Marek Karpinski

Bio: Marek Karpinski is an academic researcher from University of Bonn. The author has contributed to research in topics: Time complexity & Approximation algorithm. The author has an hindex of 50, co-authored 390 publications receiving 10130 citations. Previous affiliations of Marek Karpinski include IBM & University of Nottingham.

An XOR-based erasure-resilient coding scheme

Abstract: An (m; n; b; r)-erasure-resilient coding scheme consists of an encoding algorithm and a decoding algorithm with the following properties. The encoding algorithm produces a set of n packets each containing b bits from a message of m packets containing b bits. The decoding algorithm is able to recover the message from any set of r packets. Erasure-resilient codes have been used to protect real-time traac sent through packet based networks against packet losses. In this paper we describe a erasure-resilient coding scheme that is based on a version of Reed-Solomon codes and which has the property that r = m: Both the encoding and decoding algorithms run in quadratic time and have been customized to give the rst real-time implementations of Priority Encoding Transmission (PET) 2],,1] for medium quality video transmission on Sun SPARCstation 20 workstations.

Resolution for Quantified Boolean Formulas

Abstract: A complete and sound resolution operation directly applicable to the quantified Boolean formulas is presented. If we restrict the resolution to unit resolution, then the completeness and soundness for extended quantified Horn formulas is shown. We prove that the truth of a quantified Horn formula can be decided in O(rn) time, where n is the length of the formula and r is the number of universal variables, whereas in contrast the evaluation problem for extended quantified Horn formulas is coNP-complete for formulas with prefix ??. Further, we show that the resolution is exponential for extended quantified Horn formulas.

Polynomial time approximation schemes for dense instances of NP-hard problems

Abstract: We present a unified framework for designing polynomial time approximation schemes (PTASs) for “dense” instances of many NP-hard optimization problems, including maximum cut, graph bisection, graph separation, minimum k-way cut with and without specified terminals, and maximum 3-satisfiability. By dense graphs we mean graphs with minimum degree Ω(n), although our algorithms solve most of these problems so long as the average degree is Ω(n). Denseness for non-graph problems is defined similarly. The unified framework begins with the idea of exhaustive sampling: picking a small random set of vertices, guessing where they go on the optimum solution, and then using their placement to determine the placement of everything else. The approach then develops into a PTAS for approximating certain smooth integer programs where the objective function and the constraints are “dense” polynomials of constant degree.

On Some Tighter Inapproximability Results

Abstract: We give a number of improved inapproximability results, including the best up to date explicit approximation thresholds for bounded occurrence satisfiability problems like MAX-2SAT and E2-LIN-2, and the bounded degree graph problems, like MIS, NodeCover, and MAX CUT. We prove also for the first time inapproximability of the problem of Sorting by Reversals and display an explicit approximation threshold.

The Nature of Statistical Learning Theory

Abstract: Setting of the learning problem consistency of learning processes bounds on the rate of convergence of learning processes controlling the generalization ability of learning processes constructing learning algorithms what is important in learning theory?.

Tensor Decompositions and Applications

Abstract: This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

k-means++: the advantages of careful seeding

Abstract: The k-means method is a widely used clustering technique that seeks to minimize the average squared distance between points in the same cluster. Although it offers no accuracy guarantees, its simplicity and speed are very appealing in practice. By augmenting k-means with a very simple, randomized seeding technique, we obtain an algorithm that is Θ(logk)-competitive with the optimal clustering. Preliminary experiments show that our augmentation improves both the speed and the accuracy of k-means, often quite dramatically.

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Pattern recognition and neural networks

Abstract: From the Publisher: Pattern recognition has long been studied in relation to many different (and mainly unrelated) applications, such as remote sensing, computer vision, space research, and medical imaging. In this book Professor Ripley brings together two crucial ideas in pattern recognition; statistical methods and machine learning via neural networks. Unifying principles are brought to the fore, and the author gives an overview of the state of the subject. Many examples are included to illustrate real problems in pattern recognition and how to overcome them.This is a self-contained account, ideal both as an introduction for non-specialists readers, and also as a handbook for the more expert reader.