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NP-hardness
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In computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-timeProbabilistic analysis of algorithms (303 words) [view diff] exact match in snippet view article find links to article
approach to estimate the computational complexity of an algorithm or a computational problem. It starts from an assumption about a probabilistic distributionASR-complete (140 words) [view diff] exact match in snippet view article find links to article
complexity theory, a term to indicate that the difficulty of a computational problem is equivalent to solving the central automatic speech recognitionGadget (computer science) (1,604 words) [view diff] exact match in snippet view article
fundamental units of a different computational problem. Gadgets are typically used to construct reductions from one computational problem to another, as part ofCombinatorial auction (1,079 words) [view diff] exact match in snippet view article find links to article
game-theoretic challenges compared to traditional auctions. An example of a computational problem is how to efficiently determine the allocation once the bids haveStrong NP-completeness (714 words) [view diff] exact match in snippet view article find links to article
computational problems that is a special case of NP-completeness. A general computational problem may have numerical parameters. For example, the input to the bin3-dimensional matching (1,550 words) [view diff] exact match in snippet view article find links to article
matching, often abbreviated as 3DM, is also the name of a well-known computational problem: finding a largest 3-dimensional matching in a given hypergraphSimultaneous localization and mapping (3,878 words) [view diff] exact match in snippet view article find links to article
Simultaneous localization and mapping (SLAM) is the computational problem of constructing or updating a map of an unknown environment while simultaneouslyTonelli–Shanks algorithm (3,751 words) [view diff] exact match in snippet view article find links to article
composite moduli: finding square roots modulo composite numbers is a computational problem equivalent to integer factorization. An equivalent, but slightlyHome prime (870 words) [view diff] exact match in snippet view article find links to article
subject is really one in recreational mathematics. The outstanding computational problem as of 2016[update] is whether HP(49) = HP(77) can be calculatedGene prediction (3,555 words) [view diff] exact match in snippet view article find links to article
research community, gene finding has been redefined as a largely computational problem. Determining that a sequence is functional should be distinguishedKronecker substitution (312 words) [view diff] exact match in snippet view article find links to article
representation of p(x). One application of this method is to reduce the computational problem of multiplying polynomials to the (potentially simpler) problemFloating-point error mitigation (1,109 words) [view diff] exact match in snippet view article find links to article
measured in petaflops, floating-point error is a major concern for computational problem solvers. The following sections describe the strengths and weaknessesFine-grained reduction (831 words) [view diff] exact match in snippet view article find links to article
complexity theory, a fine-grained reduction is a transformation from one computational problem to another, used to relate the difficulty of improving the timeXuong tree (387 words) [view diff] exact match in snippet view article find links to article
graph in polynomial time, by a transformation to a more general computational problem on matroids, the matroid parity problem for linear matroids. BeinekeQuery complexity (244 words) [view diff] exact match in snippet view article find links to article
computational complexity describes the number of queries needed to solve a computational problem for an input that can be accessed only through queries. See in particular:Mordell–Weil theorem (619 words) [view diff] exact match in snippet view article find links to article
unanswered: Calculation of the rank. This is still a demanding computational problem, and does not always have effective solutions. Meaning of the rank:Data publishing (2,056 words) [view diff] exact match in snippet view article find links to article
emerging topic in computer science and it has been defined as a computational problem. Indeed, citing data poses significant challenges to computer scientistsJoseph Zachary (343 words) [view diff] case mismatch in snippet view article find links to article
Zachary, Joseph L. (1996). Introduction to Scientific Programming: Computational Problem Solving Using Maple and C. Springer-Verlag. ISBN 0-387-94630-6.Parallel parking problem (190 words) [view diff] exact match in snippet view article find links to article
Robotics and planning computational problemEconomic materialism (1,657 words) [view diff] exact match in snippet view article find links to article
quality of life Reduction (complexity) – Transformation of one computational problem to another Conspicuous consumption – Concept in sociology and economyGeneral-purpose programming language (1,495 words) [view diff] exact match in snippet view article find links to article
Turing complete, meaning that they can theoretically solve any computational problem. Domain-specific languages are often similarly Turing complete butShifted force method (983 words) [view diff] exact match in snippet view article find links to article
interactions are long-range in nature, presenting a challenging computational problem in the simulation of particulate systems. To determine the net forcesMinkowski's theorem (2,350 words) [view diff] exact match in snippet view article find links to article
