Quantum optimization algorithms
... are quantum algorithms that are used to solve optimization problems. Mathematical optimization ... Ramana, Motakuri V. (1997). "An exact duality theory for semidefinite programming and its complexity implications". ... and an algorithm for learning the fit parameters. Because the quantum algorithm is mainly based on the HHL algorithm, it ... The quantum algorithm provides a quadratic improvement over the best classical algorithm in the general case, and an ...
Universal portfolio algorithm
The universal portfolio algorithm is a portfolio selection algorithm from the field of machine learning and information theory ... Cover, Thomas M. (1991). "Universal Portfolios". Mathematical Finance. 1 (1): 1-29. doi:10.1111/j.1467-9965.1991.tb00002.x. ... The algorithm rebalances the portfolio at the beginning of each trading period. At the beginning of the first trading period it ... The algorithm learns adaptively from historical data and maximizes the log-optimal growth rate in the long run. It was ...
Euclidean algorithm
Elementary Number Theory, Group Theory and Ramanujan Graphs. London Mathematical Society Student Texts. Vol. 55. Cambridge ... "Euclidean Algorithm". MathWorld. Euclid's Algorithm at cut-the-knot Euclid's algorithm at PlanetMath. The Euclidean Algorithm ... are probably the binary algorithm and Euclid's algorithm for smaller numbers, and either Lehmer's algorithm or Lebealean's ... Providence, RI: American Mathematical Society. pp. 327-340. ISBN 9780821887592. MR 2076257. The algorithms that are used the ...
Verhoeff algorithm
... check digit algorithm Verhoeff, J. (1969). Error Detecting Decimal Codes (Tract 29). The Mathematical Centre, Amsterdam. ... Kirtland, Joseph (2001). "5. Group Theory and the Verhoeff Check Digit Scheme". Identification Numbers and Check Digit Schemes ... Algorithm Detailed description of the Verhoeff algorithm (Modular arithmetic, Checksum algorithms, Error detection and ... A similar code is the Damm algorithm, which has similar qualities. The Verhoeff algorithm can be implemented using three tables ...
Quantum algorithm
It can be used to solve problems in graph theory. The algorithm makes use of classical optimization of quantum operations to ... Communications in Mathematical Physics. 227 (3): 587-603. arXiv:quant-ph/0001071. Bibcode:2002CMaPh.227..587F. doi:10.1007/ ... The algorithm is frequently used as a subroutine in other algorithms. Shor's algorithm solves the discrete logarithm problem ... The best-known algorithms are Shor's algorithm for factoring and Grover's algorithm for searching an unstructured database or ...
FKT algorithm
Kasteleyn, P. W. (1967), "Graph theory and crystal physics", in Harary, F. (ed.), Graph Theory and Theoretical Physics, New ... Zurich: European Mathematical Society. pp. 963-984. Cayley, Arthur (1847). "Sur les determinants gauches" [On skew determinants ... The FKT algorithm has seen extensive use in holographic algorithms on planar graphs via matchgates. For example, consider the ... The key idea of the FKT algorithm is to convert the problem into a Pfaffian computation of a skew-symmetric matrix derived from ...
Generalized Hebbian algorithm
Hertz, John; Anders Krough; Richard G. Palmer (1991). Introduction to the Theory of Neural Computation. Redwood City, CA: ... Journal of Mathematical Biology. 15 (3): 267-273. doi:10.1007/BF00275687. PMID 7153672. S2CID 16577977. BF00275687. (Articles ... The generalized Hebbian algorithm (GHA), also known in the literature as Sanger's rule, is a linear feedforward neural network ... The name originates because of the similarity between the algorithm and a hypothesis made by Donald Hebb about the way in which ...
Galactic algorithm
Ingber, Lester (1993). "Simulated annealing: Practice versus theory". Mathematical and Computer Modelling. 18 (11): 29-57. doi: ... This algorithm is not galactic and is used in practice. Further extensions of this, using sophisticated group theory, are the ... A galactic algorithm is one that outperforms other algorithms for problems that are sufficiently large, but where "sufficiently ... Even if they are never used in practice, galactic algorithms may still contribute to computer science: An algorithm, even if ...
