Parameterized Algorithms and Data Reduction for Safe Convoy Routing

We study a problem that models safely routing a convoy through a transportation network, where any vertex adjacent to the travel path of the convoy requires additional precaution: Given a graph G=(V,E), two vertices s,t in V, and two integers k,l, we search for a simple s-t-path with at most k vertices and at most l neighbors. We study the problem in two types of transportation networks: graphs with small crossing number, as formed by road networks, and tree-like graphs, as formed by waterways. For graphs with constant crossing number, we provide a subexponential 2^O(sqrt n)-time algorithm and prove a matching lower bound. We also show a polynomial-time data reduction algorithm that reduces any problem instance to an equivalent instance (a so-called problem kernel) of size polynomial in the vertex cover number of the input graph. In contrast, we show that the problem in general graphs is hard to preprocess. Regarding tree-like graphs, we obtain a 2^O(tw) * l^2 * n-time algorithm for graphs of treewidth tw, show that there is no problem kernel with size polynomial in tw, yet show a problem kernel with size polynomial in the feedback edge number of the input graph

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

Study of high temperature and high density plasmoids in axially symmetrical magnetic fields

Within the framework of an Institutional Partnership of the Alexander von Humboldt Foundation, the Budker Institute of Nuclear Physics Novisibirsk (BINP) and Forschungszentrum Dresden-Rossendorf worked together in a joint project devoted to the research at the coupled GDT-SHIP facility of the BINP with the focus on the study of plasma phenomena within the SHIP mirror section. The project began at July 1st, 2005 and ended on August 30th, 2008. It included work packages of significant theoretical, computational and analyzing investigations. The focus of this final report is on the presentation of results achieved whereas the work that was done is described briefly only. Chapter 2 illustrates the GDT-SHIP facility and describes shortly the planned topics of the SHIP plasma research. Chapter 3 explains the main extensions and modifications of the Integrated Transport Code System (ITCS) which were necessary for the calculations of the fast ion and neutral gas particle fields in SHIP, describes briefly the scheme of computations and presents significant results of pre-calculations from which conclusions were drawn regarding the experimental program of SHIP. In chapter 4, the theoretical and computational investigations of self-organizing processes in two-component plasmas of the GDT-SHIP device are explained and the results hitherto achieved are presented. In chapter 5, significant results of several experiments with moderate and with enhanced plasma parameters are presented and compared with computational results obtained with the ITCS. Preparing neutron measurements which are planned for neutron producing experiments with deuterium injection, Monte Carlo neutron transport calculations with the MCNP code were also carried out. The results are presented. Finally, from the results obtained within the joint research project important conclusions are drawn in chapter 6

MEP: a 3D PIC Code for the Simulation of the Dynamics of a Non-Neutral Plasma

The three-dimensional evolution of a pure electron plasma is studied by means of a newly developed particle-in-cell code which solves the drift-Poisson system where kinetic effects in the motion parallel to the magnetic field are taken into account. Different results relevant to the non-linear dynamics of trapped plasmas and low-energy electron beams are presented. [All rights reserved Elsevier]

Three-dimensional PIC simulation of electron plasmas

The three-dimensional evolution of a pure electron plasma is studied by means of a particle-in-cell code which solves the drift-Poisson system where kinetic effects in the motion parallel to the magnetic field are taken into account. Different results relevant to the nonlinear dynamics of trapped plasmas and low-energy electron beams are presented