2,927 research outputs found
Twin-width I: tractable FO model checking
Inspired by a width invariant defined on permutations by Guillemot and Marx
[SODA '14], we introduce the notion of twin-width on graphs and on matrices.
Proper minor-closed classes, bounded rank-width graphs, map graphs, -free
unit -dimensional ball graphs, posets with antichains of bounded size, and
proper subclasses of dimension-2 posets all have bounded twin-width. On all
these classes (except map graphs without geometric embedding) we show how to
compute in polynomial time a sequence of -contractions, witness that the
twin-width is at most . We show that FO model checking, that is deciding if
a given first-order formula evaluates to true for a given binary
structure on a domain , is FPT in on classes of bounded
twin-width, provided the witness is given. More precisely, being given a
-contraction sequence for , our algorithm runs in time where is a computable but non-elementary function. We also prove that
bounded twin-width is preserved by FO interpretations and transductions
(allowing operations such as squaring or complementing a graph). This unifies
and significantly extends the knowledge on fixed-parameter tractability of FO
model checking on non-monotone classes, such as the FPT algorithm on
bounded-width posets by Gajarsk\'y et al. [FOCS '15].Comment: 49 pages, 9 figure
Analysing the visual dynamics of spatial morphology
Recently there has been a revival of interest in visibility analysis of architectural configurations. The new analyses rely heavily on computing power and statistical analysis, two factors which, according to the postpositivist school of geography, should immediately cause us to be wary. Thedanger, they would suggest, is in the application of a reductionist formal mathematical description in order to `explain' multilayered sociospatial phenomena. The author presents an attempt to rationalise how we can use visibility analysis to explore architecture in this multilayered context by considering the dynamics that lead to the visual experience. In particular, it is recommended that we assess the visualprocess of inhabitation, rather than assess the visibility in vacuo. In order to investigate the possibilities and limitations of the methodology, an urban environment is analysed by means of an agent-based model of visual actors within the configuration. The results obtained from the model are compared with actual pedestrian movement and other analytic measurements of the area: the agents correlate well both with human movement patterns and with configurational relationship as analysed by space-syntax methods. The application of both methods in combination improves on the correlation with observed movement of either, which in turn implies that an understanding of both the process of inhabitation and the principles of configuration may play a crucial role in determining the social usage of space
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
Algorithm Engineering for Realistic Journey Planning in Transportation Networks
Diese Dissertation beschäftigt sich mit der Routenplanung in Transportnetzen. Es werden neue, effiziente algorithmische Ansätze zur Berechnung optimaler Verbindungen in öffentlichen Verkehrsnetzen, Straßennetzen und multimodalen Netzen, die verschiedene Transportmodi miteinander verknüpfen, eingeführt. Im Fokus der Arbeit steht dabei die Praktikabilität der Ansätze, was durch eine ausführliche experimentelle Evaluation belegt wird
Efficient Irregular Wavefront Propagation Algorithms on Hybrid CPU-GPU Machines
In this paper, we address the problem of efficient execution of a computation
pattern, referred to here as the irregular wavefront propagation pattern
(IWPP), on hybrid systems with multiple CPUs and GPUs. The IWPP is common in
several image processing operations. In the IWPP, data elements in the
wavefront propagate waves to their neighboring elements on a grid if a
propagation condition is satisfied. Elements receiving the propagated waves
become part of the wavefront. This pattern results in irregular data accesses
and computations. We develop and evaluate strategies for efficient computation
and propagation of wavefronts using a multi-level queue structure. This queue
structure improves the utilization of fast memories in a GPU and reduces
synchronization overheads. We also develop a tile-based parallelization
strategy to support execution on multiple CPUs and GPUs. We evaluate our
approaches on a state-of-the-art GPU accelerated machine (equipped with 3 GPUs
and 2 multicore CPUs) using the IWPP implementations of two widely used image
processing operations: morphological reconstruction and euclidean distance
transform. Our results show significant performance improvements on GPUs. The
use of multiple CPUs and GPUs cooperatively attains speedups of 50x and 85x
with respect to single core CPU executions for morphological reconstruction and
euclidean distance transform, respectively.Comment: 37 pages, 16 figure
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