Concepts inAn improved LP-based approximation for steiner tree
Randomized rounding
Within computer science and operations research, many combinatorial optimization problems are computationally intractable to solve exactly (to optimality). Many such problems do admit fast approximation algorithms¿that is, algorithms that are guaranteed to return an approximately optimal solution given any input. Randomized rounding is a widely used approach for designing and analyzing such approximation algorithms.
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Steiner tree problem
The Steiner tree problem, or the minimum Steiner tree problem, named after Jakob Steiner, is a problem in combinatorial optimization, which may be formulated in a number of settings, with the common part being that it is required to find the shortest interconnect for a given set of objects.
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APX
In complexity theory the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short). In simple terms, problems in this class have efficient algorithms that can find an answer within some fixed percentage of the optimal answer.
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Linear programming relaxation
In mathematics, the linear programming relaxation of a 0-1 integer program is the problem that arises by replacing the constraint that each variable must be 0 or 1 by a weaker constraint, that each variable belong to the interval [0,1 0,1]. That is, for each constraint of the form of the original integer program, one instead uses a pair of linear constraints The resulting relaxation is a linear program, hence the name.
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Spanning tree
In the mathematical field of graph theory, a spanning tree T of a connected, undirected graph G is a tree composed of all the vertices and some (or perhaps all) of the edges of G. Informally, a spanning tree of G is a selection of edges of G that form a tree spanning every vertex. That is, every vertex lies in the tree, but no cycles (or loops) are formed. On the other hand, every bridge of G must belong to T.
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Approximation algorithm
In computer science and operations research, approximation algorithms are algorithms used to find approximate solutions to optimization problems. Approximation algorithms are often associated with NP-hard problems; since it is unlikely that there can ever be efficient polynomial time exact algorithms solving NP-hard problems, one settles for polynomial time sub-optimal solutions.
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Open problem
In science and mathematics, an open problem or an open question is a known problem that can be accurately stated, and has not yet been solved (no solution for it is known). Some questions remain unanswered for centuries before solutions are found. Two notable examples in mathematics that have been solved and closed by researchers in the late twentieth century are Fermat's Last Theorem and the four color map theorem.
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NP-hard
NP-hard, in computational complexity theory, is a class of problems that are, informally, "at least as hard as the hardest problems in NP". A problem H is NP-hard if and only if there is an NP-complete problem L that is polynomial time Turing-reducible to H (i.e. , L¿¿¿TH). In other words, L can be solved in polynomial time by an oracle machine with an oracle for H.
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