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42. On the split structure of lifted groupsAleksander Malnič, Rok Požar, 2016, izvirni znanstveni članek Opis: Let ▫$\wp \colon \tilde{X} \to X$▫ be a regular covering projection of connected graphs with the group of covering transformations ▫$\rm{CT}_\wp$▫ being abelian. Assuming that a group of automorphisms ▫$G \le \rm{Aut} X$▫ lifts along $\wp$ to a group ▫$\tilde{G} \le \rm{Aut} \tilde{X}$▫, the problem whether the corresponding exact sequence ▫$\rm{id} \to \rm{CT}_\wp \to \tilde{G} \to G \to \rm{id}$▫ splits is analyzed in detail in terms of a Cayley voltage assignment that reconstructs the projection up to equivalence. In the above combinatorial setting the extension is given only implicitly: neither ▫$\tilde{G}$▫ nor the action ▫$G\to \rm{Aut} \rm{CT}_\wp$▫ nor a 2-cocycle ▫$G \times G \to \rm{CT}_\wp$▫, are given. Explicitly constructing the cover ▫$\tilde{X}$▫ together with ▫$\rm{CT}_\wp$▫ and ▫$\tilde{G}$▫ as permutation groups on ▫$\tilde{X}$▫ is time and space consuming whenever ▫$\rm{CT}_\wp$▫ is large; thus, using the implemented algorithms (for instance, HasComplement in Magma) is far from optimal. Instead, we show that the minimal required information about the action and the 2-cocycle can be effectively decoded directly from voltages (without explicitly constructing the cover and the lifted group); one could then use the standard method by reducing the problem to solving a linear system of equations over the integers. However, along these lines we here take a slightly different approach which even does not require any knowledge of cohomology. Time and space complexity are formally analyzed whenever ▫$\rm{CT}_\wp$▫ is elementary abelian. Ključne besede: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product Objavljeno v RUP: 14.10.2015; Ogledov: 3018; Prenosov: 158 Celotno besedilo (422,56 KB) |
43. Spread of influence in weighted networks under time and budget constraintsFerdinando Cicalese, Gennaro Cordasco, Luisa Gargano, Martin Milanič, Joseph Peters, Ugo Vaccaro, 2015, izvirni znanstveni članek Ključne besede: social networks, spread of influence, viral marketing, dynamic monopolies, exact polynomial time algorithm Objavljeno v RUP: 14.10.2015; Ogledov: 2887; Prenosov: 197 Povezava na celotno besedilo |
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46. Further results on the relation between nonlinearity and resiliency for Boolean functionsEnes Pašalić, Thomas Johansson, 1999, objavljeni znanstveni prispevek na konferenci (vabljeno predavanje) Opis: A good design of a Boolean function used in a stream cipher requires that the function satisfies certain criteria in order to resist different attacks. In this paper we study the tradeoff between two such criteria, the nonlinearity and the resiliency. The results are twofold. Firstly, we establish the maximum nonlinearity for a fixed resiliency in certain cases. Secondly, we present a simple search algorithm for finding Boolean functions with good nonlinearity and some fixed resiliency. Ključne besede: Boolean functions, cryptography, optimisation, search problems, stream cipher, attacks, maximum nonlinearity, search algorithm, fixed resiliency Objavljeno v RUP: 15.10.2013; Ogledov: 3202; Prenosov: 133 Povezava na celotno besedilo |
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