2,927 research outputs found

    Twin-width I: tractable FO model checking

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    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, KtK_t-free unit dd-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 dd-contractions, witness that the twin-width is at most dd. We show that FO model checking, that is deciding if a given first-order formula ϕ\phi evaluates to true for a given binary structure GG on a domain DD, is FPT in ∣ϕ∣|\phi| on classes of bounded twin-width, provided the witness is given. More precisely, being given a dd-contraction sequence for GG, our algorithm runs in time f(d,∣ϕ∣)⋅∣D∣f(d,|\phi|) \cdot |D| where ff 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

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    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

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    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

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    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

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    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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