Search the repository

On the split structure of lifted groups
Aleksander Malnič, Rok Požar, 2016, original scientific article

Abstract: 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.
Keywords: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product
Published in RUP: 15.10.2015; Views: 2773; Downloads: 157
Full text (422,56 KB)

Characteristics of Cold-Ring Pattern on Meteosat/SEVIRI IR Satellite Images over Slovenia and their relation to hail reports
Mateja Iršič Žibert, Boštjan Muri, Janez Žibert, 2012, published scientific conference contribution

Keywords: meteosat second generation, cold ring shape, cold U/V shape, automatic detection algorithm
Published in RUP: 15.10.2013; Views: 3712; Downloads: 27
Link to full text

Further results on the relation between nonlinearity and resiliency for Boolean functions
Enes Pašalić, Thomas Johansson, 1999, published scientific conference contribution (invited lecture)

Abstract: 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.
Keywords: Boolean functions, cryptography, optimisation, search problems, stream cipher, attacks, maximum nonlinearity, search algorithm, fixed resiliency
Published in RUP: 15.10.2013; Views: 2953; Downloads: 132
Link to full text

The traveling visitor problem and the Koper algorithms for solving it
Milan Đorđević, Andrej Brodnik, 2012, published scientific conference contribution abstract

Keywords: visitor problem, algorithm
Published in RUP: 15.10.2013; Views: 3563; Downloads: 40
Link to full text

On hereditary efficiently dominatable graphs
Martin Milanič, 2011, unpublished conference contribution

Keywords: perfect code, efficient domination, efficiently dominatable graph, polynomial time algorithm
Published in RUP: 15.10.2013; Views: 3122; Downloads: 67
Link to full text