Knapsack problem - Knapsack problem The knapsack problem is a problem in complexity theory, cryptography, and applied mathematics. Given a set of items, each with a cost and a value, determine the number of each item to include in a collection so that the total cost is less than some given cost and the total value is as large as possible. The name derives from the scenario of choosing treasures to stuff into your knapsack, when you can only carry so much weight. The decision problem form of the knapsack problem is the question "can a value of at least V be achieved without exceeding the cost C?" The 0/1 knapsack problem restricts the number of each items to zero or one. Of particular interest is the special case.
Subset sum problem - Subset sum problem The subset sum problem is an important problem in complexity theory and cryptography. The problem is this: given a set of integers, does any subset sum to exactly zero? For example, given the set {-7, -3, -2, 5, 8}, the answer is YES because the subset {-3, -2, 5} sums to zero. The problem is NP-Complete, and is perhaps the simplest such problem to describe. An equivalent problem is this: given a set of integers and an integer s, does any subset sum to s? Subset sum can also be thought of as a special case of the knapsack problem. Although the problem was described above in terms of integers and addition, it can actually be defined using any group. For example, the problem could.
Field Marshal - be drawn between "court marshals" and "military marshals". In 1560, France established the title Marshal of France (Maréchal de France), and by the time of the Thirty Years War, most Continental armies had a field marshal or two. Great Britain was a relative latecomer; the Duke of Argyll became her first field marshal in 1736 (however, for an alternate meaning of the word in England, see note 1). The field marshal's special symbol was a baton, famously mentioned by Napoleon: "Every French soldier carries a marshal's baton in his knapsack". The Maréchaux de France carried as their insignia of rank blue batons with gold fleurs-de-lis, engraved with the motto "Decus pacis, terror belli ("The symbol of peace, the terror of war"). Hermann Göring, holder of the singular rank "Marshal of the.
Emergency preparedness - for each team's leader, and four for each role in the EOC. Alternates agree to carry pagers or cellular phones. Amateur radio operators train and organize to offer civil emergency communication services at their own expense, and form service organizations for this purpose. Other preparations preposition training, supplies and equipment for use in the response and recovery stages. For example, storm shelters and evacuation routes are very helpful for extreme weather. In floods, prepositioned caches of food, fuel, boats and radio equipment can be very helpful. Many cities also offer training for community emergency response team. Basically, this is mass training to provide teams of amateur emergency workers in every neighborhood. These are truly useful because in an emergency, real firemen are instantly overloaded, with hundreds of calls, and the ability.
Asymmetric key algorithm - from the other. These are the 'public key / private key' algorithms, since one key of the pair can be published without affecting security of messages. In our analogy above, Bob might publish instructions on how to make a lock ("public key"); but the lock is of a type where it is very difficult to deduce from these instructions how to make a key which will open that lock ("private key"). Those wishing to send messages to Bob use the public key to encrypt the message; Bob uses his private key to decrypt it. Of course, there is the possibility that someone could "pick" either of Bob's or Alice's locks. Unlike the case with the one-time pad or its equivalents, there is no currently known asymmetric key algorithm which has been.
Trapdoor function - the mid-1970s with the publication of asymmetric encryption techniques by Diffie, Hellman, and Merkle. Several function classes have been proposed, and it soon became obvious that trapdoor functions are harder to find than was initially thought. In particular, the knapsack problem (in any of several flavors) turned out -- rather quickly -- to not be a trapdoor function. Currently, the best known such functions are prime factoring (in the RSA algorithm), the discrete logarithm problem (in the ElGamal algorithm and some others) and the elliptic curve problem. The last is rather newer than the others and has not been quite as useful as had been initially thought..
Public-key cryptography - requirements of the asymmetric key algorithm with which they are to be used. Like all key management, this is not trivially done. The theory behind asymmetric key algorithms was first published by Whitfield Diffie and Martin Hellman in 1975, and since then, several implementations have been created. One widely-used asymmetric key algorithm is RSA. It uses exponentiation modulo a product of two large primes to encrypt and decrypt. The public key exponent differs from the private key exponent, and determining one exponent from the other is believed to be fundamentally hard without knowing the primes. Another is ElGamal (developed by Taher ElGamal then of Netscape) which relies on the difficulty of the discrete logarithm problem. A third is a group of algorithms based on elliptic curves, first discovered by Neil Koblitz.
NP-complete - ones most likely not to be in P. The reason is that if you could find a way to solve an NP-complete problem quickly, then you could use that algorithm to solve all NP problems quickly. (A more formal definition is given below. See also Complexity classes P and NP). One example of an NP-complete problem is the subset sum problem which is: given a finite set of integers, determine whether any non-empty subset of them adds up to zero. A supposed answer is very easy to verify for correctness, but no-one knows a faster way to solve the problem than to try every single possible subset, which is very slow. At present, all known algorithms for NP-complete problems require time which is exponential in the problem size. It is unknown.
