Petra Šparl

2-local 4/3-competitive algorithm for multicoloring hexagonal graphs

An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is generally modeled as a subgraph of the infinite triangular lattice. Frequency assignment problem can be abstracted as a multicoloring problem on a weighted hexagonal graph, where the weights represent the number of calls to be assigned at vertices. In this paper we present a distributed algorithm for multicoloring hexagonal graphs using only the local clique numbers ω1(v) and ω2(v) at each vertex v of the given hexagonal graph, which can be computed from local information available at the vertex. We prove the algorithm uses no more than ⌈4ω(G)/3⌉ colors for any hexagonal graph G, without explicitly computing the global clique number ω(G). We also prove that our algorithm is 2-local, i.e., the computation at a vertex v ∈ G uses only information about the demands of vertices whose graph distance from v is less than or equal to 2.

2-Local 5/4-competitive algorithm for multicoloring triangle-free hexagonal graphs

An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is generally modeled as a subgraph of the infinite triangular lattice. The distributed frequency assignment problem can be abstracted as a multicoloring problem on a weighted hexagonal graph, where the weight vector represents the number of calls to be assigned at vertices. In this paper we present a 2-local distributed algorithm for multicoloring triangle-free hexagonal graphs using only the local clique numbers ω1 (υ) and ω2(υ) at each vertex υ of the given hexagonal graph, which can be computed from local information available at the vertex. We prove that the algorithm uses no more than [5ω(G)/4] + 3 colors for any triangle-free hexagonal graph G, without explicitly computing the global clique number ω(G). Hence the competitive ratio of the algorithm is 5/4.

Extended Technology Acceptance Model for SPSS Acceptance among Slovenian Students of Social Sciences

Abstract Background and Purpose - IBM SPSS Statistics is among the most widely used programs for statistical analysis in social sciences. Due to many practical values it is frequently used as a tool for teaching statistical concepts in many social science university programs. In our opinion, motivation to learn and to use SPSS during the studying process plays a significant role in building a positive attitude towards SPSS which influences its usage at the professional level after finishing study. Design/Methodology/Approach - The aim of this paper is the development of the model for analysing the acceptance of the SPSS among university students of social sciences. The model is based on the widely known Technology Acceptance Model (TAM). In addition to the traditional components of the TAM, six external variables were included. The model is tested using the web survey on the university students of social sciences from seven faculties at three Slovenian universities. Results - The evaluation of the questionnaire was performed. Descriptive statistics were calculated. The dependencies among the model components were studied and the significant dependencies were pointed out. Conclusion - The results of the empirical study prove that all external variables considered in the model are relevant, and directly influence both key components of the traditional TAM, ≫Perceived Usefulness≪ and ≫Perceived Ease of Use≪. Therefore, our model is useful to study the adoption and continuous utilization of SPSS among the students of social sciences. The obtained results are useful for educators, and can help them to improve the learning process.

2-local distributed algorithms for generalized coloring of hexagonal graphs

A 2-local distributed approximation algorithm for multicoloring of a triangle-free hexagonal graph which uses at most ⌈(5/4)ω(G)⌉+3 colors is presented.

2-local 7/6-competitive algorithm for multicolouring a sub-class of hexagonal graphs

Abstract An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is often modelled as a subgraph of the infinite triangular lattice. The distributed frequency assignment problem can be abstracted as a multicolouring problem on a weighted hexagonal graph, where the weight vector represents the number of calls to be assigned at vertices. In this paper, we present a 2-local distributed algorithm for multicolouring triangle-free hexagonal graphs with no adjacent centres (i.e. vertices which has at least two neighbours in G, which are not on the same line) and with arbitrary demands. The algorithm is using only the local clique numbers at each vertex v of the given hexagonal graph, which can be computed from local information available at the vertex. We prove that the algorithm uses no more than ⌈ 7ω(G)/6⌉+5 colours for any triangle-free hexagonal graph with no adjacent centres G, without explicitly computing the global clique number ω(G). Hence the competitive ratio of the algorithm is 7/6.

