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Abraham Punnen(apunnensfu.ca) Abstract: An instance of the quadratic assignment problem (QAP) with cost matrix Q is said to be linearizable if there exists an instance of the linear assignment problem (LAP) with cost matrix C such that for each assignment, the QAP and LAP objective function values are identical. The QAP linearization problem can be solved in O(n4) time. However, for the special cases of KoopmansBeckmann QAP and the multiplicative assignment problem the input size is of O(n^2). We show that the QAP linearization problem for these special cases can be solved in O(n^2) time. For symmetric KoopmansBeckmann QAP, Bookhold [4] gave a sufficient condition for linearizability and raised the question if the condition is necessary. We show that Bookhold’s condition is also necessary for linearizability of symmetric Koopmans Beckmann QAP. Keywords: Quadratic Assignment problem, linearization, polynomially solvable cases Category 1: Combinatorial Optimization Citation: A.P. Punnen and S.N. Kabadi,A LINEAR TIME ALGORITHM FOR THE KOOPMANSBECKMANN QAP LINEARIZATION AND RELATED PROBLEMS, Manuscript, Department of Mathematics, Simon Fraser University, June 27, 2011. Download: [PDF] Entry Submitted: 11/24/2011 Modify/Update this entry  
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