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Perspectives of Monge properties in optimization

Rainer E. Burkard, Bettina Klinz, Rüdiger Rudolf
1996 Discrete Applied Mathematics  
In this paper we present a survey on Monge matrices and related Monge properties and their role in combinatorial optimization.  ...  of Monge properties.  ...  Woeginger for several stimulating discussions on the recognition of permuted Monge structures and to Alok Aggarwal, Ulrich Faigle and Gerhard J.  ... 
doi:10.1016/0166-218x(95)00103-x fatcat:4znuac6vofbb5imb4fdk2eyy3q

Interval matrices with Monge property [article]

Martin Černý
2019 arXiv   pre-print
We generalize Monge property of real matrices for interval matrices. We define two classes of interval matrices with Monge property - in a strong and in a weak sense.  ...  We study fundamental properties of both classes. We show several different characterizations of the strong Monge property.  ...  We presented lists of closure properties under operations on ISM and IWM and under operations combining both classes of matrices.  ... 
arXiv:1912.11656v1 fatcat:tgccl2xq3jdsrfjkmbnq6z33o4

On the recognition of permuted bottleneck Monge matrices

Bettina Klinz, Rüdiger Rudolf, Gerhard J. Woeginger
1995 Discrete Applied Mathematics  
We first deal with the special case of Cl bottleneck Monge matrices. Next, we derive several fundamental properties on the combinatorial structure of bottleneck Monge matrices with arbitrary entries.  ...  The matrix A is termed permuted bottleneck Monge matrix, if there exist row and column permutations such that the permuted matrix becomes a bottleneck Monge matrix.  ...  On the one hand, we obtain a better understanding of bottleneck Monge matrices which facilitates the recognition of permuted bottleneck Monge matrices.  ... 
doi:10.1016/0166-218x(94)00019-a fatcat:w6224vn5gzg7nbbadgo42hk7ya

An O(n2) algorithm for maximum cycle mean of Monge matrices in max-algebra

Martin Gavalec, Ján Plávka
2003 Discrete Applied Mathematics  
A similar result is presented for matrices with inverse Monge property. The standard algorithm for the general case works in O(n 3 ) time. ? (M. Gavalec), jan.plavka@tuke.sk (J.  ...  An O(n 2 ) algorithm is described for computing the maximum cycle mean (eigenvalue) for n × n matrices, A = (aij) fulÿlling Monge property, aij + a kl 6 a il + a kj for any i ¡ k, j ¡ l.  ...  Monge matrices A (with A satisfying the weak Monge property); is given in [3] .  ... 
doi:10.1016/s0166-218x(02)00395-5 fatcat:f5qtitao6bdfro727vwr4vmjbe

Monge properties of sequence alignment

Luís M.S. Russo
2012 Theoretical Computer Science  
We focus on the fact that these matrices have the Monge property and are sparse in some sense.  ...  In this paper we study the properties of matrices that contain alignment scores between a string and all the sub-strings of another string.  ...  Acknowledgements I am grateful to Gad Landau for proposing the DIST multiplication problem, for enlightening discussions on Tiskin's results and references to Monge properties.  ... 
doi:10.1016/j.tcs.2011.12.068 fatcat:xklelti2o5a3rdlzzgy5v2bk4m

Remarks on Monge matrices

Miroslav Fiedler
2002 Mathematica Bohemica  
In the final part, we shall deal with matrices we will call matrices with the weak Monge property.  ...  In addition, by the well known spectral properties of compound matrices, the eigenvalues of B (2) are −nεγ 1 , . . . , −nεγ n−1 and n−1 2 eigenvalues of the form ε 2 γ i γ j , 1 i < j n − 1.  ... 
doi:10.21136/mb.2002.133983 fatcat:dqtjp5i3rrbz5ga6w67i4b7oai

Page 8872 of Mathematical Reviews Vol. , Issue 2002M [page]

2002 Mathematical Reviews  
Remarkable properties are proved when the row sums of these matrices form a monotone vector.” 2002m:15032 15A57 15A48 Fiedler, Miroslav (CZ-AOS-IC; Prague) Remarks on Monge matrices.  ...  In the paper some new properties of Monge matrices are in- vestigated; among them, it is shown that: a square equilibrated Monge matrix has a nonpositive eigenvalue of maximum modu- lus and the corresponding  ... 

