Aspects of combinatorics include counting the structures of a given kind and size ( enumerative combinatorics ), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ( as in combinatorial designs and matroid theory ), finding " largest ", " smallest ", or " optimal " objects ( extremal combinatorics and combinatorial optimization ), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems ( algebraic combinatorics ).

There is a close connection between machine learning and compression: a system that predicts the posterior probabilities of a sequence given its entire history can be used for optimal data compression ( by using arithmetic coding on the output distribution ), while an optimal compressor can be used for prediction ( by finding the symbol that compresses best, given the previous history ).

The large possible variance in time justifies performing query optimization, though finding the exact optimal way to execute a query, among all possibilities, is typically very complex, time consuming by itself, may be too costly, and often practically impossible.

The large possible variance in time justifies performing query optimization, though finding the exact optimal way to execute a query, among all possibilities, is typically very complex, time consuming by itself, may be too costly, and often practically impossible.

: the problem of finding optimal colorings of graphs that are not necessarily planar.

Channel coding is concerned with finding such nearly optimal codes that can be used to transmit data over a noisy channel with a small coding error at a rate near the channel capacity.

This supplied a mathematical explanation for the apparent computational difficulty of finding optimal tours.

The purpose of bidding is to exchange information with your partner so that you can arrive at an optimal contract, while preventing the opponents from finding their optimal contract.

Creating Golomb rulers is easy, but finding the optimal Golomb rulers for a specified order is computationally very challenging.

The fact that the problem with four or more pegs is an open problem does not imply that no algorithm exists for finding ( all of ) the optimal solutions.

It was proposed by Herbert A. Simon as an alternative basis for the mathematical modeling of decision making, as used in economics and related disciplines ; it complements rationality as optimization, which views decision-making as a fully rational process of finding an optimal choice given the information available.

Coase argues that the size of a firm ( as measured by how many contractual relations are " internal " to the firm and how many " external ") is a result of finding an optimal balance between the competing tendencies of the costs outlined above.

Hart, Nilsson and Raphael then jointly developed a proof that the revised A2 algorithm was optimal for finding shortest paths under certain well-defined conditions.

The splitting circle method is useful for finding the roots of polynomials of high degree to arbitrary precision ; it has almost optimal complexity in this setting.

Thus, the sustainable management requires finding out what business activities fit into the Earth ’ s carrying capacity, and also defining the optimal levels of those activities.

* Branch and bound, a general algorithm for finding optimal solutions

As an example of a problem that is unlikely to exhibit optimal substructure, consider the problem of finding the cheapest airline ticket from Buenos Aires to Moscow.

* Response surface methodology, sequential experimentation for improvement and for finding an optimal response

For example, its earliest application was in finding mixture models with the optimal number of classes.

For example, if city A and city B are next to each other, while city C is farther away, the total distance traveled will be shorter if cities A and B are visited one after the other before visiting city C. Since finding an optimal solution to the TSP is an NP-hard task, heuristic-based approximation methods ( such as local searches ) are useful for devising close-to-optimal solutions.

combined PSO and TS to create a novel hybrid TS-PSO algorithm which conducts both global search and local search in each iteration so that the probability of finding the optimal minima significantly increase.

Branch and bound ( BB or B & B ) is a general algorithm for finding optimal solutions of various optimization problems, especially in discrete and combinatorial optimization.

In view of the increasing shortage of usable surface and ground water in many parts of the Nation and the importance of finding new sources of supply to meet its present and future water needs, it is the policy of the Congress to provide for the development of practicable low-cost means for the large-scale production of water of a quality suitable for municipal, industrial, agricultural, and other beneficial consumptive uses from saline water, and for studies and research related thereto.

" The university was not challenged about the origin of its interracial dating policy, and the District Court accepted " on the basis of a full evidentiary record " BJU's argument that the rule was a sincerely held religious conviction, a finding affirmed by all subsequent courts.

