Concepts of Combinatorial OptimizationCombinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aims to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. Concepts of Combinatorial Optimization, is divided into three parts:

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01 variable apply assignment associated Ax s b BILLIONNET binary bivalent variables branch calculate coefficients column combinatorial optimization problems complexity Computing constraint programming conv(S convex corresponding cost decision decision problem defined denote deterministic algorithm dual duality dynamic programming edges eliminate equal evaluation example exists expressed extreme points facet feasible solution formulation given graph G heuristic implication graph impose the restriction integer linear programming integer programming interior point iteration knapsack problem Lagrangian Let us consider linear relaxation lower bound Mathematical Programming matrix maximization maximum MILP minimizing minimum monotonicity node NPhard objective function obtain Operations Research optimal policy optimal solution optimum partition polyhedra polyhedron polynomial polytope positive primal principle probabilistic algorithms pseudoBoolean function qpBf quadratic programming satisfied separation simplex algorithm solve stable set strategy subset techniques theorem traveling salesman problem tree upper bound vertex vertices weight