Glushkov's construction algorithm
Jean-Éric Pin (Nov 2016). Mathematical Foundations of Automata Theory (PDF). Paris.{{cite book}}: CS1 maint: location missing ... In computer science theory - particularly formal language theory - Glushkov's construction algorithm, invented by Victor ... Аналитик V.M. Glushkov (1961). "The abstract theory of automata". Russian Mathematical Surveys (in Russian). 16 (5): 1-53. ... The converse of Glushkov's algorithm is Kleene's algorithm, which transforms a finite automaton into a regular expression. The ...
Gillespie algorithm
Doob, Jacob L. (1942). "Topics in the Theory of Markoff Chains". Transactions of the American Mathematical Society. 52 (1): 37- ... In probability theory, the Gillespie algorithm (or the Doob-Gillespie algorithm or Stochastic Simulation Algorithm, the SSA) ... Adapted techniques generally compromise the exactitude of the theory behind the algorithm as it connects to the master equation ... We will now describe how to apply the Gillespie algorithm to this system. In the algorithm, we advance forward in time in two ...
Algorithm characterizations
Theory of algorithms. [Translated by Jacques J. Schorr-Kon and PST staff] Imprint Moscow, Academy of Sciences of the USSR, 1954 ... "does not pretend to mathematical precision" (p. 1). His 1954 monograph was his attempt to define algorithm more accurately; he ... "Goodness" of an algorithm, "best" algorithms: Knuth states that "In practice, we not only want algorithms, we want good ... Algorithm characterizations are attempts to formalize the word algorithm. Algorithm does not have a generally accepted formal ...
Lenstra-Lenstra-Lovász lattice basis reduction algorithm
Theory of cryptography, Computational number theory, Lattice points). ... "Introduction to Mathematical Cryptography Errata" (PDF). Brown University Mathematics Dept. Retrieved 5 May 2015. Bosma, Wieb ... The algorithm can be used to find integer solutions to many problems. In particular, the LLL algorithm forms a core of one of ... The LLL algorithm has found numerous other applications in MIMO detection algorithms and cryptanalysis of public-key encryption ...
Convex hull algorithms
Avis, David; Bremner, David; Seidel, Raimund (1997), "How good are convex hull algorithms?", Computational Geometry: Theory and ... ACM Transactions on Mathematical Software. 22 (4): 469-483. doi:10.1145/235815.235821. ... A much simpler algorithm was developed by Chan in 1996, and is called Chan's algorithm. Known convex hull algorithms are listed ... Such algorithms are called output-sensitive algorithms. They may be asymptotically more efficient than Θ(n log n) algorithms in ...
Michael O. Rabin
Rabin, MO (1980). "Probabilistic algorithm for testing primality". Journal of Number Theory. 12 (1): 128-138. doi:10.1016/0022- ... Transactions of the American Mathematical Society. 141: 1-35. doi:10.2307/1995086. JSTOR 1995086. Rabin, MO (1976). " ... "Probabilistic algorithms". Algorithms and Complexity, Proc. Symp. Pittsburgh. ... As to the origins of what was to become computational complexity theory, the next summer Rabin returned to the Lamb Estate. ...
Ralph Gordon Stanton
... graph theory, including graph models of networks; and algorithms. Stanton's influence on the young University of Waterloo ... Stanton's main areas of research were in statistics and applied statistics; algebra; mathematical biology; combinatorial design ... Stanton also helped organize the first Southeastern Conference on Combinatorics, Graph Theory, and Computing. He continued as ... Stanton founded and administered three not-for-profit corporations dedicated to mathematical research and communication. " ...
Bohemian matrices
Borwein, Peter B.; Jörgenson, Loki (December 2001). "Visible Structures in Number Theory". American Mathematical Monthly. 108 ( ... Thornton, Steven E (April 2019). Algorithms for Bohemian Matrices (PhD thesis). Western University. Archived from the original ... Bolyai Society Mathematical Studies. Vol. 17. pp. 257-289. arXiv:math/0611321. doi:10.1007/978-3-540-77200-2_13. ISBN 978-3-540 ... The results of graph theory can be used to explain some of the phenomena encountered in Bohemian matrix experiments. Conversely ...