Awareness and attitude towards Green IS in Slovenian enterprises

Abstract Background: This study draws upon the use of Information Systems in support of achieving sustainability, known as Green IS. Furthermore, this study builds on the premise that Green IS offers the opportunity for organizations to act proactively in terms of environmental preservation as well as to mitigate the effects of global climate change and other environmental problems. Aim: In particular, this study aims to assess the extent of awareness among managers regarding the use and the acceptance of Green IS in Slovenian enterprises. Method: Using empirical data based on a large-scale survey among senior managers within Slovenian enterprises this study utilized several statistical methods (such as t-test, analysis of variance and multiple linear regression) to analyse the research questions. Results: In general, findings seem to suggest that institutional mechanisms might be a plausible explanation for differences regarding the attitude towards Green IS adoption. For instance, enterprises with at least one implemented sustainability related certificate expressed higher levels of willingness to use Green IS in order to facilitate the achievement of sustainable development. Moreover, the results of the regression analysis revealed that both Institutional Mimetic pressure and Internal Environment Impact has positive impact on Green IS adoption. Conclusion: The main conclusion is that the internal environmental impact is considered the most influential factor of the attitude towards Green IS adoption. The culture or individual perception of managers and employees play an important role in the Green IS adoption. Indeed, enterprises that have no intention of improving their environmental performance, but adopt Green IS by the means of seeking legitimacy among external stakeholders, cannot provide a sustainable improvement in environmental management.

Multicoloring of cannonball graphs

The frequency allocation problem that appeared in the design of cellular telephone networks can be regarded as a multicoloring problem on a weighted hexagonal graph, which opened some still interesting mathematical problems. We generalize the multicoloring problem into higher dimension and present the first approximation algorithms for multicoloring of the so called cannonball graphs.

Simpler multicoloring of triangle-free hexagonal graphs

Given a graph G and a demand function p : V ( G ) � N , a proper n - p ]coloring is a mapping f : V ( G ) � 2 { 1 , � , n } such that | f ( v ) | � p ( v ) for every vertex v � V ( G ) and f ( v ) � f ( u ) = 0� for any two adjacent vertices u and v . The least integer n for which a proper n - p ]coloring exists, � p ( G ) , is called multichromatic number of G . Finding multichromatic number of induced subgraphs of the triangular lattice (called hexagonal graphs) has applications in cellular networks. Weighted clique number of a graph G , ω p ( G ) , is the maximum weight of a clique in G , where the weight of a clique is the total demand of its vertices. McDiarmid and Reed (2000)�8] conjectured that � p ( G ) � ( 9 / 8 ) ω p ( G ) + C for triangle-free hexagonal graphs, where C is some absolute constant. In this article, we provide an algorithm to find a 7-3]coloring of triangle-free hexagonal graphs (that is, when p ( v ) = 3 for all v � V ( G ) ), which implies that � p ( G ) � ( 7 / 6 ) ω p ( G ) + C . Our result constitutes a shorter alternative to the inductive proof of Havet (2001)�5] and improves the short proof of Sudeep and Vishwanathan (2005)�17], who proved the existence of a 14-6]coloring. (It has to be noted, however, that our proof makes use of the 4-color theorem.) All steps of our algorithm take time linear in | V ( G ) | , except for the 4-coloring of an auxiliary planar graph. The new techniques may shed some light on the conjecture of McDiarmid and Reed (2000)�8].

A note on n-tuple colourings and circular colourings of planar graphs with large odd girth

The existence of planar graphs with odd girth 2k+1 and high girth that cannot be (2k+1, k)-coloured was left as an open question by Klostermeyer and Zhang. In this note we show that such graphs exist for arbitrarily large k. We also show that these graphs have fractional chromatic number greater than 2+1/k.

Management Competencies and Organizational Performance in CEE: A Comparison of Slovenia and Austria

Abstract Today management competencies are seen as the only long-term strategic advantage of any company. However, from corporate experience we know that only 10 % of the knowledge acquired is transferred into entrepreneurial practice. Current trends in management development often overemphasize individual learning and ignore the missing fit between individual behavior and organizational performance. To meet these demands, we collected competency attributions of managers attending executive courses in Austria and Slovenia. A questionnaire with closed and open question will help to explore and compare the relation between organizational performance and current management competencies in these countries. The results confirm our predictions to a lesser extent. However, they represent a basis for further examination of the relationship between managerial competencies and organizational performance.