Pierre Hansen

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Cahiers du GERAD

369 results — page 1 of 19

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In this paper we study the spectral properties of the threshold graphs. In particular, we give lower and upper bounds for the largest and smallest eigenvalue...

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The energy of a graph \(G\), denoted by \({\cal E}(G)\), is defined as the sum of the absolute values of all eigenvalues of \(G\). In this paper we stu...

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In the present paper, we prove lower and upper bounds for each of the ratios \(GA/\delta\), as well as a lower bound on \(GA/\sqrt{\delta}\), in terms of...

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A small polygon is a polygon of unit diameter. The question of finding the largest area of small \(n-\)gons has been answered for some values of \(n\)....

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The Integral Simplex Using Decomposition (ISUD) algorithm has been developed recently to solve large set partitioning problems (SPPs) in a primal way, i.e.,...

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Clustering is the subject of active research in several fields such as operations research, statistics, pattern recognition, and machine learning. The range ...

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Clustering is an automated and powerful technique for data analysis. It aims to divide a given set of data points into clusters which are homogeneous and/o...

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Let \({\mathcal D(G)}\), \({\mathcal D}^L(G)={\mathcal Diag(Tr)} - {\mathcal D(G)}\) and \({\mathcal D}^Q(G)={\mathcal Diag(Tr)} + {\mathcal D(G)}\) b...

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Let \(G\) be a graph of order \(n\). The energy \(\mathcal{E}(G)\) of a simple graph \(G\) is the sum of absolute values of the eigenvalues of its ...

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Given an integer solution, the integral simplex using decomposition (ISUD) seeks a descent direction that leads to an improved adjacent integer solution. It ...

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Necessary and sufficient conditions are provided for the existence of a simple graph, or a simple connected graph with given numbers \(m_{ij}\) of edges ...

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The distance, distance Laplacian and distance signless Laplacian spectra of a connected graph \(G\) are the spectra of the distance, distance Laplacian and...

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The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 ...

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Graph theoretical heuristics are used extensively in many fields to solve approximately large scale optimization problems. Graph theoretical heuristics can a...

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In the present paper we are interested in the study of the distance Laplacian eigenvalues of a connected graph with fixed order \(n\) and chromatic number ...

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The geometric-arithmetic index \(GA\) of a graph \(G\) is the sum of ratios, over all edges of \(G\), of the geometric mean to the arithmetic mean of t...

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In the present paper, we prove lower and upper bounds for each of the ratios \(GA/\delta\), \(GA/\overline{d}\) and \(\Delta\), in terms of the order `...

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In the present paper, we compare the geometric-arithmetic index \(GA\) and the chromatic number \(\chi\) of a connected graph with given order. We prove,...

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Variable neighborhood search (VNS) is a framework for building heuristics, based upon systematic changes of neighborhoods both in a descent phase, to find a...

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In this paper, the first steps toward the use of the Variable Neighborhood Search metaheuristic are explained. The method is presented step by step using an...

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