Towards Optimal and Expressive Kernelization for d-Hitting Set

d-Hitting Set is the NP-hard problem of selecting at most k vertices of a hypergraph so that each hyperedge, all of which have cardinality at most d, contains at least one selected vertex. The applications of d-Hitting Set are, for example, fault diagnosis, automatic program verification, and the noise-minimizing assignment of frequencies to radio transmitters. We show a linear-time algorithm that transforms an instance of d-Hitting Set into an equivalent instance comprising at most O(k^d) hyperedges and vertices. In terms of parameterized complexity, this is a problem kernel. Our kernelization algorithm is based on speeding up the well-known approach of finding and shrinking sunflowers in hypergraphs, which yields problem kernels with structural properties that we condense into the concept of expressive kernelization. We conduct experiments to show that our kernelization algorithm can kernelize instances with more than 10^7 hyperedges in less than five minutes. Finally, we show that the number of vertices in the problem kernel can be further reduced to O(k^{d-1}) with additional O(k^{1.5 d}) processing time by nontrivially combining the sunflower technique with d-Hitting Set problem kernels due to Abu-Khzam and Moser.Comment: This version gives corrected experimental results, adds additional figures, and more formally defines "expressive kernelization

Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU

The NP-hard Multiple Hitting Set problem is finding a minimum-cardinality set intersecting each of the sets in a given input collection a given number of times. Generalizing a well-known data reduction algorithm due to Weihe, we show a problem kernel for Multiple Hitting Set parameterized by the Dilworth number, a graph parameter introduced by Foldes and Hammer in 1978 yet seemingly so far unexplored in the context of parameterized complexity theory. Using matrix multiplication, we speed up the algorithm to quadratic sequential time and logarithmic parallel time. We experimentally evaluate our algorithms. By implementing our algorithm on GPUs, we show the feasability of realizing kernelization algorithms on SIMD (Single Instruction, Multiple Date) architectures.Comment: Added experiments on one more data se

Global Constraint Catalog, 2nd Edition

This report presents a catalogue of global constraints where each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing filtering algorithms

Global Constraint Catalog, 2nd Edition (revision a)

This report presents a catalogue of global constraints where each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing filtering algorithms

Exploiting a Hypergraph Model for Finding Golomb Rulers

Golomb rulers are special rulers where for any two marks it holds that the distance between them is unique. They find applications in radio frequency selection, radio astronomy, data encryption, communication networks, and bioinformatics. An important subproblem in constructing “compact” Golomb rulers is Golomb Subruler (GSR), which asks whether it is possible to make a given ruler Golomb by removing at most k marks. We initiate a study of GSR from a parameterized complexity perspective. In particular, we consider a natural hypergraph characterization of rulers and investigate the construction and structure of the corresponding hypergraphs. We exploit their properties to derive polynomial-time data reduction rules that reduce a given instance of GSR to an equivalent one with O(k3) marks. Finally, we complement a recent computational complexity study of GSR by providing a simplified reduction that shows NP-hardness even when all integers are bounded by a polynomial in the input length

Advances in Grid Computing

This book approaches the grid computing with a perspective on the latest achievements in the field, providing an insight into the current research trends and advances, and presenting a large range of innovative research papers. The topics covered in this book include resource and data management, grid architectures and development, and grid-enabled applications. New ideas employing heuristic methods from swarm intelligence or genetic algorithm and quantum encryption are considered in order to explain two main aspects of grid computing: resource management and data management. The book addresses also some aspects of grid computing that regard architecture and development, and includes a diverse range of applications for grid computing, including possible human grid computing system, simulation of the fusion reaction, ubiquitous healthcare service provisioning and complex water systems