Merkle-Hellman - RSA, it has been broken. MH is based on the subset sum problem (a special case of the knapsack problem): given a list of numbers and a third number, which is the sum of a subset of these numbers, determine the subset. In general, this problem is known to be NP-hard; however, there are some 'easy' instances which can be solved efficiently. The Merkle-Hellman is based on transforming an easy instance into a difficult instance, and back again. It was broken by Shamir, not by attacking the knapsack problem, but rather by breaking the conversion from an easy knapsack to a hard one. The algorithm is as follows: KEY GENERATION - To encrypt n-bit messages, choose a superincreasing sequence w = (w1, w2, ..., wn) of n natural numbers (excluding zero)..
List of group theory topics - groups and their classification 13 Understanding groups as permutation groups History, major contributors Joseph-Louis Lagrange Niels Abel Evariste Galois Augustin Louis Cauchy Arthur Cayley Otto Ludwig Hölder Camille Jordan Ludwig Sylow Ferdinand Georg Frobenius Sophus Lie Felix Klein William Burnside Richard Dedekind David Hilbert Max August Zorn John Thompson Martin Dunwoody John Conway Famous problems Classification of finite simple groups Word problem for groups Subset sum problem Burnside's problem Whitehead problem Applications Computer algebra system Exponentiating by squaring Knapsack problem Shor's algorithm Cryptography Discrete logarithm Triple DES Caesar cipher Definitions in common with other mathematical ideas Binary operation Bilinear operator Commutative Associativity Equivalence relation Equivalence class Bijection Multiplication table Lattice Up to Congruence relation Prime number Mathematical objects which have (or make use of) a group operation Number Real number Integer.
List of mathematical topics (J-L) - Abraham Gotthelf -- KdV equation -- Kêng-Chih, Tsu -- Kepler, Johannes -- Kepler's laws of planetary motion -- Kepler solid -- Kernel (algebra) -- Kernel (category theory) -- Kernel of a homomorphism -- Kernel trick -- Key -- Kidinnu -- Killing field -- Kinematics -- Kinetic energy -- Kirchoff's Laws -- Kleene algebra -- Kleene star -- Kleene, Stephen -- Kleene's recursion theorem -- Klein bottle -- Klein, Felix -- Klein four-group -- Klein quartic -- Knapsack problem -- Knaster-Tarski theorem -- Knight's tour -- Knot invariant -- Knot polynomial -- Knot theory -- Knuth, Donald -- Knuth -yllion -- Knuths up-arrow notation -- Koch snowflake -- Kodaira, Kunihiko -- Kolmogorov, Andrey Nikolaevich -- Kolmogorov-Arnold-Moser theorem -- Kolmogorov Smirnov test -- Kolmogorov space -- Kolmogorov's zero-one law -- König's lemma --.
List of combinatorics topics - made since 1960. This page is complementary to the list of graph theory topics: graph theory being the part of combinatorial mathematics that is most like a separate discipline. In general, combinatorics is as much about problem solving as theory building. Since combinatorial mathematics is effectively the environment for the study of data structures in computer science, there are very many topics that arise there. The same could be said for other fields, such as error-correcting codes, bioinformatics. Table of contents showTocToggle("show","hide") 1 General combinatorial principles and methods 2 Problem solving as an art 3 Some general theories 4 Topics 5 Letters 6 Data structure concepts 7 People General combinatorial principles and methods To begin with, some general principles: Trial and error, brute force search, bogosort Pigeonhole principle Mathematical induction Recurrence.
List of computability and complexity topics - automaton Pushdown automaton Context-free grammar Chomsky hierarchy Context-sensitive language Recursively enumerable language Markov algorithm String rewriting system L-system Cellular automaton Conway's Game of Life Turing machine Turing-complete Turing tarpit Oracle machine Lambda calculus Combinatory logic Combinator Parallel computing Flynn's taxonomy Quantum computer Church-Turing thesis Recursive function Decision problems Entscheidungsproblem Halting problem Correctness Post correspondence problem Decidable language Undecidable language Word problem for groups Wang tile Definability questions Computable number Definable number Halting probability Algorithmic information theory Data compression Complexity theory Polynomial time Exponential time Time hierarchy theorem Polynomial-time many-one reduction Polynomial-time Turing reduction Complexity classes Complexity classes P and NP P-complete NP, NP-complete, NP-hard, NP-equivalent Co-NP, Co-NP-complete Sharp-P, Sharp-P-complete PSPACE, PSPACE-complete EXPSPACE, EXPTIME, EXPTIME-complete BPP BQP Class NC RP UP (complexity) ZPP Named problems Clique problem Hamiltonian cycle problem Integer factorization.