certain magnitude bound, finding this vector is in general a hard computational problem. Finding the vector within a factor guaranteed by Minkowski's boundNondeterministic Turing machine (1,626 words) [view diff] exact match in snippet view article find links to article
but every branch must reject for the string to be rejected. Any computational problem that can be solved by a DTM can also be solved by a NTM, and viceGraph isomorphism (1,637 words) [view diff] exact match in snippet view article find links to article
it is a problem to be tackled with an algorithmic approach. The computational problem of determining whether two finite graphs are isomorphic is calledGenome project (1,822 words) [view diff] exact match in snippet view article find links to article
and the process continues. Genome assembly is a very difficult computational problem, made more difficult because many genomes contain large numbersOptimal substructure (742 words) [view diff] exact match in snippet view article find links to article
Property of a computational problemPolynomial-time reduction (1,472 words) [view diff] exact match in snippet view article find links to article
\mathbb {R} } defined from the existential theory of the reals, a computational problem that is known to be NP-hard and in PSPACE, but is not known to beOccupancy grid mapping (651 words) [view diff] exact match in snippet view article find links to article
p(m_{i})} represents the probability that cell i is occupied. The computational problem with estimating the posterior p ( m ∣ z 1 : t , x 1 : t ) {\displaystyleCovering problems (938 words) [view diff] exact match in snippet view article find links to article
Type of computational problemUniversal algebra (3,021 words) [view diff] exact match in snippet view article find links to article
existential sentence φ {\displaystyle \varphi } . It is proved that every computational problem can be formulated as CSPA for some algebra A. For example, the n-coloringFractional job scheduling (1,605 words) [view diff] exact match in snippet view article find links to article
performance, for example, decreasing the makespan. Moreover, the computational problem of finding an optimal schedule may become easier, as some of thePercolation theory (3,133 words) [view diff] exact match in snippet view article find links to article
degree distribution follows a power law Shortest path problem – Computational problem of graph theory Broadbent, Simon; Hammersley, John (1957). "PercolationP versus NP problem (7,797 words) [view diff] exact match in snippet view article find links to article
in P or to be NP-complete. The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. An importantCluster graph (647 words) [view diff] exact match in snippet view article find links to article
cluster graphs are exactly the graphs of subchromatic number 1. The computational problem of finding a small set of edges to add or remove from a graph toStructure formation (2,171 words) [view diff] exact match in snippet view article find links to article
cooling. Understanding these processes is an enormously difficult computational problem, because they can involve the physics of gravity, magnetohydrodynamicsLila Kari (696 words) [view diff] exact match in snippet view article find links to article
(1999), "The evolution of cellular computing: Nature's solution to a computational problem", Biosystems, 52 (1–3): 3–13, Bibcode:1999BiSys..52....3L, CiteSeerX 10Peter Buneman (1,067 words) [view diff] case mismatch in snippet view article find links to article
Peter Buneman, Susan Davidson, James Frew. "Why Data Citation Is a Computational Problem". cacm.acm.org. ACM Press. Retrieved 15 February 2024.{{cite web}}:Flow-shop scheduling (901 words) [view diff] exact match in snippet view article find links to article
Class of computational problemSokoban (3,204 words) [view diff] exact match in snippet view article find links to article
been studied using the theory of computational complexity. The computational problem of solving Sokoban puzzles was first shown to be NP-hard. FurtherLeximin order (1,591 words) [view diff] exact match in snippet view article find links to article
lexicographic order. Lexicographic max-min optimization is the computational problem of finding a maximal element of the leximin order in a given setLattice-based cryptography (2,872 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \mathbb {Z} ^{3}} . The most important lattice-based computational problem is the shortest vector problem (SVP or sometimes GapSVP), whichScientific programming language (756 words) [view diff] case mismatch in snippet view article find links to article
2025. Zachary, Joseph. "Introduction to Scientific Programming: Computational Problem Solving Using Maple and C". University of Utah. Retrieved 13 MaySubway Challenge (2,679 words) [view diff] exact match in snippet view article find links to article
Challenge, a similar challenge in London Travelling salesman problem, a computational problem where the goal is to find the shortest route that runs through allChIP sequencing (3,353 words) [view diff] exact match in snippet view article find links to article
ChIP-seq peak-calling tools by Thomas et al. (2017). Another relevant computational problem is differential peak calling, which identifies significant differencesEvolutionary algorithm (4,543 words) [view diff] exact match in snippet view article find links to article
programs, and their fitness is determined by their ability to solve a computational problem. There are many variants of Genetic Programming: Cartesian geneticErdős–Pósa theorem (1,324 words) [view diff] exact match in snippet view article find links to article
