Marc Benkert

Visone Software for Visual Social Network Analysis

We are developing a social network tool that is powerful, comprehensive, and yet easy to use. The unique feature of our tool is the integration of network analysis and visualization. In a long-term interdisciplinary research collaboration, members of our group had implemented several prototypes to explore and demonstrate the feasibility of novel methods. These prototypes have been revised and combined into a stand-alone tool which will be extended regularly.

Morphing polylines: A step towards continuous generalization

We study the problem of morphing between two polylines that represent linear geographical features like roads or rivers generalized at two different scales. This problem occurs frequently during continuous zooming in interactive maps. Situations in which generalization operators like typification and simplification replace, for example, a series of consecutive bends by fewer bends are not always handled well by traditional morphing algorithms. We attempt to cope with such cases by modeling the problem as an optimal correspondence problem between characteristic parts of each polyline. A dynamic programming algorithm is presented that solves the matching problem in O(nm) time, where n and m are the respective numbers of characteristic parts of the two polylines. In a case study we demonstrate that the algorithm yields good results when being applied to data from mountain roads, a river and a region boundary at various scales.

Reporting flock patterns

Data representing moving objects is rapidly getting more available, especially in the area of wildlife GPS tracking. It is a central belief that information is hidden in large data sets in the form of interesting patterns. One of the most common spatio-temporal patterns sought after is flocks. A flock is a large enough subset of objects moving along paths close to each other for a certain pre-defined time. We give a new definition that we argue is more realistic than the previous ones, and we present fast approximation algorithms to report flocks. The algorithms are analysed both theoretically and experimentally.

FINDING POPULAR PLACES

Widespread availability of location aware devices (such as GPS receivers) promotes capture of detailed movement trajectories of people, animals, vehicles and other moving objects. We investigate sp...

Algorithms for Multi-Criteria Boundary Labeling

We present new algorithms for labeling a set P of n points in the plane with labels that are aligned to one side of the bounding box of P . The points are connected to their labels by curves (leaders) that consist of two segments: a horizontal segment, and a second segment at a xed angle with the rst. Our algorithms nd a collection of crossing-free leaders that minimizes the total number of bends, the total length, or any other ‘badness’ function of the leaders. A generalization to labels on two opposite sides of the bounding box of P is considered and an experimental evaluation of the performance is included.

Delineating Boundaries for Imprecise Regions

Abstract In geographic information retrieval, queries often name geographic regions that do not have a well-defined boundary, such as “Southern France.” We provide two algorithmic approaches to the problem of computing reasonable boundaries of such regions based on data points that have evidence indicating that they lie either inside or outside the region. Our problem formulation leads to a number of subproblems related to red-blue point separation and minimum-perimeter polygons, many of which we solve algorithmically. We give experimental results from our implementation and a comparison of the two approaches.

Minimizing intra-edge crossings in wiring diagrams and public transportation maps

In this paper we consider a new problem that occurs when drawing wiring diagrams or public transportation networks. Given an embedded graph G = (V, E) (e.g., the streets served by a bus network) and a set L of paths in G (e.g., the bus lines), we want to draw the paths along the edges of G such that they cross each other as few times as possible. For esthetic reasons we insist that the relative order of the paths that traverse a node does not change within the area occupied by that node. Our main contribution is an algorithm that minimizes the number of crossings on a single edge {u, v} ∈ E if we are given the order of the incoming and outgoing paths. The difficulty is deciding the order of the paths that terminate in u or v with respect to the fixed order of the paths that do not end there. Our algorithm uses dynamic programming and takes O(n2) time, where n is the number of terminating paths.

Constructing minimum-interference networks

A wireless ad-hoc network can be represented as a graph in which the nodes represent wireless devices, and the links represent pairs of nodes that communicate directly by means of radio signals. The interference caused by a link between two nodes u and v can be defined as the number of other nodes that may be disturbed by the signals exchanged by u and v. Given the position of the nodes in the plane, links are to be chosen such that the maximum interference caused by any link is limited and the network fulfills desirable properties such as connectivity, bounded dilation or bounded link diameter. We give efficient algorithms to find the links in two models. In the first model, the signal sent by u to v reaches exactly the nodes that are not farther from u than v is. In the second model, we assume that the boundary of a signals reach is not known precisely and that our algorithms should therefore be based on acceptable estimations. The latter model yields faster algorithms.

The minimum manhattan network problem: a fast factor-3 approximation

Given a set of nodes in the plane and a constant t ≥ 1, a Euclidean t-spanner is a network in which, for any pair of nodes, the ratio of the network distance and the Euclidean distance of the two nodes is at most t. These networks have applications in transportation or communication network design and have been studied extensively. In this paper we study 1-spanners under the Manhattan (or L1-) metric. Such networks are called Manhattan networks. A Manhattan network for a set of nodes can be seen as a set of axis-parallel line segments whose union contains an x- and y-monotone path for each pair of nodes. It is not known whether it is NP-hard to compute minimum Manhattan networks, i.e. Manhattan networks of minimum total length. In this paper we present a factor-3 approximation algorithm for this problem. Given a set of n nodes, our algorithm takes O(n log n) time and linear space.

A POLYNOMIAL-TIME APPROXIMATION ALGORITHM FOR A GEOMETRIC DISPERSION PROBLEM

We consider the following packing problem. Let α be a fixed real in (0, 1]. We are given a bounding rectangle ρ and a set of n possibly intersecting unit disks whose centers lie in ρ. The task is to pack a set of m disjoint disks of radius α into ρ such that no disk in B intersects a disk in , where m is the maximum number of unit disks that can be packed. In this paper we present a polynomial-time algorithm for α = 2/3. So far only the case of packing squares has been considered. For that case, Baur and Fekete have given a polynomial-time algorithm for α = 2/3 and have shown that the problem cannot be solved in polynomial time for any α > 13/14 unless .