He opposed Howard's policy on asylum-seekers, campaigned in support of an Australian Republic and attacked what he perceived as a lack of integrity in Australian politics, together with former Labor prime minister Gough Whitlam, finding much common ground with his predecessor.

They explained to each other the reasons for their foreign policy hostility in the 1930s, finding common ground in the anti-capitalism of both countries.

# preparation of report and other documents containing information, analysis, historical background research finding, policy suggestions and so forth, to facilitate deliberations and decision making by other organs.

This policy is a federal law called the Nuclear Waste Policy Act, which made the U. S. Department of Energy responsible for finding a site, building, and operating an underground disposal facility called a geologic repository.

Several reporters unwilling, or refusing the new course, like Peter himself, are forced to go away, finding a new safe haven in the Front Line, the only magazine willing to accept people fired by Bennett, pursuing a scorched earth policy over them.

He delves into the purported purpose of prison, finding it hard to believe that " corrections " and deterrence are its true goals using the policy to block education of inmates and the psychological problems caused by isolation and non-contact visits as support for his argument of an ulterior motive, to " erode one's humanity ".

The Council for some years did not accept this politically embarrassing finding, and instead maintained that the charity " owed " the Council £ 30m, charged compound interest on what it termed a " debt " ( which eventually rose to a claim of some £ 60m ), and to recoup it tried to offer the whole palace for sale-a policy their successors are still trying to carry out despite being stalled in the High Court in 2007.

Lynbrook has a fairly serious academic honesty and internet policy, where many students have previously been expelled for cheating on a test, finding the answer keys to the exam, hacking into the network, etc.

The Carbon War Room is an independent non-profit focused on finding market based solutions to reduce carbon emissions at the gigaton scale, either by creating new business models or identifying policy reforms.

Also, finding a solution to an abstract function does not directly yield a policy recommendation!

It also enables the Christian community to speak with one voice when dealing with local government ; however, the focus is usually on finding ways to cooperate in serving the community, rather than dictating policy.

Dobelle agreed to resign from the presidency and not to apply for any other University of Hawaii positions, and the university agreed to a two-year non-tenured research position and a settlement of $ 1. 6 million in cash, a state pension for life, and a fully paid $ 2 million life insurance policy, and assumed all legal costs of $ 1. 2 million, with no finding of wrongdoing on the part of either Dobelle or the board.

As an organization with expertise in law, technology, and policy, CDT works to enhance free expression and privacy in communications technologies by finding practical and innovative solutions to public policy challenges while protecting civil liberties.

Also in 2002, President Bush withdrew funding from the United Nations Population Fund based on a finding that UNPF ’ s activities facilitated China ’ s one-child-only / forced abortion policy.

India grew rapidly in the 1950s, and in the late 1950s the Commission started facing difficulties in finding suitable managers for the large number of public sector enterprises that were being established in India as a part of its industrial policy.

Britain's chosen Governor, Frederick Lugard, with limited resources, slowly negotiated with, and sometimes coerced, the emirates of the north into accepting British rule, finding that the only way this could be achieved was with the consent of local rulers through a policy of indirect rule which he developed from a necessary improvisation into a sophisticated political theory.

The Appellate Division holds that the same treatment must be applied to out-of-state same-sex marriages, but the ruling could be overturned on a finding that same-sex marriage violates New York's public policy.

After finding that there was " overwhelming textual and historical evidence that the New York Legislature intended to allow the immediate assignment of a policy by an insured to one lacking an insurable interest ", the Kramer Court concluded that " it is not our role ..... to engraft an intent or good faith requirement onto a statute that so manifestly permits an insured to immediately and freely assign such a policy.

Cecil Rhodes, then prime minister of Cape Colony, was strongly in favor of a more energetic policy than was supported by the Imperial government, and at the end of March 1895 the high commissioner, finding himself, it is believed, out of touch with his ministers, returned home a few months before the expiry of his term of office.

Russification policy had closed several Estonian organizations and prominent students, including Jaan Tõnisson, started speaking up, finding support among ethnic Estonians.