set of vertices whose removal destroys all cycles. This is a hard computational problem; if we are not able to solve it exactly, we can instead try to findRegular number (3,277 words) [view diff] exact match in snippet view article find links to article
1972 hailed Inaqibıt-Anu as "the first man in history to solve a computational problem that takes longer than one second of time on a modern electronicComplexity and Real Computation (852 words) [view diff] exact match in snippet view article find links to article
to provide a lower bound on the time complexity of an associated computational problem. The book is aimed at the level of a graduate student or researcherCarathéodory's theorem (convex hull) (2,343 words) [view diff] exact match in snippet view article
extended this colorful theorem from points to convex bodies. The computational problem of finding the colorful set lies in the intersection of the complexityProtein (10,974 words) [view diff] exact match in snippet view article find links to article
important part of protein structure characterisation. A more complex computational problem is the prediction of intermolecular interactions, such as in molecularCentral processing unit (11,434 words) [view diff] exact match in snippet view article find links to article
applications, so-called "embarrassingly parallel problems". Frequently, a computational problem that can be solved quickly with high TLP design strategies likeBin packing problem (7,098 words) [view diff] exact match in snippet view article find links to article
for example, minimizing the number of total bin. Moreover, the computational problem of finding an optimal schedule may become easier, as some of theGimbal lock (2,650 words) [view diff] exact match in snippet view article find links to article
system – Continuously computed dead reckoning Motion planning – Computational problem Quaternions and spatial rotation – Correspondence between quaternionsHam sandwich theorem (2,708 words) [view diff] exact match in snippet view article find links to article
In computational geometry, this ham sandwich theorem leads to a computational problem, the ham sandwich problem. In two dimensions, the problem is this:Computational social choice (1,538 words) [view diff] exact match in snippet view article find links to article
complexity shields against manipulation are less effective. Another computational problem associated with preference restrictions is that of recognizing whenRead (biology) (2,055 words) [view diff] exact match in snippet view article
sequencing" (SRS). After sequencing short reads, it then becomes a computational problem and many computer programs and techniques have been developed toSet cover problem (3,011 words) [view diff] exact match in snippet view article find links to article
Red-blue set cover. Set-cover abduction. Monotone dualization is a computational problem equivalent to either listing all minimal hitting sets or listingCompetitive equilibrium (3,841 words) [view diff] exact match in snippet view article find links to article
unit-demand valuations coupled with the given non-GS valuation. For the computational problem of finding a competitive equilibrium in a special kind of a marketMatroid intersection (1,822 words) [view diff] exact match in snippet view article find links to article
in G, ensuring that the selected edge set has no cycles. Another computational problem on matroids, the matroid parity problem, was formulated by LawlerBellman equation (3,990 words) [view diff] exact match in snippet view article find links to article
output from a dynamic system Optimal substructure – Property of a computational problem Recursive competitive equilibrium Stochastic dynamic programming –Addition (10,217 words) [view diff] exact match in snippet view article find links to article
the reciprocal value of a sum of reciprocal values Prefix sum, computational problem of finding running totals Pythagorean addition, combining two sideTuring test (12,615 words) [view diff] exact match in snippet view article find links to article
deliberately avoid appearing too intelligent. If it were to solve a computational problem that is practically impossible for a human to solve, then the interrogatorComputational hardness assumption (3,302 words) [view diff] exact match in snippet view article find links to article
functional encryption (multilinear jigsaw puzzles) The most fundamental computational problem on lattices is the shortest vector problem (SVP): given a latticeQuantum supremacy (5,940 words) [view diff] exact match in snippet view article find links to article
called NISQ devices. Such proposals include (1) a well-defined computational problem, (2) a quantum algorithm to solve this problem, (3) a comparisonOutline of thought (5,215 words) [view diff] exact match in snippet view article find links to article
starting point for solving it Reduction – Transformation of one computational problem to another – transforming the problem into another problem for whichKnapsack problem (7,744 words) [view diff] exact match in snippet view article find links to article
Computer programming portal Bin packing problem – Mathematical and computational problem Change-making problem – Choosing the fewest coins to make a givenHomomorphic encryption (4,692 words) [view diff] exact match in snippet view article find links to article
BLLN schemes that rely on an overstretched variant of the NTRU computational problem. This NTRU variant was subsequently shown vulnerable to subfieldK-server problem (1,379 words) [view diff] exact match in snippet view article find links to article
Computational problem of interest in computer scienceChromatic polynomial (4,325 words) [view diff] exact match in snippet view article find links to article
