2,087 research outputs found

    Dynamic Connectivity in Disk Graphs

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    Let S ⊆ R2 be a set of n sites in the plane, so that every site s ∈ S has an associated radius rs > 0. Let D(S) be the disk intersection graph defined by S, i.e., the graph with vertex set S and an edge between two distinct sites s, t ∈ S if and only if the disks with centers s, t and radii rs , rt intersect. Our goal is to design data structures that maintain the connectivity structure of D(S) as sites are inserted and/or deleted in S. First, we consider unit disk graphs, i.e., we fix rs = 1, for all sites s ∈ S. For this case, we describe a data structure that has O(log2 n) amortized update time and O(log n/ log log n) query time. Second, we look at disk graphs with bounded radius ratio Ψ, i.e., for all s ∈ S, we have 1 ≤ rs ≤ Ψ, for a parameter Ψ that is known in advance. Here, we not only investigate the fully dynamic case, but also the incremental and the decremental scenario, where only insertions or only deletions of sites are allowed. In the fully dynamic case, we achieve amortized expected update time O(Ψ log4 n) and query time O(log n/ log log n). This improves the currently best update time by a factor of Ψ. In the incremental case, we achieve logarithmic dependency on Ψ, with a data structure that has O(α(n)) amortized query time and O(log Ψ log4 n) amortized expected update time, where α(n) denotes the inverse Ackermann function. For the decremental setting, we first develop an efficient decremental disk revealing data structure: given two sets R and B of disks in the plane, we can delete disks from B, and upon each deletion, we receive a list of all disks in R that no longer intersect the union of B. Using this data structure, we get decremental data structures with a query time of O(log n/ log log n) that supports deletions in O(n log Ψ log4 n) overall expected time for disk graphs with bounded radius ratio Ψ and O(n log5 n) overall expected time for disk graphs with arbitrary radii, assuming that the deletion sequence is oblivious of the internal random choices of the data structures

    Algorithms and complexity for approximately counting hypergraph colourings and related problems

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    The past decade has witnessed advancements in designing efficient algorithms for approximating the number of solutions to constraint satisfaction problems (CSPs), especially in the local lemma regime. However, the phase transition for the computational tractability is not known. This thesis is dedicated to the prototypical problem of this kind of CSPs, the hypergraph colouring. Parameterised by the number of colours q, the arity of each hyperedge k, and the vertex maximum degree Δ, this problem falls into the regime of Lovász local lemma when Δ ≲ qᵏ. In prior, however, fast approximate counting algorithms exist when Δ ≲ qᵏ/³, and there is no known inapproximability result. In pursuit of this, our contribution is two-folded, stated as follows. • When q, k ≥ 4 are evens and Δ ≥ 5·qᵏ/², approximating the number of hypergraph colourings is NP-hard. • When the input hypergraph is linear and Δ ≲ qᵏ/², a fast approximate counting algorithm does exist

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Borel versions of the Local Lemma and LOCAL algorithms for graphs of finite asymptotic separation index

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    Asymptotic separation index is a parameter that measures how easily a Borel graph can be approximated by its subgraphs with finite components. In contrast to the more classical notion of hyperfiniteness, asymptotic separation index is well-suited for combinatorial applications in the Borel setting. The main result of this paper is a Borel version of the Lov\'asz Local Lemma -- a powerful general-purpose tool in probabilistic combinatorics -- under a finite asymptotic separation index assumption. As a consequence, we show that locally checkable labeling problems that are solvable by efficient randomized distributed algorithms admit Borel solutions on bounded degree Borel graphs with finite asymptotic separation index. From this we derive a number of corollaries, for example a Borel version of Brooks's theorem for graphs with finite asymptotic separation index

