1. The minor crossing number of graphs with an excluded minorDrago Bokal, Gašper Fijavž, David Richard Wood, 2008, izvirni znanstveni članek Opis: The minor crossing number of a graph ▫$G$▫ is the minimum crossing number of a graph that contains ▫$G$▫ as a minor. It is proved that for every graph ▫$H$▫ there is a constant ▫$c$▫, such that every graph ▫$G$▫ with no ▫$H$▫-minor has minor crossing number at most ▫$c|V(G)|$▫.
Ključne besede: mathematics, graph theory, graph minor, excluded minor, crossing number, minor crossing number
Objavljeno: 10.07.2015; Ogledov: 273; Prenosov: 42
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2. Planar decompositions and the minor crossing number of graphsDrago Bokal, Gašper Fijavž, David Richard Wood, 2008, objavljeni povzetek znanstvenega prispevka na konferenci Ključne besede: matematika, teorija grafov, graf, grafovski minor, prepovedan minor, prekrižno število, minorsko prekrižno število, mathematics, graph theory, graph minor, excluded minor, crossing number, minor crossing number
Objavljeno: 10.07.2015; Ogledov: 222; Prenosov: 24
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3. A modular hybrid approach to employee timetablingDrago Bokal, Gašper Fijavž, Bor Harej, Andrej Taranenko, Klemen Žagar, 2008, objavljeni znanstveni prispevek na konferenci Opis: We consider a classical employee timetabling problem: a set of employees with various skill levels, qualifications, workload and availability distributions has to be assigned to a set of shifts, each requiring a prescribed number of qualified employees and spanning a given time period. The novelty of our approach is a hybrid combination of the methods proposed in bibliography, such that we leverage the advantages of known methods while minimizing their disadvantages. Thus, we first apply the generalized local hill-climbing with randomized neighborhoods to quickly reach the vicinity of local optima, and then use the tabu search to explore more of the search space around those solutions. Our experiments show that the resulting hybrid technique performs better than the comparable approaches presented in bibliography due to the hybrid nature of the technique. In addition, we propose a modular design that utilizes dependency injection to compose the the search algorithm. Together with careful modeling, this approach allows for constant-time evaluation of each possible step in the neighborhood and for an easy evaluation of different hybrid combinations that can be combined and parameterized at runtime.
Ključne besede: operacijsko raziskovanje, razporejanje zaposlenih, urniki, lokalna optimizacija, operations research, employee timetabling, generalized local hill-climbing, tabu search, hybrid local optimization
Objavljeno: 10.07.2015; Ogledov: 237; Prenosov: 30
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