Assignment Problems, Revised Reprint
Assignment Problems is a useful tool for researchers, practitioners and graduate students. In 10 self-contained chapters, it provides a comprehensive treatment of assignment problems from their conceptual beginnings through present-day theoretical, algorithmic and practical developments. The topics covered include bipartite matching algorithms, linear assignment problems, quadratic assignment problems, multi-index assignment problems and many variations of these. Researchers will benefit from the detailed exposition of theory and algorithms related to assignment problems, including the basic linear sum assignment problem and its variations. Practitioners will learn about practical applications of the methods, the performance of exact and heuristic algorithms, and software options. This book also can serve as a text for advanced courses in areas related to discrete mathematics and combinatorial optimisation. The revised reprint provides details on a recent discovery related to one of Jacobi's results, new material on inverse assignment problems and quadratic assignment problems, and an updated bibliography.
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adjacency matrix admissible transformation algorithm for LSAP assignment polytope augmenting path axial 3AP bipartite graph bottleneck assignment problem Cited combinatorial optimization complexity computational constraints convex corresponding cost coefficients cost matrix defined denote Discr dual variables edge i,j elements entries feasible solution feasible tree flow given graph G heuristic Hungarian algorithm implementation instances integer iteration Koopmans—Beckmann labeled layered graph LBAP linear assignment problem linear programming lower bound LSAP Math matroid maximum matching method minimum Monge matrix Monge property node nonnegative NP-hard objective function objective function value obtained Oper optimal solution path algorithm perfect matching permutation matrix pivots planar polynomial polytope primal solution Procedure processors Proposition quadratic assignment problem R.E. Burkard random reduced cost Rendl rows and columns Section shortest path simplex algorithm solved sum assignment problem symmetric tabu search Theorem unassigned updated vector vertices Volgenant