User context and user location in particular play an important role in location-based services (LBS). The location can be determined by various positioning methods. These are typically evaluated with average positioning error or percentile values, which are not the most suitable metrics for evaluation of how a positioning method functions in the semantic space. Therefore, we propose a new method for evaluation of positioning accuracy in the semantic space. We focus on two types of semantic user locations that are widely available in urban areas: the street address and the categories of the surrounding points of interest (POIs). We demonstrate its use on ten different positioning methods: a standalone satellite navigation device, GPS module on a smartphone, two versions of Foursquare positioning service, Google positioning service, a positioning service of the local mobile operator, and four other possible variants of mobile operator-based positioning methods. The evaluation suggest that approach with the street addresses is more promising approach due to either sparse or unevenly distributed POIs. Furthermore, some of the positioning methods that are less accurate in Euclidean space, such as a combination of the GPS data with the mobile operator-based method that relies on the propagation models, performed comparably well in the semantic space as the methods that are using more accurate technologies, such as Google and Foursquare.

COBISS.SI-ID: 11107668

Let $G$ be a unit disk graph in the plane defined by $n$ disks whose positions are known. For the case when $G$ is unweighted, we give a simple algorithm to compute a shortest path tree from a given source in $O(n\log n)$ time. For the case when $G$ is weighted, we show that a shortest path tree from a given source can be computed in $O(n^{1+\varepsilon})$ time, improving the previous best time bound of $O(n^{4/3+\varepsilon})$.

COBISS.SI-ID: 17194841

Frequency assignment has been the motivation behind a large corpus of mathematical research, but the technological progress in telecommunications introduced complexity that makes unclear how to apply existing abstract mathematical models. New insight of the technology is required to close the gap between mathematical optimization and relevant telecommunications problems. In this contribution, we present a taxonomy of realistic problem instances related to configuring Wi-Fi routers and demonstrate the need for understanding technological details of the problem when developing mathematical models for realistic use cases. We point out that several minor things like the unit in which interference between Wi-Fi routers is measured (dBm or mW) have influence on the optimal configurations of network. At the end of the paper we provide an instance with a large sample of real Wi-Fi routers and demonstrate that even the simplest, one access point optimization yields significant improvements.

COBISS.SI-ID: 21616648