Subtotally positive and Monge matrices

Miroslav Fiedler
2006 Linear Algebra and its Applications  
Spectral properties of square k-subtotally positive matrices are studied.  ...  Finally, completion problems for 2-subtotally positive matrices and their additive counterpart, the anti-Monge matrices, are investigated.  ...  The rest is a consequence of the general transformation in the class of anti-Monge matrices ([1], Lemma B). Let us turn now to further problems on Monge or anti-Monge matrices.  ... 
doi:10.1016/j.laa.2005.08.020 fatcat:zwyetvro45asfjjzmwkkj5pus4

Permuting matrices to avoid forbidden submatrices

Bettina Klinz, Rüdiger Rudolf, Gerhard J. Woeginger
1995 Discrete Applied Mathematics  
We survey several known and new results on the algorithmic complexity of this problem, mostly dealing with (0, l)-matrices.  ...  .~ a fixed set of matrices, we consider the pmbiem of deciding whether the rows and columns of a matrix can he permuted in such a way that the resulting matrix M avoids all matrices in .~'.  ...  Furthermore we are grateful to Ron Shamir, Jeremy Spinrad and an anonymous referee for their detailed comments on an earlier version of this paper which helped to improve the presentation.  ... 
doi:10.1016/0166-218x(94)00054-h fatcat:dl6pwpzhqrfxjkwmb7dtkjzpqu

The quadratic assignment problem with a monotone anti-Monge and a symmetric Toeplitz matrix: Easy and hard cases

Rainer E. Burkard, Eranda Çela, Günter Rote, Gerhard J. Woeginger
1998 Mathematical programming  
(P2) The Traveling Salesman Problem on symmetric Monge distance matrices.  ...  This paper investigates a restricted version of the Quadratic Assignment Problem (QAP), where one of the coefficient matrices is an Anti-Monge matrix with non-decreasing rows and columns and the other  ...  that for even integers n, the Toeplitz matrices generated by queer-looking function f(i) = cos (cos2rci/n) have the constant permutation property with respect to monotone Anti-Monge matrices.  ... 
doi:10.1007/bf01585868 fatcat:gu2ty3ui2bfyjiqm4slnaxfovi

The quadratic assignment problem with a monotone anti-monge and a symmetric toeplitz matrix: Easy and hard cases [chapter]

Rainer E. Burkard, Eranda Çela, Günther Rote, Gerhard J. Woeginger
1996 Lecture Notes in Computer Science  
(P2) The Traveling Salesman Problem on symmetric Monge distance matrices.  ...  This paper investigates a restricted version of the Quadratic Assignment Problem (QAP), where one of the coefficient matrices is an Anti-Monge matrix with non-decreasing rows and columns and the other  ...  that for even integers n, the Toeplitz matrices generated by queer-looking function f(i) = cos (cos2rci/n) have the constant permutation property with respect to monotone Anti-Monge matrices.  ... 
doi:10.1007/3-540-61310-2_16 fatcat:454nnukfd5hdldfolnjghef5uq

Equilibrated anti-Monge matrices

Miroslav Fiedler
2001 Linear Algebra and its Applications  
We show that the class of such matrices is closed under multiplication. Moreover, we show some spectral properties for square equilibrated anti-Monge matrices. (M.  ...  We present some new results on Monge matrices, formulated for their centrally symmetric version, called anti-Monge matrices.  ...  Introduction Recently, the author published [2] some remarks on the class of Monge matrices.  ... 
doi:10.1016/s0024-3795(01)00283-x fatcat:l2obrkwlcfbafgohrigw4m2fua

The cone of Monge matrices: Extremal rays and applications

R�diger Rudolf, Gerhard J. Woeginger
1995 Mathematical Methods of Operations Research  
We present an additive characterization of Monge matrices based on the extremal rays of the cone of nonnegative Monge matrices.  ...  By using this characterization, a simple proof for an old result by Supnick (1957) on the traveling salesman problem on Monge matrices is derived.  ...  , Austria 1 The Cone of Monge Matrices 2 2 The Cone of Monge Matrices  ... 
doi:10.1007/bf01415751 fatcat:xwg3zs3elrft3b2abhwldudm4q

Robustness of Interval Monge Matrices in Fuzzy Algebra

Máté Hireš, Monika Molnárová, Peter Drotár
2020 Mathematics  
An interval Monge matrix is the set of all Monge matrices from an interval matrix with Monge lower and upper bound matrices.  ...  In this paper, we study the robustness of Monge matrices with inexact data over max–min algebra.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math8040652 fatcat:ft3ceqgs3jbm5psvhiwzjacxdm

Recognition of d-dimensional Monge arrays

Rüdiger Rudolf
1994 Discrete Applied Mathematics  
It is known that the d-dimensional axial transportation (assignment) problem can easily be solved by a greedy algorithm if and only if the underlying cost array fulfills the d-dimensional Monge property  ...  By using this algorithm a wider class of d-dimensional axial transportation problems and in particular of the d-dimensional axial assignment problems can be solved efficiently.  ...  Acknowledgement We would like to thank Vladimir Deineko for making available to us a description of his algorithm for solving our problem in two dimensions. References  ... 
doi:10.1016/0166-218x(92)00189-s fatcat:bgc27mkswvcidflg3fderogpfi
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