Zsolt Fekete

A Note on [ k, l ]-sparse Graphs

In this note we provide a Henneberg-type constructive characterization theorem of [k, l]-sparse graphs, that is, the graphs for which the number of induced edges in any subset X of nodes is at most κ|X| − l. We consider the case 0 ≤ l ≤ κ.

Source location with rigidity and tree packing requirements

We consider the following two problems: (i) given a graph, find a minimum size vertex-set such that the pinning of it makes the graph rigid in the plane. (ii) Given a graph, contract a minimum size vertex-set such that the resulting graph has two edge-disjoint spanning trees. We prove that these problems are polynomially solvable.

An Inductive Construction for Plane Laman Graphs via Vertex Splitting

We prove that all planar Laman graphs (i.e. minimally generically rigid graphs with a non-crossing planar embedding) can be generated from a single edge by a sequence of vertex splits. It has been shown recently [6,12] that a graph has a pointed pseudo-triangular embedding if and only if it is a planar Laman graph. Due to this connection, our result gives a new tool for attacking problems in the area of pseudo-triangulations and related geometric objects. One advantage of vertex splitting over alternate constructions, such as edge-splitting, is that vertex splitting is geometrically more local.

Uniquely localizable networks with few anchors

In the network localization problem the locations of some nodes (called anchors) as well as the distances between some pairs of nodes are known, and the goal is to determine the location of all nodes. The localization problem is said to be solvable (or uniquely localizable) if there is a unique set of locations consistent with the given data. Recent results from graph rigidity theory made it possible to characterize the solvability of the localization problem in two dimensions. In this paper we address the following related optimization problem: given the set of known distances in the network, make the localization problem solvable by designating a smallest set of anchor nodes. We develop a polynomial-time 3-approximation algorithm for this problem by proving new structural results in graph rigidity and by using tools from matroid theory.

Rigid Two-Dimensional Frameworks with Two Coincident Points

Let G = (V, E) be a graph and

Interest point and segmentation-based photo annotation

{u, v \in V}

SZTAKI @ ImageCLEF 2008: visual feature analysis in segmented images

u,v∈V be two distinct vertices. We give a necessary and sufficient condition for the existence of an infinitesimally rigid two-dimensional bar-and-joint framework (G, p), in which the positions of u and v coincide. We also determine the rank function of the corresponding modified generic rigidity matroid on ground-set E. The results lead to efficient algorithms for testing whether a graph has such a coincident realization with respect to a designated vertex pair and, more generally, for computing the rank of G in the matroid.

QoS Aware and Fair Resource Allocation Scheme in Transport Networks

OWLAP (Operative Workbench for Large-scale Analytics and Presentation) is a visual analytics tool that allows the user to browse and drill down the multidimensional data on-line with the possibility to export result into a zooming presentation framework. We address the challenges of multidimensional visualization by aiding the cognitively hard task of understanding attributes, finding patterns and outliers. We successfully solved the challenge of real time Big Data OLAP reporting by a home developed multithreaded inmemory database manager. Our additional focus is the automatic management of summary preparation that we aid by scripting the presentation framework of Prezi Inc.