Assignment Problems, Revised Reprint
This book provides a comprehensive treatment of assignment problems from their conceptual beginnings in the 1920s through present-day theoretical, algorithmic, and practical developments. 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. The authors have organized the book into 10 self-contained chapters to make it easy for readers to use the specific chapters of interest to them without having to read the book linearly. The topics covered include bipartite matching algorithms, linear assignment problems, quadratic assignment problems, multi-index assignment problems, and many variations of these problems. Exercises in the form of numerical examples provide readers with a method of self-study or students with homework problems, and an associated webpage offers applets that readers can use to execute some of the basic algorithms as well as links to computer codes that are available online. Researchers will benefit from the book's detailed exposition of theory and algorithms related to assignment problems, including the basic linear sum assignment problem and its many 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 discrete mathematics, integer programming, combinatorial optimization, and algorithmic computer science.
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adjacency matrix admissible transformation algorithm for LSAP assignment polytope augmenting path axial 3AP bipartite graph bottleneck assignment problem Burkard Cited combinatorial optimization complexity computational constraints convex corresponding cost coefﬁcients cost matrix cycle deﬁned Deﬁnition denote Discr dual variables edges efﬁcient elements entries feasible solution feasible tree ﬁnd ﬁnding ﬁrst ﬁxed ﬂow fulﬁlls given graph G heuristic Hungarian algorithm implementation instances integer iteration Koopmans—Beckmann labeled layered graph LBAP linear assignment problem 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 Pardalos perfect matching permutation matrix pivots polynomial polytope primal solution Procedure processors Proposition QAP(A quadratic assignment problem random reduced cost Rendl rows and columns Section shortest path simplex algorithm solved sum assignment problem symmetric tabu search Theorem unassigned updated vector vertex cover vertices Volgenant