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2. Recognizing Cartesian products in linear timeWilfried Imrich, Iztok Peterin, 2007, izvirni znanstveni članek Opis: We present an algorithm that determines the prime factors of connected graphs with respect to the Cartesian product in linear time and space. This improves a result of Aurenhammer et al. [Cartesian graph factorization at logarithmic cost per edge, Comput. Complexity 2 (1992) 331-349], who compute the prime factors in ▫$O(mlog n)$▫ time, where ▫$m$▫ denotes the number of vertices of ▫$G$▫ and ▫$n$▫ the number of edges. Our algorithm is conceptually simpler. It gains its efficiency by the introduction of edge-labellings.
Ključne besede: matematika, teorija grafov, kartezični produkt grafov, linearni algoritem, razcep, mathematics, graph theory, Cartesian product graphs, linear algorithm, decomposition
Objavljeno v DKUM: 10.07.2015; Ogledov: 1727; Prenosov: 134
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3. The obnoxious center problem on weighted cactus graphsBlaž Zmazek, Janez Žerovnik, 2001, objavljeni povzetek znanstvenega prispevka na konferenci Opis: The obnoxious center problem in a graph ▫$G$▫ asks for a location on an edge of the graph such that the minimum weighted distance from this point to a vertex of the graph is as large as possible. An algorithm is given which finds the obnoxious center on a weighted cactus graph in ▫$O(cn)$▫ time, where ▫$n$▫ is the number of vertices and ▫$c$▫ is the number of different vertex weights (called marks).
Ključne besede: matematika, operacijsko raziskovanje, teorija grafov, lokacijski problemi, problem centra, nezaželjeni centri, algoritmi z linearno časovno zahtevnostjo, mathematics, operations research, graph theory, location problems, center problem, obnoxious facilities, linear time algorithm
Objavljeno v DKUM: 10.07.2015; Ogledov: 1343; Prenosov: 97
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4. Assignment problems in logisticsJanez Povh, 2008, izvirni znanstveni članek Opis: We consider two classical problems from location theory which may serve as theoretical models for several logistic problems where one wants to assign elements of a set A to elements of a set B such that some linear or quadratic function attains its minimum. It turns out that linear objective function yields a linear assignment problem, which can be solved easily by several primal-dual methods like Hungarian method, Shortest augmenting path method etc. On the other hand, taking quadratic objective function into account makes the problem much harder. The resulting quadratic assignment problem is a very useful model but also very tough problem from theoretical and practical point of view. We list several well-known applications of these models and also the most effective methods to solve the problem. However, it is still a challenging task to solve this problem to optimality when the size of underlying sets A and B is greater than 25 and currently impossible task when the size is greater than 35.
Ključne besede: quadratic assignment problem, linear assignment problem, branch and bound algorithm, heuristics
Objavljeno v DKUM: 05.06.2012; Ogledov: 2051; Prenosov: 136
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