closer and closer to the optimal solution as they progress. In principle, if run for an infinite amount of time, they will find the optimal solution. Their merit is that they can find a solution very close to the optimal solution in a relatively short time. Such algorithms include local search, tabu search, simulated annealing, and genetic algorithms. Some of them, like simulated annealing, are non-deterministic algorithms while others, like tabu search, are deterministic. When a bound on the error of the non-optimal solution is known, the algorithm is further categorized as an approximation algorithm. By field of study See also: List of algorithms Every field of science has its own problems and needs efficient algorithms. Related problems in one field are often studied together. Some example classes are search algorithms, sorting algorithms, merge algorithms, numerical algorithms, graph algorithms, string algorithms, computational geometric algorithms, combinatorial algorithms, medical algorithms, machine learning, cryptography, data compression algorithms and parsing techniques. Fields tend to overlap with each other, and algorithm advances in one field may improve those of other, sometimes completely unrelated, fields. For example, dynamic programming was invented for optimization of resource consumption in industry but is now used in solving a broad range of problems in many fields. By complexity See also: Complexity class and Parameterized complexity Algorithms can be classified by the amount of time they need to complete compared to their input size: Constant time: if the time needed by the algorithm is the same, regardless of the input size. E.g. an access to an array element. Logarithmic time: if the time is a logarithmic function of the input size. E.g. binary search algorithm. Linear time: if the time is proportional to the input size. E.g. the traverse of a list. Polynomial time: if the time is a power of the input size. E.g. the bubble sort algorithm has quadratic time complexity. Exponential time: if the time is an exponential function of the input size. E.g. Brute-force search. Some problems may have multiple algorithms of differing complexity, while other problems might have no algorithms or no known efficient algorithms. There are also mappings from some problems to other problems. Owing to this, it was found to be more suitable to classify the problems themselves instead of the algorithms into equivalence classes based on the complexity of the best possible algorithms for them. Continuous algorithms The adjective "continuous" when applied to the word "algorithm" can mean: An algorithm operating on data that represents continuous quantities, even though this data is represented by discrete approximations—such algorithms are studied in numerical analysis; or An algorithm in the form of a differential equation that operates continuously on the data, running on an analog computer.[78] Legal issues See also: Software patent Algorithms, by themselves, are not usually patentable. In the United States, a claim consisting solely of simple manipulations of abstract concepts, numbers, or signals does not constitute "processes" (USPTO 2006), and hence algorithms are not patentable (as in Gottschalk v. Benson). However practical applications of algorithms are sometimes patentable. For example, in Diamond v. Diehr, the application of a simple feedback algorithm to aid in the curing of synthetic rubber was deemed patentable. The patenting of software is highly controversial, and there are highly criticized patents involving algorithms, especially data compression algorithms, such as Unisys' LZW patent. Additionally, some cryptographic algorithms have export restrictions (see export of cryptography). History: Development of the notion of "algorithm" Ancient Near East The earliest evidence of algorithms is found in the Babylonian mathematics of ancient Mesopotamia (modern Iraq). A Sumerian clay tablet found in Shuruppak near Baghdad and dated to circa 2500 BC described the earliest division algorithm.[10] During the Hammurabi dynasty circa 1800-1600 BC, Babylonian clay tablets described algorithms for computing formulas.[79] Algorithms were also used in Babylonian astronomy. Babylonian clay tablets describe and employ algorithmic procedures to compute the time and place of significant astronomical events.[80] Algorithms for arithmetic are also found in ancient Egyptian mathematics, dating back to the Rhind Mathematical Papyrus circa 1550 BC.[10] Algorithms were later used in ancient Hellenistic mathematics. Two examples are the Sieve of Eratosthenes, which was described in the Introduction to Arithmetic by Nicomachus,[81][12]:Ch 9.2 and the Euclidean algorithm, which was first described in Euclid's Elements (c. 300 BC).[12]:Ch 9.1 Discrete and distinguishable symbols Tally-marks: To keep track of their flocks, their sacks of grain and their money the ancients used tallying: accumulating stones or marks scratched on sticks or making discrete symbols in clay. Through the Babylonian and Egyptian use of marks and symbols, eventually Roman numerals and the abacus evolved (Dilson, p. 16–41). Tally marks appear prominently in unary numeral system arithmetic used in Turing machine and Post–Turing machine computations. Manipulation of symbols as "place holders" for numbers: algebra Muhammad ibn Musa al-Khwarizmi, a Persian mathematician, wrote the Al-jabr in the 9th century. The terms "algorism" and "algorithm" are derived from the name al-Khwarizmi, while the term "algebra" is derived from the book Al-jabr. In Europe, the word "algorithm" was originally used to refer to the sets of rules and techniques used by Al-Khwarizmi to solve algebraic equations, before later being generalized to refer to any set of rules or techniques.[82] This eventually culminated in Leibniz's notion of the calculus ratiocinator (ca 1680): A good century and a half ahead of his time, Leibniz proposed an algebra of logic, an algebra that would specify the rules for manipulating logical concepts in the manner that ordinary algebra specifies the rules for manipulating numbers.[83] Cryptographic algorithms The first cryptographic algorithm for deciphering encrypted code was developed by Al-Kindi, a 9th-century Arab mathematician, in A Manuscript On Deciphering Cryptographic Messages. He gave the first description of cryptanalysis by frequency analysis, the earliest codebreaking algorithm.