Alon Efrat

Using and determining location in a context-sensitive tour guide

In a study that provided unique insights into the challenges associated with developing location-based applications, the Lancaster Guide project used members of the general public to test a network-centric electronic tourist guide. We discuss two main topics. The first is our choice of positioning technology - beacons that broadcast using an IEEE 802.11 wireless network combined with user input. The second topic concerns techniques for generating custom tours for electronic city-guide systems. Guide generates these custom tours by taking into account multiple contextual triggers and user preferences. In practice, producing good tours and, indeed, assessing the quality of a tour are difficult tasks. While our analysis of techniques for producing custom tours is somewhat specific to the city-guide domain we believe that the majority of our work is relevant to location-based systems in general.

Matching planar maps

The subject of this paper are algorithms for measuring the similarity of patterns of line segments in the plane, a standard problem in, e.g. computer vision, geographic information systems, etc. More precisely, we will define feasible distance measures that reflect how close a given pattern H is to some part of a larger pattern G. These distance measures are generalizations of the well known Fréchet distance for curves. We will first give an efficient algorithm for the case that H is a polygonal curve and G is a geometric graph. Then, slightly relaxing the definition of distance measure we will give an algorithm for the general case where both, H and G, are geometric graphs.

Curve Matching, Time Warping, and Light Fields: New Algorithms for Computing Similarity between Curves

The problem of curve matching appears in many application domains, like time series analysis, shape matching, speech recognition, and signature verification, among others. Curve matching has been studied extensively by computational geometers, and many measures of similarity have been examined, among them being the Fréchet distance (sometimes referred in folklore as the “dog-man” distance).A measure that is very closely related to the Fréchet distance but has never been studied in a geometric context is the Dynamic Time Warping measure (DTW), first used in the context of speech recognition. This measure is ubiquitous across different domains, a surprising fact because notions of similarity usually vary significantly depending on the application. However, this measure suffers from some drawbacks, most importantly the fact that it is defined between sequences of points rather than curves. Thus, the way in which a curve is sampled to yield such a sequence can dramatically affect the quality of the result. Some attempts have been made to generalize the DTW to continuous domains, but the resulting algorithms have exponential complexity.In this paper we propose similarity measures that attempt to capture the “spirit” of dynamic time warping while being defined over continuous domains, and present efficient algorithms for computing them. Our formulation leads to a very interesting connection with finding short paths in a combinatorial manifold defined on the input chains, and in a deeper sense relates to the way light travels in a medium of variable refractivity.

Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications

Let

Guarding galleries and terrains

{\cal F}

On finding a guard that sees most and a shop that sells most

be a collection of n bivariate algebraic functions of constant maximum degree. We show that the combinatorial complexity of the vertical decomposition of the

Computing the smallest k -enclosing circle and related problems

({\le}k)

Buddy tracking-efficient proximity detection among mobile friends

-level of the arrangement

Improved Approximation Algorithms for Relay Placement

\A({\cal F})

On the union of fat wedges and separating a collection of segments by a line

is