    Mining Butterflies in Streaming Graphs

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    This thesis introduces two main-memory systems sGrapp and sGradd for performing the fundamental analytic tasks of biclique counting and concept drift detection over a streaming graph. A data-driven heuristic is used to architect the systems. To this end, initially, the growth patterns of bipartite streaming graphs are mined and the emergence principles of streaming motifs are discovered. Next, the discovered principles are (a) explained by a graph generator called sGrow; and (b) utilized to establish the requirements for efficient, effective, explainable, and interpretable management and processing of streams. sGrow is used to benchmark stream analytics, particularly in the case of concept drift detection. sGrow displays robust realization of streaming growth patterns independent of initial conditions, scale and temporal characteristics, and model configurations. Extensive evaluations confirm the simultaneous effectiveness and efficiency of sGrapp and sGradd. sGrapp achieves mean absolute percentage error up to 0.05/0.14 for the cumulative butterfly count in streaming graphs with uniform/non-uniform temporal distribution and a processing throughput of 1.5 million data records per second. The throughput and estimation error of sGrapp are 160x higher and 0.02x lower than baselines. sGradd demonstrates an improving performance over time, achieves zero false detection rates when there is not any drift and when drift is already detected, and detects sequential drifts in zero to a few seconds after their occurrence regardless of drift intervals

    Computational Approaches to Drug Profiling and Drug-Protein Interactions

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    Despite substantial increases in R&D spending within the pharmaceutical industry, denovo drug design has become a time-consuming endeavour. High attrition rates led to a long period of stagnation in drug approvals. Due to the extreme costs associated with introducing a drug to the market, locating and understanding the reasons for clinical failure is key to future productivity. As part of this PhD, three main contributions were made in this respect. First, the web platform, LigNFam enables users to interactively explore similarity relationships between ‘drug like’ molecules and the proteins they bind. Secondly, two deep-learning-based binding site comparison tools were developed, competing with the state-of-the-art over benchmark datasets. The models have the ability to predict offtarget interactions and potential candidates for target-based drug repurposing. Finally, the open-source ScaffoldGraph software was presented for the analysis of hierarchical scaffold relationships and has already been used in multiple projects, including integration into a virtual screening pipeline to increase the tractability of ultra-large screening experiments. Together, and with existing tools, the contributions made will aid in the understanding of drug-protein relationships, particularly in the fields of off-target prediction and drug repurposing, helping to design better drugs faster

    Analog Photonics Computing for Information Processing, Inference and Optimisation

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    This review presents an overview of the current state-of-the-art in photonics computing, which leverages photons, photons coupled with matter, and optics-related technologies for effective and efficient computational purposes. It covers the history and development of photonics computing and modern analogue computing platforms and architectures, focusing on optimization tasks and neural network implementations. The authors examine special-purpose optimizers, mathematical descriptions of photonics optimizers, and their various interconnections. Disparate applications are discussed, including direct encoding, logistics, finance, phase retrieval, machine learning, neural networks, probabilistic graphical models, and image processing, among many others. The main directions of technological advancement and associated challenges in photonics computing are explored, along with an assessment of its efficiency. Finally, the paper discusses prospects and the field of optical quantum computing, providing insights into the potential applications of this technology.Comment: Invited submission by Journal of Advanced Quantum Technologies; accepted version 5/06/202

    Algorithms for Computing Maximum Cliques in Hyperbolic Random Graphs

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    In this paper, we study the maximum clique problem on hyperbolic random graphs. A hyperbolic random graph is a mathematical model for analyzing scale-free networks since it effectively explains the power-law degree distribution of scale-free networks. We propose a simple algorithm for finding a maximum clique in hyperbolic random graph. We first analyze the running time of our algorithm theoretically. We can compute a maximum clique on a hyperbolic random graph G in O(m + n^{4.5(1-?)}) expected time if a geometric representation is given or in O(m + n^{6(1-?)}) expected time if a geometric representation is not given, where n and m denote the numbers of vertices and edges of G, respectively, and ? denotes a parameter controlling the power-law exponent of the degree distribution of G. Also, we implemented and evaluated our algorithm empirically. Our algorithm outperforms the previous algorithm [BFK18] practically and theoretically. Beyond the hyperbolic random graphs, we have experiment on real-world networks. For most of instances, we get large cliques close to the optimum solutions efficiently

