Melanie Schmidt

BICO: BIRCH Meets Coresets for k-Means Clustering

We design a data stream algorithm for the k-means problem, called BICO, that combines the data structure of the SIGMOD Test of Time award winning algorithm BIRCH [27] with the theoretical concept of coresets for clustering problems. The k-means problem asks for a set C of k centers minimizing the sum of the squared distances from every point in a set P to its nearest center in C. In a data stream, the points arrive one by one in arbitrary order and there is limited storage space.

Improved and simplified inapproximability for k-means

The k-means problem consists of finding k centers in the d-dimensional Euclidean space that minimize the sum of the squared distances of all points in an input set P to their closest respective center. Awasthi et. al. recently showed that there exists a constant c > 1 such that it is NP-hard to approximate the k-means objective within a factor of c. We establish that the constant c is at least 1.0013.

Earliest arrival flows in networks with multiple sinks

Earliest arrival flows model a central aspect of evacuation planning: in a dangerous situation, as many individuals as possible should be rescued at any point in time. Unfortunately, given a network with multiple sinks, flows over time satisfying this condition do not always exist. We analyze the special case of flows over time with zero transit times and characterize which networks always allow for earliest arrival flows.

Probabilistic k-Median Clustering in Data Streams

The focus of our work is introducing and constructing probabilistic coresets. A probabilistic coreset can contain probabilistic points, and the number of these points should be polylogarithmic in the input size. However, the overall storage size is also influenced by representation size of the propability distribution of each point. So, our first observation is that the size of probabilistic coresets shall be restricted in the number of points and in the representation size of the points. We propose the first (k, ε)-coreset constructions for the probabilistic k-median problem in the metric and Euclidean case. The coresets are of size poly(ε−1, k, log(W/(pmin⋅δ))), where W is the expected total weight of the weighted probabilistic input points when all weights are scaled to be at least one, pmin is the probability of a point to be realized at a certain location, and δ is the error probability of the construction. Our coreset for the Euclidean problem can be maintained in data streams.

Ingo wegener

On the 26th of November, Ingo Wegener died after a long fight with cancer. He was only 57 years old. His death is a tragic loss for everybody who knew him and for the scientific community, in particular the evolutionary computation community. Ingo Wegener was born on the fourth of December 1950 in Bremen, Germany. He studied mathematics at the University of Bielefeld where he obtained his PhD and his habilitation in 1978 and 1981, respectively. His research area was the complexity of Boolean functions. From 1980 to 1987 he was an associate professor at the University of Frankfurt. In 1987 he became a full professor at the Technische Universität Dortmund, heading the group of complexity theory and efficient algorithms. The honors and awards he received are too numerous to mention. Being appointed to the German Council of Science and Humanities as well as receiving the most important and prestigious German award for computer scientists, the Konrad-Zuse-Medaille, suffice as examples. In any case, it was his research he cared about, not awards. Among the eight books he authored is The Complexity of Boolean Functions (Wegener, 1987), an important standard textbook. He continued his research in theoretical computer science, concerned with efficient algorithms and the complexity of Boolean functions. In 2000 he published Branching Programs and Binary Decision Diagrams (Wegener, 2000), another important textbook. In 1996, as an established, important, and respected researcher in these fields, he was bold enough to make a step into an area of research that was completely new to him at this point of time: evolutionary computation. In evolutionary computation, Ingo Wegener did not follow the path of research that was laid out at that point in time. Instead, he used his knowledge from the analysis of efficient algorithms, from complexity theory, and from mathematics to establish a new and important kind of research in the field. He performed a theoretical analysis of the performance of evolutionary algorithms different from what had gone before in several ways. The analysis performed is of complete mathematical rigor, not making use of any unproven assumptions, and not considering models that differ from the real algorithm in an uncontrolled way, and further, not making use of any estimations without proving bounds on the error introduced by them. The analysis takes into account not single example functions but meaningful classes of functions. Such classes may consist of functions where the evolutionary algorithm under consideration performs provably equal (Droste et al., 2006) or they may be defined by some meaningful properties (Wegener and Witt, 2005). Finally, his analyses go far beyond the concrete evolutionary algorithms and classes of fitness functions under consideration. They contribute directly to the development of methods for the analysis of evolutionary algorithms. In addition to establishing rigorous analysis of evolutionary algorithms as an important direction of research, he was the first to extend this kind of research to classical combinatorial optimization problems. A best paper award at PPSN 2002 (Scharnow et al., 2002) demonstrates that this was greatly appreciated in the community. This appreciation continued as best paper awards at GECCO demonstrate, in 2005 for another study of a combinatorial optimization problem (Neumann and Wegener, 2005), in 2006

Theoretical Analysis of the k-Means Algorithm – A Survey

The k-means algorithm is one of the most widely used clustering heuristics. Despite its simplicity, analyzing its running time and quality of approximation is surprisingly difficult and can lead to deep insights that can be used to improve the algorithm. In this paper we survey the recent results in this direction as well as several extension of the basic k-means method.

Probabilistic k -Median Clustering in Data Streams

We define the notion of coresets for probabilistic clustering problems and propose the first (k,e)-coreset constructions for the probabilistic k-median problem in the metric and Euclidean case. The coresets are of size poly(e − 1,k,log(W/(w min ·p min ·δ))), where W is the expected total weight of the weighted probabilistic input points, w min is the minimum weight of a probabilistic input point, p min is the minimum realization probability, and δ is the error probability of the construction. We show how to maintain our coreset for Euclidean spaces in data streams.

Earliest Arrival Flows in Networks with Multiple Sinks

Abstract Earliest arrival flows model a central aspect of evacuation planning: In a dangerous situation, as many individuals as possible should be rescued at any point in time . Unfortunately, given a network with multiple sinks, flows over time satisfying this condition do not always exist. We analyze the special case of flows over time with zero transit times and characterize which networks always allow for earliest arrival flows.

Solving k-means on High-Dimensional Big Data

In recent years, there have been major efforts to develop data stream algorithms that process inputs in one pass over the data with little memory requirement. For the k-means problem, this has led to the development of several