Kissing number problem - Kissing number problem In geometry, the kissing number problem is to find the maximal number of spheres of radius 1 that can simultaneously touch the unit sphere in n-dimensional Euclidean space (or, with the restriction for their centres to be in a particular lattice). See also: sphere packing.
Vertex cover problem - Vertex cover problem In computer science, the Vertex Cover Problem is an NP-complete problem in complexity theory. A vertex cover in a graph is a subset of the verticies of the graph, chosen with the property that one of the endpoints of each edge is in the subset. In the graph at right, {1,3,5,6} is an example of a vertex cover. The vertex cover problem is the optimization problem of finding a vertex cover of minimum size in a graph. The problem is a decision problem, so we wonder if a vertex cover of size k exists in the graph. VERTEX COVER = { k <= the number of vertices in G, G is a graph with a clique of size k or less} A brute force.
Year 2000 problem - Year 2000 problem zh-cn:两千年问题 The Year 2000 Problem (also known as the Y2K problem and the Millennium Bug) was a flaw in computer program design that caused some date-related processing to operate incorrectly for dates and times after January 1, 2000. It turned into a major fear that critical industries (electricity, financial, etc.) and government functions would stop working at 12:00 AM, January 1, 2000 and at other critical dates which were billed as "event horizons." This fear was fueled by huge amounts of press coverage and speculation, as well as copious official corporate and government reports. Y2K (or Y2k) was the common slang for the year 2000 problem. (The abbreviation combines the letter Y for "year", and K for the Latin prefix kilo meaning 1000; hence, 2K.
VESA Local Bus - memory-mapped I/O and DMA, while the ISA bus handled interrupts and port-mapped I/O. The VESA Local Bus was was designed as a stop-gap solution to the problem of ISA's limited bandwidth, and had several flaws that limited its useful life substantially: 80486 dependence. The VESA Local Bus relied heavily on the 80486's memory bus design. When the Pentium processor started to gain mass acceptance, circa 1995, there were major differences in its bus design, and the VESA bus was not easily adaptable. This also made moving the bus to non-Intel architectures nearly impossible. Limited number of slots available. Most PCs that used VESA Local Bus had only one or two slots available, as opposed to 5 or 6 ISA slots. This was because, as a direct branch of the 80486 memory.
Karl Krumbacher - the work and in a special supplement. Krumbacher also founded the Byzantinische Zeitschrift (1892) and the Byzantinisches Archiv (1898). He travelled extensively and the results of a journey to Greece appeared in his Griechische Reise (1886). Other works by him are: Casio (1897), a treatise on a 9th century Byzantine poetess, with the fragments; Michael Glykas (1894); Die griechische Litteratur das Mittelalters in P. Hinneberg’s Die Kultur der Gegenwart, i. 8 (1905); Das Problem der neugriechischen Schriftsprache (1902), in which he strongly opposed the efforts of the purists to introduce the classical style into modern Greek literature, and Populäre Aufsätze (1900). This entry was originally from the 1911 Encyclopedia Britannica..
Vegetarianism - of raising a kilogram of animal protein is many times the "cost" of growing a kilogram of vegetable protein. Health: Statistics indicate that people on vegetarian diets have lower incidence of heart disease, cancer and osteoporosis. The American Dietetic Association says, "Although nondietary factors, including physical activity and abstinence from smoking and alcohol, may play a role, [a meat-free, vegetarian] diet is clearly a contributing factor" in reducing both morbidity and mortality "rates from several chronic degenerative diseases than do nonvegetarians." Researchers like Dean Ornish have had successful results treating heart disease patients with strictly vegetarian diet, exercise and stress reduction programs. There are also nutritional considerations which encourage diets emphasizing fruit, vegetables and cereals and minimising meat and fat intake. Aesthetics: Some people intuitively find meat unappetizing, particularly when raw,.
Karl Guthe Jansky - of the Sun. The signal repeated not every 24 hours, but every 23 hours and 56 minutes. This is characteristic of the fixed stars, and other objects far from our solar system (sidereal day). He eventually figured out that the radiation was coming from the Milky Way and was strongest in the direction of the center of our Milky Way galaxy, in the constellation of Sagittarius. The discovery was widely publicized, appearing in the New York Times of May 5, 1933. Jansky wanted to follow up on this discovery and investigate the radio waves from the Milky Way Galaxy in more detail. He proposed to Bell Labs to build a 30 meter diameter dish antenna. But Bell Labs had the answer they wanted about static: the static was not a problem.
