Concepts inLimitations of cross-monotonic cost sharing schemes
Scheme (mathematics)
In mathematics, a scheme is an important concept connecting the fields of algebraic geometry, commutative algebra and number theory. Schemes were introduced by Alexander Grothendieck so as to broaden the notion of algebraic variety; some consider schemes to be the basic object of study of modern algebraic geometry.
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Cost sharing
In health care, cost sharing occurs when patients pay for a portion of health care costs not covered by health insurance. Examples include copays, deductibles and coinsurance.
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Edge cover
In graph theory, an edge cover of a graph is a set of edges such that every vertex of the graph is incident to at least one edge of the set. In computer science, the minimum edge cover problem is the problem of finding an edge cover of minimum size. It is an optimization problem that belongs to the class of covering problems and can be solved in polynomial time.
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Vertex cover
In the mathematical discipline of graph theory, a vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. The problem of finding a minimum vertex cover is a classical optimization problem in computer science and is a typical example of an NP-hard optimization problem that has an approximation algorithm.
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Facility location
Facility location, also known as location analysis, is a branch of operations research and computational geometry concerning itself with mathematical modeling and solution of problems concerning optimal placement of facilities in order to minimize transportation costs, avoid placing hazardous materials near housing, outperform competitors' facilities, etc.
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Set cover problem
The set covering problem (SCP) is a classical question in computer science and complexity theory. It is a problem "whose study has led to the development of fundamental techniques for the entire field" of approximation algorithms. It was also one of Karp's 21 NP-complete problems shown to be NP-complete in 1972.
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Probabilistic method
This article is not about interactive proof systems which use probability to convince a verifier that a proof is correct, nor about probabilistic algorithms, which give the right answer with high probability but not with certainty, nor about Monte Carlo methods, which are simulations relying on pseudo-randomness.
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Maximum flow problem
In optimization theory, the maximum flow problem is to find a feasible flow through a single-source, single-sink flow network that is maximum. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow is equal to the minimum capacity of an s-t cut in the network, as stated in the max-flow min-cut theorem.
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