Pierre Hansen
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Given a graph <i>G=(V,E)</i>, the first Zagreb index <i>M</i><sub>1</sub> is the sum of its vertices squared degrees and the second Zagreb index <i>M</i><sub...
BibTeX referenceOn a Conjecture About the Szeged Index
Khalifeh, Yousefi-Azari, Ashrafi and Wagner [European J. Combin. 30 (2009) 1149-1163] conjectured that for a connected graph <i>G</i> on <i>n</i> vertices...
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The proximity <img src="/cgi-bin/mimetex.cgi?\pi"> of a graph <i>G</i> is the minimum average distance from a vertex of <i>G</i> to all others. Similarly, th...
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Given a set of entities associated with points in Euclidean space, minimum sum-of-squares clustering (MSSC) consist in partitioning this set into clusters su...
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During the last three decades, the computer has been widely used in spectral graph theory. Many results about graph eigenvalues were first conjectured, and i...
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It is observed that mutations in the formulations of test problems over time are not infrequent. Ensuing problems are illustrated with examples from geometri...
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Finding maximum likelihood parameter values for Finite Mixture Model (FMM) is often done with the Expectation Maximization (EM) algorithm. However the choice...
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A recent paper of Tuy and Hoai-Phuong published in <i>JOGO</i> (2007) 37:557--569 observes that there are errors in the reformulation of a signomial geometr...
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Necessary and sufficient conditions are provided for existence of a simple graph <i>G</i>, and for a simple and connected graph <i>G'</i> with given numbers ...
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Upper bounds on the average distance \(\overline{l}\)
between pairs of vertices of a connected graph with given order \(n\)
and minimum degree `(\delta...
The transmission of a vertex in a connected graph is the sum of all distance from that vertex to the others. It is said to be normalized if divided by <i>n-1...
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Variable neighborhood search (VNS) is a metaheuristic, or framework for building heuristics, based upon systematic change of neighborhoods both in a decent ...
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Minimum sum-of-squares clustering (MSSC) consists in partitioning a given set of <i>n</i> points into <i>k</i> clusters in order to minimize the sum of squar...
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A polygon is said to be <i>simple</i> if the only points of the plane belonging to two of its edges are its vertices. We answer the question of finding, ...
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With the help of the Graffiti system, Fajtlowicz conjectured around 1992 that the average distance between two vertices of a connected graph <i>G</i> is at ...
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Methods, models, heuristic and exact algorithms for clustering are reviewed from a mathematical programming view point.
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A recent proof of NP-hardness of Euclidean sum-of-squares clustering, due to Drineas et al., <i>Machine Learning</i> 56, 9--33, 2004, is not valid. An altern...
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Let <img src="/cgi-bin/mimetex.cgi?G=(V,E)"> be a simple, undirected graph of order <img src="/cgi-bin/mimetex.cgi?n"> and size <img src="/cgi-bin/mimetex.cg...
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In this note we suggest a simple but efficient modification of the well-known Nelder-Mead (NM) simplex search method for unconstrained optimization. Instead ...
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The hexagon and heptagon with unit diameter and maximum sum of Euclidean distances between vertices are determined by enumerating diameter configurations, an...
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