599 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    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

    Understanding and Tuning Magnetism in van der Waals Magnetic Compounds

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    The recently discovered two-dimensional (2D) magnetism has attracted intensive attention due to possible magnetic phenomenon arising from 2D magnetism and their promising potential for spintronics applications. The advances in 2D magnetism have motivated the study of layered magnetic materials, and further enhanced our ability to tune their magnetic properties. Among various layered magnets, tunable magnetism has been widely investigated in metal thiophosphates MPX3. It is a class of magnetic van der Waals (vdW) materials with antiferromagnetic ordering persisting down to atomically thin limit. Their magnetism originates from the localized moments due to 3d electrons in transition metal ions. So, their magnetic properties are strongly dependent on the choice of M. With this motivation, we synthesized metal-substituted MPX3 compounds such as Ni1-xMnxPS3 (0 ≤ x ≤ 1), Ni1-xCrxPS3 (0 ≤ x ≤ 0.09), and Fe1-xMnxPSe3 (0 ≤ x ≤ 1). The magnetic properties have been found to be very tunable with metal substitutions. Furthermore, we performed previously unexplored non-magnetic X substitution in MnPS3-xSex (0 ≤ x ≤ 3), FePS3-xSex (0 ≤ x ≤ 3), and NiPS3-xSex (0 ≤ x ≤ 1.3). Interestingly, such non-magnetic S-Se substitution also effectively modifies the magnetic exchange and anisotropy in MPX3¬. In addition to M and X substitutions, we conducted electrochemical intercalation of Li into NiPS3. We found the emergence of ferrimagnetism at low temperature in Li-intercalated NiPS3, which has never been observed due to substitution technique. Such efficient engineering of magnetism provides a suitable platform to understand low-dimensional magnetism and design future magnetic devices

    Guaranteeing the \~O(AGM/OUT) Runtime for Uniform Sampling and OUT Size Estimation over Joins

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    We propose a new method for estimating the number of answers OUT of a small join query Q in a large database D, and for uniform sampling over joins. Our method is the first to satisfy all the following statements. - Support arbitrary Q, which can be either acyclic or cyclic, and contain binary and non-binary relations. - Guarantee an arbitrary small error with a high probability always in \~O(AGM/OUT) time, where AGM is the AGM bound OUT (an upper bound of OUT), and \~O hides the polylogarithmic factor of input size. We also explain previous join size estimators in a unified framework. All methods including ours rely on certain indexes on relations in D, which take linear time to build offline. Additionally, we extend our method using generalized hypertree decompositions (GHDs) to achieve a lower complexity than \~O(AGM/OUT) when OUT is small, and present optimization techniques for improving estimation efficiency and accuracy.Comment: 19 page

