Handbook of Combinatorial Optimization: Supplement, Volume 1Ding-Zhu Du, Panos M. Pardalos 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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Handbook of Combinatorial Optimization: Supplement, Volume 1 Ding-Zhu Du,Panos M. Pardalos No preview available - 2010 |
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annealing applied approach approximation algorithms assignment problem backtracking bins bipartite graph Boolean branch and bound circuit coloring combinatorial optimization complexity constraints defined denoted DIMACS discrete dual edges efficient energy function equations feasible feedback arc set feedback vertex set given global graph coloring graph G GSAT heuristic IEEE Trans implementation input integer programming iteration literals local search lower bound LSAP Math Mathematics matrix maximal maximum clique problem maximum independent set mean field method minimization minimum feedback vertex n-queen Neural Networks node nonlinear objective function on-line optimal solution packing parallel Pardalos partition performance polynomial primal Proc procedure random ratio reduced relaxation rithm SAT algorithms SAT formula satisfiability scheduling search algorithm Section SIAM solve Steiner ratio subgraph subset T-set tabu techniques Theorem theory tree unsatisfiable upper bound variables vertex set problem vertices weight worst-case
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