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Page 55 line 6: replace " among the matched " with " among the unmatched " ; 229 line 13: replace " Palubeckis [544] " with the following (missing) reference: G. Palubeckis. The use of special graphs for obtaining lower bounds in the geometric quadratic assignment problem. 289 eqn (9.27): replace " s ∈ F " with " S ∈ F " ; 308 line 14: replace "(More)
Given three n-element sequences a i ; b i and c i of nonnega-tive real numbers, the aim is to nd two permutations and such that the sum P n i=1 a i b (i) c (i) is minimized (maximized, respectively). We show that the maximization version of this problem can be solved in polynomial time, whereas we present an NP-completeness proof for the minimization(More)
Let us denote a ⊕ b = max(a; b) and a ⊗ b = a + b for a; b ∈ R = R ∪ {−∞} and extend this pair of operations to matrices and vectors in the same way as in linear algebra. We present an O(n 2 (m + n log n)) algorithm for ÿnding all essential terms of the max-algebraic characteristic polynomial of an n × n matrix over R with m ÿnite elements. In the cases(More)