    Algorithms for sparse convolution and sublinear edit distance

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    In this PhD thesis on fine-grained algorithm design and complexity, we investigate output-sensitive and sublinear-time algorithms for two important problems. (1) Sparse Convolution: Computing the convolution of two vectors is a basic algorithmic primitive with applications across all of Computer Science and Engineering. In the sparse convolution problem we assume that the input and output vectors have at most t nonzero entries, and the goal is to design algorithms with running times dependent on t. For the special case where all entries are nonnegative, which is particularly important for algorithm design, it is known since twenty years that sparse convolutions can be computed in near-linear randomized time O(t log^2 n). In this thesis we develop a randomized algorithm with running time O(t \log t) which is optimal (under some mild assumptions), and the first near-linear deterministic algorithm for sparse nonnegative convolution. We also present an application of these results, leading to seemingly unrelated fine-grained lower bounds against distance oracles in graphs. (2) Sublinear Edit Distance: The edit distance of two strings is a well-studied similarity measure with numerous applications in computational biology. While computing the edit distance exactly provably requires quadratic time, a long line of research has lead to a constant-factor approximation algorithm in almost-linear time. Perhaps surprisingly, it is also possible to approximate the edit distance k within a large factor O(k) in sublinear time O~(n/k + poly(k)). We drastically improve the approximation factor of the known sublinear algorithms from O(k) to k^{o(1)} while preserving the O(n/k + poly(k)) running time.In dieser Doktorarbeit über feinkörnige Algorithmen und Komplexität untersuchen wir ausgabesensitive Algorithmen und Algorithmen mit sublinearer Lauf-zeit für zwei wichtige Probleme. (1) Dünne Faltungen: Die Berechnung der Faltung zweier Vektoren ist ein grundlegendes algorithmisches Primitiv, das in allen Bereichen der Informatik und des Ingenieurwesens Anwendung findet. Für das dünne Faltungsproblem nehmen wir an, dass die Eingabe- und Ausgabevektoren höchstens t Einträge ungleich Null haben, und das Ziel ist, Algorithmen mit Laufzeiten in Abhängigkeit von t zu entwickeln. Für den speziellen Fall, dass alle Einträge nicht-negativ sind, was insbesondere für den Entwurf von Algorithmen relevant ist, ist seit zwanzig Jahren bekannt, dass dünn besetzte Faltungen in nahezu linearer randomisierter Zeit O(t \log^2 n) berechnet werden können. In dieser Arbeit entwickeln wir einen randomisierten Algorithmus mit Laufzeit O(t \log t), der (unter milden Annahmen) optimal ist, und den ersten nahezu linearen deterministischen Algorithmus für dünne nichtnegative Faltungen. Wir stellen auch eine Anwendung dieser Ergebnisse vor, die zu scheinbar unverwandten feinkörnigen unteren Schranken gegen Distanzorakel in Graphen führt. (2) Sublineare Editierdistanz: Die Editierdistanz zweier Zeichenketten ist ein gut untersuchtes Ähnlichkeitsmaß mit zahlreichen Anwendungen in der Computerbiologie. Während die exakte Berechnung der Editierdistanz nachweislich quadratische Zeit erfordert, hat eine lange Reihe von Forschungsarbeiten zu einem Approximationsalgorithmus mit konstantem Faktor in fast-linearer Zeit geführt. Überraschenderweise ist es auch möglich, die Editierdistanz k innerhalb eines großen Faktors O(k) in sublinearer Zeit O~(n/k + poly(k)) zu approximieren. Wir verbessern drastisch den Approximationsfaktor der bekannten sublinearen Algorithmen von O(k) auf k^{o(1)} unter Beibehaltung der O(n/k + poly(k))-Laufzeit

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    On the structure of graphs with forbidden induced substructures

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    One of the central goals in extremal combinatorics is to understand how the global structure of a combinatorial object, e.g. a graph, hypergraph or set system, is affected by local constraints. In this thesis we are concerned with structural properties of graphs and hypergraphs which locally do not look like some type of forbidden induced pattern. Patterns can be single subgraphs, families of subgraphs, or in the multicolour version colourings or families of colourings of subgraphs. Erdős and Szekeres\u27s quantitative version of Ramsey\u27s theorem asserts that in every 22-edge-colouring of the complete graph on nn vertices there is a monochromatic clique on at least 12logn\frac{1}{2}\log n vertices. The famous Erdős-Hajnal conjecture asserts that forbidding fixed colourings on subgraphs ensures much larger monochromatic cliques. The conjecture is open in general, though a few partial results are known. The first part of this thesis will be concerned with different variants of this conjecture: A bipartite variant, a multicolour variant, and an order-size variant for hypergraphs. In the second part of this thesis we focus more on order-size pairs; an order-size pair (n,e)(n,e) is the family consisting of all graphs of order nn and size ee, i.e. on nn vertices with ee edges. We consider order-size pairs in different settings: The graph setting, the bipartite setting and the hypergraph setting. In all these settings we investigate the existence of absolutely avoidable pairs, i.e. fixed pairs that are avoided by all order-size pairs with sufficiently large order, and also forcing densities of order-size pairs (m,f)(m,f), i.e. for nn approaching infinity, the limit superior of the fraction of all possible sizes ee, such that the order-size pair (n,e)(n,e) does not avoid the pair (m,f)(m,f)
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