[13] Mechanical contrivances with discrete states The clock: Bolter credits the invention of the weight-driven clock as "The key invention [of Europe in the Middle Ages]", in particular, the verge escapement[84] that provides us with the tick and tock of a mechanical clock. "The accurate automatic machine"[85] led immediately to "mechanical automata" beginning in the 13th century and finally to "computational machines"—the difference engine and analytical engines of Charles Babbage and Countess Ada Lovelace, mid-19th century.[86] Lovelace is credited with the first creation of an algorithm intended for processing on a computer—Babbage's analytical engine, the first device considered a real Turing-complete computer instead of just a calculator—and is sometimes called "history's first programmer" as a result, though a full implementation of Babbage's second device would not be realized until decades after her lifetime. Logical machines 1870 – Stanley Jevons' "logical abacus" and "logical machine": The technical problem was to reduce Boolean equations when presented in a form similar to what is now known as Karnaugh maps. Jevons (1880) describes first a simple "abacus" of "slips of wood furnished with pins, contrived so that any part or class of the [logical] combinations can be picked out mechanically ... More recently, however, I have reduced the system to a completely mechanical form, and have thus embodied the whole of the indirect process of inference in what may be called a Logical Machine" His machine came equipped with "certain moveable wooden rods" and "at the foot are 21 keys like those of a piano [etc] ...". With this machine he could analyze a "syllogism or any other simple logical argument".[87] This machine he displayed in 1870 before the Fellows of the Royal Society.[88] Another logician John Venn, however, in his 1881 Symbolic Logic, turned a jaundiced eye to this effort: "I have no high estimate myself of the interest or importance of what are sometimes called logical machines ... it does not seem to me that any contrivances at present known or likely to be discovered really deserve the name of logical machines"; see more at Algorithm characterizations. But not to be outdone he too presented "a plan somewhat analogous, I apprehend, to Prof. Jevon's abacus ... [And] [a]gain, corresponding to Prof. Jevons's logical machine, the following contrivance may be described. I prefer to call it merely a logical-diagram machine ... but I suppose that it could do very completely all that can be rationally expected of any logical machine".[89] Jacquard loom, Hollerith punch cards, telegraphy and telephony – the electromechanical relay: Bell and Newell (1971) indicate that the Jacquard loom (1801), precursor to Hollerith cards (punch cards, 1887), and "telephone switching technologies" were the roots of a tree leading to the development of the first computers.[90] By the mid-19th century the telegraph, the precursor of the telephone, was in use throughout the world, its discrete and distinguishable encoding of letters as "dots and dashes" a common sound. By the late 19th century the ticker tape (ca 1870s) was in use, as was the use of Hollerith cards in the 1890 U.S. census. Then came the teleprinter (ca. 1910) with its punched-paper use of Baudot code on tape. Telephone-switching networks of electromechanical relays (invented 1835) was behind the work of George Stibitz (1937), the inventor of the digital adding device. As he worked in Bell Laboratories, he observed the "burdensome' use of mechanical calculators with gears. "He went home one evening in 1937 intending to test his idea... When the tinkering was over, Stibitz had constructed a binary adding device".[91] Davis (2000) observes the particular importance of the electromechanical relay (with its two "binary states" open and closed): It was only with the development, beginning in the 1930s, of electromechanical calculators using electrical relays, that machines were built having the scope Babbage had envisioned."[92] Mathematics during the 19th century up to the mid-20th century Symbols and rules: In rapid succession, the mathematics of George Boole (1847, 1854), Gottlob Frege (1879), and Giuseppe Peano (1888–1889) reduced arithmetic to a sequence of symbols manipulated by rules. Peano's The principles of arithmetic, presented by a new method (1888) was "the first attempt at an axiomatization of mathematics in a symbolic language".[93] But Heijenoort gives Frege (1879) this kudos: Frege's is "perhaps the most important single work ever written in logic. ... in which we see a " 'formula language', that is a lingua characterica, a language written with special symbols, "for pure thought", that is, free from rhetorical embellishments ... constructed from specific symbols that are manipulated according to definite rules".[94] The work of Frege was further simplified and amplified by Alfred North Whitehead and Bertrand Russell in their Principia Mathematica (1910–1913). The paradoxes: At the same time a number of disturbing paradoxes appeared in the literature, in particular, the Burali-Forti paradox (1897), the Russell paradox (1902–03), and the Richard Paradox.[95] The resultant considerations led to Kurt Gödel's paper (1931)—he specifically cites the paradox of the liar—that completely reduces rules of recursion to numbers. Effective calculability: In an effort to solve the Entscheidungsproblem defined precisely by Hilbert in 1928, mathematicians first set about to define what was meant by an "effective method" or "effective calculation" or "effective calculability" (i.e., a calculation that would succeed). In rapid succession the following appeared: Alonzo Church, Stephen Kleene and J.B. Rosser's ?-calculus[96] a finely honed definition of "general recursion" from the work of Gödel acting on suggestions of Jacques Herbrand (cf. Gödel's Princeton lectures of 1934) and subsequent simplifications by Kleene.[97] Church's proof[98] that the Entscheidungsproblem was unsolvable, Emil Post's definition of effective calculability as a worker mindlessly following a list of instructions to move left or right through a sequence of rooms and while there either mark or erase a paper or observe the paper and make a yes-no decision about the next instruction.[99] Alan Turing's proof of that the Entscheidungsproblem was unsolvable by use of his "a- [automatic-] machine"[100]—in effect almost identical to Post's "formulation", J. Barkley Rosser's definition of "effective method" in terms of "a machine".[101] S.C. Kleene's proposal of a precursor to "Church thesis" that he called "Thesis I",[102] and a few years later Kleene's renaming his Thesis "Church's Thesis"[103] and proposing "Turing's Thesis


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