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The solution time of a combinatorial problem can be reduced by adding new constraints, referred as symmetry breaking constraints, such that some of the symmetric solutions are eliminated from the search space while preserving the existence of at least one solution. [1] Symmetry is common in many real-life combinatorial problems.
A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
The multidimensional assignment problem (MAP) is a fundamental combinatorial optimization problem which was introduced by William Pierskalla. [1] This problem can be seen as a generalization of the linear assignment problem. [2] In words, the problem can be described as follows:
The Fano matroid, derived from the Fano plane.Matroids are one of many kinds of objects studied in algebraic combinatorics. Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
Journal of Algebraic Combinatorics is a peer-reviewed scientific journal covering algebraic combinatorics. It was established in 1992 and is published by Springer Science+Business Media . The editor-in-chief is Ilias S. Kotsireas ( Wilfrid Laurier University ).
European Chapter on Combinatorial Optimization; Extremal combinatorics; F. Floorplan (microelectronics) G. Generalized assignment problem; Gilbert–Pollack conjecture;
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...
Journal of Medical Biochemistry: Biochemistry: Walter de Gruyter: English: 1982–present Journal of Medical Biography: Medical Personnel: SAGE Publishing: English: 1993–present Journal of Medical Case Reports: Medicine: BioMed Central: English: 2007–present Journal of Medical Economics: Medicine: Taylor and Francis Group: English: 1998 ...