Metric k-center
Boston, MA, USA: American Mathematical Society. ISBN 978-0821849118. Vazirani, Vijay V. (2003), Approximation Algorithms, ... Computational problems in graph theory, Approximation algorithms, NP-hard problems). ... by the greedy algorithm, say in ith iteration. But since the greedy algorithm always chooses the point furthest away from the ... In graph theory, this means finding a set of k vertices for which the largest distance of any point to its closest vertex in ...
Monadic second-order logic
Mathematical Systems Theory. 2 (1): 57-81. doi:10.1007/BF01691346. ISSN 1433-0490. S2CID 31513761. Meyer, Albert R. (1975). ... It is particularly important in the logic of graphs, because of Courcelle's theorem, which provides algorithms for evaluating ... As a consequence of this result, the following theories are decidable: The monadic second-order theory of trees. The monadic ... In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order ...
Markov algorithm
The Theory of Algorithms. American Mathematical Society Translations, series 2, 15, 1-14. (Translation from the Russian, Trudy ... Markov algorithm interpreter Markov algorithm interpreter Markov algorithm interpreters at Rosetta-Code (Articles lacking in- ... Refal is a programming language based on Markov algorithms. Normal algorithms are verbal, that is, intended to be applied to ... after which the algorithm stops with the result , , {\displaystyle ,,} . For other examples, see below. Any normal algorithm is ...
Church-Turing thesis
"The Theory of Algorithms". American Mathematical Society Translations. 2 (15): 1-14. Olszewski, Adam; Woleński, Jan; Janusz, ... Manna, Zohar (2003) [1974]. Mathematical Theory of Computation. Dover. ISBN 978-0-486-43238-0.{{cite book}}: CS1 maint: ... The argument that super-recursive algorithms are indeed algorithms in the sense of the Church-Turing thesis has not found broad ... then the hypothesis is an hypothesis about the application of the mathematical theory developed from the definition. For the ...
Coordinate descent
"Coordinate descent algorithms". Mathematical Programming. 151 (1): 3-34. arXiv:1502.04759. doi:10.1007/s10107-015-0892-3. S2CID ... Journal of Optimization Theory and Applications, Kluwer Academic/Plenum Publishers, vol. 54, no. 3, pp. 471-477, doi:10.1007/ ... so the algorithm will not take any step, even though both steps together would bring the algorithm closer to the optimum. While ... Suppose that the algorithm is at the point (-2, -2); then there are two axis-aligned directions it can consider for taking a ...
Maximally matchable edge
Journal of Algorithms. 10 (4): 557-567. doi:10.1016/0196-6774(89)90005-9.. (Graph theory, Matching (graph theory)). ... Lovász, László; Plummer, Michael (2009-08-18). Matching Theory. Providence, Rhode Island: American Mathematical Society. doi: ... In graph theory, a maximally matchable edge in a graph is an edge that is included in at least one maximum-cardinality matching ... Note that M is a perfect matching in H. Hence, using the algorithm of the previous subsection, it is possible to find all edges ...
Duality gap
Minoux, Michel (1986). Mathematical programming: Theory and algorithms. Egon Balas (forward); Steven Vajda (trans) from the ( ... Ahuja, Ravindra K.; Magnanti, Thomas L.; Orlin, James B. (1993). Network Flows: Theory, Algorithms and Applications. Prentice ... Abstract Duality for Practitioners". Convex analysis and minimization algorithms, Volume II: Advanced theory and bundle methods ... Shapiro, Jeremy F. (1979). Mathematical programming: Structures and algorithms. New York: Wiley-Interscience [John Wiley & Sons ...
Duality (optimization)
Minoux, Michel (1986). Mathematical programming: Theory and algorithms. Egon Balas (forward); Steven Vajda (trans) from the ( ... Minoux, Michel (1986). Mathematical programming: Theory and algorithms. Egon Balas (forward); Steven Vajda (trans) from the ( ... In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed ... ISBN 978-1-4419-2026-3. Ahuja, Ravindra K.; Magnanti, Thomas L.; Orlin, James B. (1993). Network Flows: Theory, Algorithms and ...
