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Books > Science & Mathematics > Mathematics > Combinatorics & graph theory
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Handbook of Combinatorial Optimization - Supplement Volume A (Hardcover, 1999 ed.)
Loot Price: R4,822
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Handbook of Combinatorial Optimization - Supplement Volume A (Hardcover, 1999 ed.)
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Combinatorial (or discrete) optimization is one of the most active
fields in the interface of operations research, computer science,
and applied math ematics. Combinatorial optimization problems arise
in various applications, including communications network design,
VLSI design, machine vision, air line crew scheduling, corporate
planning, computer-aided design and man ufacturing, database query
design, cellular telephone frequency assignment, constraint
directed reasoning, and computational biology. Furthermore,
combinatorial optimization problems occur in many diverse areas
such as linear and integer programming, graph theory, artificial
intelligence, and number theory. All these problems, when
formulated mathematically as the minimization or maximization of a
certain function defined on some domain, have a commonality of
discreteness. Historically, combinatorial optimization starts with
linear programming. Linear programming has an entire range of
important applications including production planning and
distribution, personnel assignment, finance, alloca tion of
economic resources, circuit simulation, and control systems. Leonid
Kantorovich and Tjalling Koopmans received the Nobel Prize (1975)
for their work on the optimal allocation of resources. Two
important discover ies, the ellipsoid method (1979) and interior
point approaches (1984) both provide polynomial time algorithms for
linear programming. These algo rithms have had a profound effect in
combinatorial optimization. Many polynomial-time solvable
combinatorial optimization problems are special cases of linear
programming (e.g. matching and maximum flow). In addi tion, linear
programming relaxations are often the basis for many approxi mation
algorithms for solving NP-hard problems (e.g. dual heuristics)."
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