question if some of the coefficients are easy to compute. However the computational problem of computing ar for a fixed r ≥ 1 and a given graph G is #P-hardEnvy-free pricing (2,559 words) [view diff] exact match in snippet view article find links to article
help the seller attain a higher revenue. Many authors studied the computational problem of finding a price-vector that maximizes the seller's revenue, subjectPseudo-polynomial transformation (1,044 words) [view diff] exact match in snippet view article find links to article
O(\log(n))} . Suppose that L {\displaystyle L} is an encoding of a computational problem Π {\displaystyle \Pi } over alphabet Σ {\displaystyle \Sigma }Natural computing (5,191 words) [view diff] exact match in snippet view article find links to article
L. The evolution of cellular computing: Nature's solution to a computational problem[permanent dead link]. Biosystems, 52, 1/3 (1999) 3-13. AngeleskaSmall Latin squares and quasigroups (3,515 words) [view diff] exact match in snippet view article find links to article
Finding a given Latin square's isomorphism class can be a difficult computational problem for squares of large order. To reduce the problem somewhat, a LatinOptimal network design (581 words) [view diff] exact match in snippet view article find links to article
terminals are connected, but pay as little as possible. They study the computational problem of checking whether a Nash equilibrium exists. For some specialBlichfeldt's theorem (1,935 words) [view diff] exact match in snippet view article find links to article
replace the single set S {\displaystyle S} with a family of sets. A computational problem related to Blichfeldt's theorem has been shown to be complete forPerfect graph (7,055 words) [view diff] exact match in snippet view article find links to article
separation oracle. Beyond solving these problems, another important computational problem concerning perfect graphs is their recognition, the problem of testingTimeline of quantum computing and communication (22,807 words) [view diff] exact match in snippet view article find links to article
secure communication. David Deutsch and Richard Jozsa propose a computational problem that can be solved efficiently with the deterministic Deutsch–JozsaDifferential algebra (7,853 words) [view diff] exact match in snippet view article find links to article
Ovchinnikov, A. I. (2009). "On the generalized Ritt problem as a computational problem". Journal of Mathematical Sciences. 163 (5): 515–522. arXiv:0809Third-generation sequencing (4,039 words) [view diff] exact match in snippet view article find links to article
generation of sequencing technologies, de novo assembly is a major computational problem. It is normally approached by an iterative process of finding andMassively parallel communication (797 words) [view diff] exact match in snippet view article find links to article
consisting of S {\displaystyle S} words of memory. The input to a computational problem in this model is distributed arbitrarily across all of the machinesProbabilistic numerics (4,270 words) [view diff] exact match in snippet view article find links to article
Bayesian inference). Formally, this means casting the setup of the computational problem in terms of a prior distribution, formulating the relationship betweenTensor rank decomposition (6,321 words) [view diff] exact match in snippet view article find links to article
Romani, F. (1980). "Approximate solutions for the bilinear form computational problem". SIAM Journal on Scientific Computing. 9 (4): 692–697. doi:10.1137/0209053Generalized distributive law (6,400 words) [view diff] exact match in snippet view article find links to article
the concepts. MPF or marginalize a product function is a general computational problem which as special case includes many classical problems such as computationPLS (complexity) (5,471 words) [view diff] exact match in snippet view article
the first swap of the Fiduccia-Mattheyses. Consider the following computational problem: Given some instance I {\displaystyle I} of a PLS problem L {\displaystyleKernel methods for vector output (4,220 words) [view diff] exact match in snippet view article find links to article
classification and used to find estimates for the hyperparameters. The main computational problem in the Bayesian viewpoint is the same as the one appearing in regularizationFair allocation of items and money (3,957 words) [view diff] exact match in snippet view article find links to article
polynomial time using value-queries. Caragiannis and Ioannidis study the computational problem of minimizing the subsidy: For a constant number of agents, theyPhylogenetic reconciliation (15,304 words) [view diff] exact match in snippet view article find links to article
replaced by a single transfer. One of the first ideas to define a computational problem and approach a resolution was, in a host/symbiont framework, toThiele's voting rules (1,657 words) [view diff] exact match in snippet view article find links to article
general, solving the global optimization problem is an NP-hard computational problem, except when f(r)=r. Therefore, Thiele suggested two greedy approximationSmall set expansion hypothesis (1,502 words) [view diff] exact match in snippet view article find links to article
application of the small set expansion hypothesis concerns the computational problem of approximating the treewidth of graphs, a structural parameterOptimal kidney exchange (1,857 words) [view diff] exact match in snippet view article find links to article
cycles of length at most k, for any fixed k ≥ 3, is an NP-hard computational problem (this can be proved by reduction from the problem of 3-dimensionalSIRIUS (software) (5,859 words) [view diff] exact match in snippet view article
fragmentation tree similarity. Finding an optimal solution to the resulting computational problem is NP-hard, therefore Gibbs sampling is used. ZODIAC stands for