Relaxation (iterative method)
Minoux, M. (1986). Mathematical programming: Theory and algorithms. Egon Balas (foreword) (Translated by Steven Vajda from the ... These are not to be confused with relaxation methods in mathematical optimization, which approximate a difficult problem by a ... reprinted by Dover, 2003) Abraham Berman, Robert J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, 1994, SIAM. ... Nonnegative Matrices in the Mathematical Sciences, 1994, SIAM. ISBN 0-89871-321-8. Ortega, J. M.; Rheinboldt, W. C. (2000). ...
Nimrod Megiddo
His interests include combinatorial optimization, algorithm design and analysis, game theory, and machine learning. He was one ... Fellows award for contributions to the theory and application of mathematical programming, including parametric searches, ... "Applying parallel computation algorithms in the design of serial algorithms", Journal of the ACM, 30 (4): 852-865, doi:10.1145/ ... Megiddo received the 2014 John von Neumann Theory Prize, the 1992 ICS Prize, and is a 1992 Frederick W. Lanchester Prize ...
Lagrange multiplier
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a ... In control theory this is formulated instead as costate equations. Moreover, by the envelope theorem the optimal value of a ... Convex analysis and minimization algorithms. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of ... In optimal control theory, the Lagrange multipliers are interpreted as costate variables, and Lagrange multipliers are ...
Relaxation (approximation)
Minoux, M. (1986). Mathematical programming: Theory and algorithms. Chichester: A Wiley-Interscience Publication. John Wiley & ... In mathematical optimization and related fields, relaxation is a modeling strategy. A relaxation is an approximation of a ... ISBN 978-0-02-398415-0. Roubíček, T. (1997). Relaxation in Optimization Theory and Variational Calculus. Berlin: Walter de ... Relaxation techniques complement or supplement branch and bound algorithms of combinatorial optimization; linear programming ...
Richard E. Bellman
Introduction to the Mathematical Theory of Control Processes 1970. Algorithms, Graphs and Computers 1972. Dynamic Programming ... Mathematical Aspects of Scheduling and Applications 1983. Mathematical Methods in Medicine 1984. Partial Differential Equations ... Though discovering the algorithm after Ford he is referred to in the Bellman-Ford algorithm, also sometimes referred to as the ... one of the most important journals in the field of Mathematical Biology. In 1985, the Bellman Prize in Mathematical Biosciences ...
Lagrangian relaxation
Minoux, M. (1986). Mathematical programming: Theory and algorithms. Egon Balas (foreword) (Translated by Steven Vajda from the ... Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin (1993). Network Flows: Theory, Algorithms and Applications. Prentice ... Advanced theory and bundle methods. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical ... ISBN 3-540-56852-2. Lasdon, Leon S. (2002). Optimization theory for large systems (reprint of the 1970 Macmillan ed.). Mineola ...
Bernstein-Sato polynomial
Sato, Mikio (1990) [1970]. "Theory of prehomogeneous vector spaces (algebraic part)". Nagoya Mathematical Journal. 120: 1-34. ... Devising ways to bypass the combinatorial explosion of the brute force algorithm would be of great value in such applications. ... It has applications to singularity theory, monodromy theory, and quantum field theory. Severino Coutinho (1995) gives an ... Translations of Mathematical Monographs. Vol. 217. Providence, R.I.: American Mathematical Society. ISBN 978-0-8218-2766-6. MR ...
Low-discrepancy sequence
An implementation of the algorithm in Fortran is available from Netlib. Discrepancy theory Markov chain Monte Carlo Quasi-Monte ... Bratley, Paul; Fox, Bennett L. (1988). "Algorithm 659". ACM Transactions on Mathematical Software. 14: 88-100. doi:10.1145/ ... ISBN 0-521-43108-5. Collected Algorithms of the ACM (See algorithms 647, 659, and 738.) Quasi-Random Sequences from the GNU ... Quasirandom numbers can also be combined with search algorithms. A binary tree Quicksort-style algorithm ought to work ...