    Study of Climate Variability Patterns at Different Scales – A Complex Network Approach

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    Das Klimasystem der Erde besteht aus zahlreichen interagierenden Teilsystemen, die sich über verschiedene Zeitskalen hinweg verändern, was zu einer äußerst komplizierten räumlich-zeitlichen Klimavariabilität führt. Das Verständnis von Prozessen, die auf verschiedenen räumlichen und zeitlichen Skalen ablaufen, ist ein entscheidender Aspekt bei der numerischen Wettervorhersage. Die Variabilität des Klimas, ein sich selbst konstituierendes System, scheint in Mustern auf großen Skalen organisiert zu sein. Die Verwendung von Klimanetzwerken hat sich als erfolgreicher Ansatz für die Erkennung der räumlichen Ausbreitung dieser großräumigen Muster in der Variabilität des Klimasystems erwiesen. In dieser Arbeit wird mit Hilfe von Klimanetzwerken gezeigt, dass die Klimavariabilität nicht nur auf größeren Skalen (Asiatischer Sommermonsun, El Niño/Southern Oscillation), sondern auch auf kleineren Skalen, z.B. auf Wetterzeitskalen, in Mustern organisiert ist. Dies findet Anwendung bei der Erkennung einzelner tropischer Wirbelstürme, bei der Charakterisierung binärer Wirbelsturm-Interaktionen, die zu einer vollständigen Verschmelzung führen, und bei der Untersuchung der intrasaisonalen und interannuellen Variabilität des Asiatischen Sommermonsuns. Schließlich wird die Anwendbarkeit von Klimanetzwerken zur Analyse von Vorhersagefehlern demonstriert, was für die Verbesserung von Vorhersagen von immenser Bedeutung ist. Da korrelierte Fehler durch vorhersagbare Beziehungen zwischen Fehlern verschiedener Regionen aufgrund von zugrunde liegenden systematischen oder zufälligen Prozessen auftreten können, wird gezeigt, dass Fehler-Netzwerke helfen können, die räumlich kohärenten Strukturen von Vorhersagefehlern zu untersuchen. Die Analyse der Fehler-Netzwerk-Topologie von Klimavariablen liefert ein erstes Verständnis der vorherrschenden Fehlerquelle und veranschaulicht das Potenzial von Klimanetzwerken als vielversprechendes Diagnoseinstrument zur Untersuchung von Fehlerkorrelationen.The Earth’s climate system consists of numerous interacting subsystems varying over a multitude of time scales giving rise to highly complicated spatio-temporal climate variability. Understanding processes occurring at different scales, both spatial and temporal, has been a very crucial problem in numerical weather prediction. The variability of climate, a self-constituting system, appears to be organized in patterns on large scales. The climate networks approach has been very successful in detecting the spatial propagation of these large scale patterns of variability in the climate system. In this thesis, it is demonstrated using climate network approach that climate variability is organized in patterns not only at larger scales (Asian Summer Monsoon, El Niño-Southern Oscillation) but also at shorter scales, e.g., weather time scales. This finds application in detecting individual tropical cyclones, characterizing binary cyclone interaction leading to a complete merger, and studying the intraseasonal and interannual variability of the Asian Summer Monsoon. Finally, the applicability of the climate network framework to understand forecast error properties is demonstrated, which is crucial for improvement of forecasts. As correlated errors can arise due to the presence of a predictable relationship between errors of different regions because of some underlying systematic or random process, it is shown that error networks can help to analyze the spatially coherent structures of forecast errors. The analysis of the error network topology of a climate variable provides a preliminary understanding of the dominant source of error, which shows the potential of climate networks as a very promising diagnostic tool to study error correlations

    A survey of Bayesian Network structure learning

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