36,654 research outputs found

    Exploring Subexponential Parameterized Complexity of Completion Problems

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    Let F{\cal F} be a family of graphs. In the F{\cal F}-Completion problem, we are given a graph GG and an integer kk as input, and asked whether at most kk edges can be added to GG so that the resulting graph does not contain a graph from F{\cal F} as an induced subgraph. It appeared recently that special cases of F{\cal F}-Completion, the problem of completing into a chordal graph known as Minimum Fill-in, corresponding to the case of F={C4,C5,C6,}{\cal F}=\{C_4,C_5,C_6,\ldots\}, and the problem of completing into a split graph, i.e., the case of F={C4,2K2,C5}{\cal F}=\{C_4, 2K_2, C_5\}, are solvable in parameterized subexponential time 2O(klogk)nO(1)2^{O(\sqrt{k}\log{k})}n^{O(1)}. The exploration of this phenomenon is the main motivation for our research on F{\cal F}-Completion. In this paper we prove that completions into several well studied classes of graphs without long induced cycles also admit parameterized subexponential time algorithms by showing that: - The problem Trivially Perfect Completion is solvable in parameterized subexponential time 2O(klogk)nO(1)2^{O(\sqrt{k}\log{k})}n^{O(1)}, that is F{\cal F}-Completion for F={C4,P4}{\cal F} =\{C_4, P_4\}, a cycle and a path on four vertices. - The problems known in the literature as Pseudosplit Completion, the case where F={2K2,C4}{\cal F} = \{2K_2, C_4\}, and Threshold Completion, where F={2K2,P4,C4}{\cal F} = \{2K_2, P_4, C_4\}, are also solvable in time 2O(klogk)nO(1)2^{O(\sqrt{k}\log{k})} n^{O(1)}. We complement our algorithms for F{\cal F}-Completion with the following lower bounds: - For F={2K2}{\cal F} = \{2K_2\}, F={C4}{\cal F} = \{C_4\}, F={P4}{\cal F} = \{P_4\}, and F={2K2,P4}{\cal F} = \{2K_2, P_4\}, F{\cal F}-Completion cannot be solved in time 2o(k)nO(1)2^{o(k)} n^{O(1)} unless the Exponential Time Hypothesis (ETH) fails. Our upper and lower bounds provide a complete picture of the subexponential parameterized complexity of F{\cal F}-Completion problems for F{2K2,C4,P4}{\cal F}\subseteq\{2K_2, C_4, P_4\}.Comment: 32 pages, 16 figures, A preliminary version of this paper appeared in the proceedings of STACS'1

    Dynamics, robustness and fragility of trust

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    Trust is often conveyed through delegation, or through recommendation. This makes the trust authorities, who process and publish trust recommendations, into an attractive target for attacks and spoofing. In some recent empiric studies, this was shown to lead to a remarkable phenomenon of *adverse selection*: a greater percentage of unreliable or malicious web merchants were found among those with certain types of trust certificates, then among those without. While such findings can be attributed to a lack of diligence in trust authorities, or even to conflicts of interest, our analysis of trust dynamics suggests that public trust networks would probably remain vulnerable even if trust authorities were perfectly diligent. The reason is that the process of trust building, if trust is not breached too often, naturally leads to power-law distributions: the rich get richer, the trusted attract more trust. The evolutionary processes with such distributions, ubiquitous in nature, are known to be robust with respect to random failures, but vulnerable to adaptive attacks. We recommend some ways to decrease the vulnerability of trust building, and suggest some ideas for exploration.Comment: 17 pages; simplified the statement and the proof of the main theorem; FAST 200

    Reliability analysis of dynamic systems by translating temporal fault trees into Bayesian networks

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    Classical combinatorial fault trees can be used to assess combinations of failures but are unable to capture sequences of faults, which are important in complex dynamic systems. A number of proposed techniques extend fault tree analysis for dynamic systems. One of such technique, Pandora, introduces temporal gates to capture the sequencing of events and allows qualitative analysis of temporal fault trees. Pandora can be easily integrated in model-based design and analysis techniques. It is, therefore, useful to explore the possible avenues for quantitative analysis of Pandora temporal fault trees, and we identify Bayesian Networks as a possible framework for such analysis. We describe how Pandora fault trees can be translated to Bayesian Networks for dynamic dependability analysis and demonstrate the process on a simplified fuel system model. The conversion facilitates predictive reliability analysis of Pandora fault trees, but also opens the way for post-hoc diagnostic analysis of failures

    The Stratigraphic Record of Pre-breakup Geodynamics: Evidence from the Barrow Delta, offshore Northwest Australia

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    The structural and stratigraphic evolution of rift basins and passive margins has been widely studied, with many analyses demonstrating that delta systems can provide important records of post-rift geodynamic processes. However, the apparent lack of ancient syn-breakup delta systems and the paucity of seismic imaging across continent-ocean boundaries means the transition from continental rifting to oceanic spreading remains poorly understood. The Early Cretaceous Barrow Group of the North Carnarvon Basin, offshore NW Australia was a major deltaic system that formed during the latter stages of continental rifting, and represents a rich sedimentary archive, documenting uplift, subsidence and erosion of the margin. We use a regional database of 2D and 3D seismic and well data to constrain the internal architecture of the Barrow Group. Our results highlight three major depocentres: the Exmouth and Barrow sub-basins, and southern Exmouth Plateau. Over-compaction of pre-Cretaceous sedimentary rocks in the South Carnarvon Basin, and pervasive reworking of Permian and Triassic palynomorphs in the offshore Barrow Group, suggests that the onshore South Carnarvon Basin originally contained a thicker sedimentary succession, which was uplifted and eroded prior to breakup. Backstripping of sedimentary successions encountered in wells in the Exmouth Plateau depocentre indicate anomalously rapid tectonic subsidence (≤0.24 mm yr-1) accommodated Barrow Group deposition, despite evidence for minimal, contemporaneous upper crustal extension. Our results suggest that classic models of uniform extension cannot account for the observations of uplift and subsidence in the North Carnarvon Basin, and may indicate a period of depth-dependent extension or dynamic topography preceding breakup

    Exploring trade-offs in buffer requirements and throughput constraints for synchronous dataflow graphs

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