27,779 research outputs found

    BeSpaceD: Towards a Tool Framework and Methodology for the Specification and Verification of Spatial Behavior of Distributed Software Component Systems

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    In this report, we present work towards a framework for modeling and checking behavior of spatially distributed component systems. Design goals of our framework are the ability to model spatial behavior in a component oriented, simple and intuitive way, the possibility to automatically analyse and verify systems and integration possibilities with other modeling and verification tools. We present examples and the verification steps necessary to prove properties such as range coverage or the absence of collisions between components and technical details

    Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance

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    We present two on-line algorithms for maintaining a topological order of a directed nn-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles mm arc additions in O(m3/2)O(m^{3/2}) time. For sparse graphs (m/n=O(1)m/n = O(1)), this bound improves the best previous bound by a logarithmic factor, and is tight to within a constant factor among algorithms satisfying a natural {\em locality} property. Our second algorithm handles an arbitrary sequence of arc additions in O(n5/2)O(n^{5/2}) time. For sufficiently dense graphs, this bound improves the best previous bound by a polynomial factor. Our bound may be far from tight: we show that the algorithm can take Ω(n222lgn)\Omega(n^2 2^{\sqrt{2\lg n}}) time by relating its performance to a generalization of the kk-levels problem of combinatorial geometry. A completely different algorithm running in Θ(n2logn)\Theta(n^2 \log n) time was given recently by Bender, Fineman, and Gilbert. We extend both of our algorithms to the maintenance of strong components, without affecting the asymptotic time bounds.Comment: 31 page
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