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17
Variable Neighborhood Search
, 1997
"... Variable neighborhood search (VNS) is a recent metaheuristic for solving combinatorial and global optimization problems whose basic idea is systematic change of neighborhood within a local search. In this survey paper we present basic rules of VNS and some of its extensions. Moreover, applications a ..."
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Cited by 201 (17 self)
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Variable neighborhood search (VNS) is a recent metaheuristic for solving combinatorial and global optimization problems whose basic idea is systematic change of neighborhood within a local search. In this survey paper we present basic rules of VNS and some of its extensions. Moreover, applications are briefly summarized. They comprise heuristic solution of a variety of optimization problems, ways to accelerate exact algorithms and to analyze heuristic solution processes, as well as computerassisted discovery of conjectures in graph theory.
A tight analysis of the maximal matching heuristic
 In Proc. of The Eleventh International Computing and Combinatorics Conference (COCOON), LNCS
, 2005
"... Abstract. We study the algorithm that iteratively removes adjacent vertices from a simple, undirected graph until no edge remains. This algorithm is a wellknown 2approximation to three classical NPhard optimization problems: MINIMUM VERTEX COVER, MINIMUM MAXIMAL MATCHING and MINIMUM EDGE DOMINATI ..."
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Cited by 2 (2 self)
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Abstract. We study the algorithm that iteratively removes adjacent vertices from a simple, undirected graph until no edge remains. This algorithm is a wellknown 2approximation to three classical NPhard optimization problems: MINIMUM VERTEX COVER, MINIMUM MAXIMAL MATCHING and MINIMUM EDGE DOMINATING SET. We show that the worstcase approximation factor of this simple method can be expressed in a finer way when assumptions on the density of the graph is made. For graphs with an average degree at least ɛn, called weakly ɛdense graphs, we show that the asymptotic approximation factor is min{2, 1/(1 − √ 1 − ɛ)}. For graphs with a minimum degree at least ɛn – strongly ɛdense graphs – we show that the asymptotic approximation factor is min{2, 1/ɛ}. These bounds are obtained through a careful analysis of the tight examples. 1
A Survey of Research on Automated Mathematical ConjectureMaking, Graphs and
 Fajtlowicz (Editors), American Mathematical Society
"... Abstract. The first attempt at automating mathematical conjecturemaking appeared in the late1950s. It was not until the mid1980s though that a program produced statements of interest to research mathematicians and actually contributed to the advancement of mathematics. A central and important ide ..."
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Cited by 2 (0 self)
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Abstract. The first attempt at automating mathematical conjecturemaking appeared in the late1950s. It was not until the mid1980s though that a program produced statements of interest to research mathematicians and actually contributed to the advancement of mathematics. A central and important idea underlying this program is the Principle of the Strongest Conjecture: make the strongest conjecture for which no counterexample is known. These two programs as well as other attempts to automate mathematical conjecturemaking are surveyed—the success of a conjecturemaking program, it is found, correlates strongly whether the program is designed to produce statements that are relevant to answering or advancing our mathematical questions. 1.
Comparing the Zagreb Indices
, 2006
"... Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds québécois de la recherche sur la nature et les technologies. ..."
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Cited by 2 (0 self)
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Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds québécois de la recherche sur la nature et les technologies.
Computers and Discovery in Algebraic Graph Theory
 Edinburgh, 2001), Linear Algebra Appl
, 2001
"... We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory. ..."
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We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory.
Contents lists available at ScienceDirect Linear Algebra and its Applications
"... journal homepage: www.elsevier.com/locate/laa On the reduced signless Laplacian spectrum of a degree maximal graph ..."
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journal homepage: www.elsevier.com/locate/laa On the reduced signless Laplacian spectrum of a degree maximal graph
From Assortative to Dissortative Networks: . . .
, 2010
"... We consider a dynamic model of network formation where agents form and sever links based on the centrality of their potential partners. We show that the existence of capacity constrains in the amount of links an agent can maintain introduces a transition from dissortative to assortative networks. Th ..."
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We consider a dynamic model of network formation where agents form and sever links based on the centrality of their potential partners. We show that the existence of capacity constrains in the amount of links an agent can maintain introduces a transition from dissortative to assortative networks. This effect can shed light on the distinction between technological and social networks as it gives a simple mechanism explaining how and why this transition occurs.
inequality ∗
, 2009
"... Recently Hansen and Vukičević [10] proved that the inequality M1/n ≤ M2/m, where M1 and M2 are the first and second Zagreb indices, holds for chemical graphs, and Vukičević and Graovac [17] proved that this also holds for trees. In both works is given a distinct counterexample for which this inequal ..."
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Recently Hansen and Vukičević [10] proved that the inequality M1/n ≤ M2/m, where M1 and M2 are the first and second Zagreb indices, holds for chemical graphs, and Vukičević and Graovac [17] proved that this also holds for trees. In both works is given a distinct counterexample for which this inequality is false in general. Here, we present some classes of graphs with prescribed degrees, that satisfy M1/n ≤ M2/m. Namely every graph G whose degrees of vertices are in the interval [c, c + ⌈ √ c ⌉] for some integer c, satisfies this inequality. In addition, we prove that for any ∆ ≥ 5, there is an infinite family of graphs of maximum degree ∆ such that the inequality is false. Moreover, an alternative and slightly shorter proof for trees is presented, as well as for unicyclic graphs.