The Power of Dynamic Distance Oracles: Efficient Dynamic Algorithms for the Steiner Tree

In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an $n$-vertex graph $G=(V,E,w)$ with positive real edge weights, and our goal is to maintain a tree which is a good approximation of the minimum Steiner tree spanning a terminal set $S \subseteq V$, which changes over time. The changes applied to the terminal set are either terminal additions (incremental scenario), terminal removals (decremental scenario), or both (fully dynamic scenario). Our task here is twofold. We want to support updates in sublinear $o(n)$ time, and keep the approximation factor of the algorithm as small as possible. We show that we can maintain a $(6+\varepsilon)$-approximate Steiner tree of a general graph in $\tilde{O}(\sqrt{n} \log D)$ time per terminal addition or removal. Here, $D$ denotes the stretch of the metric induced by $G$. For planar graphs we achieve the same running time and the approximation ratio of $(2+\varepsilon)$. Moreover, we show faster algorithms for incremental and decremental scenarios. Finally, we show that if we allow higher approximation ratio, even more efficient algorithms are possible. In particular we show a polylogarithmic time $(4+\varepsilon)$-approximate algorithm for planar graphs. One of the main building blocks of our algorithms are dynamic distance oracles for vertex-labeled graphs, which are of independent interest. We also improve and use the online algorithms for the Steiner tree problem.Comment: Full version of the paper accepted to STOC'1

Man-made Surface Structures from Triangulated Point Clouds

Photogrammetry aims at reconstructing shape and dimensions of objects captured with cameras, 3D laser scanners or other spatial acquisition systems. While many acquisition techniques deliver triangulated point clouds with millions of vertices within seconds, the interpretation is usually left to the user. Especially when reconstructing man-made objects, one is interested in the underlying surface structure, which is not inherently present in the data. This includes the geometric shape of the object, e.g. cubical or cylindrical, as well as corresponding surface parameters, e.g. width, height and radius. Applications are manifold and range from industrial production control to architectural on-site measurements to large-scale city models. The goal of this thesis is to automatically derive such surface structures from triangulated 3D point clouds of man-made objects. They are defined as a compound of planar or curved geometric primitives. Model knowledge about typical primitives and relations between adjacent pairs of them should affect the reconstruction positively. After formulating a parametrized model for man-made surface structures, we develop a reconstruction framework with three processing steps: During a fast pre-segmentation exploiting local surface properties we divide the given surface mesh into planar regions. Making use of a model selection scheme based on minimizing the description length, this surface segmentation is free of control parameters and automatically yields an optimal number of segments. A subsequent refinement introduces a set of planar or curved geometric primitives and hierarchically merges adjacent regions based on their joint description length. A global classification and constraint parameter estimation combines the data-driven segmentation with high-level model knowledge. Therefore, we represent the surface structure with a graphical model and formulate factors based on likelihood as well as prior knowledge about parameter distributions and class probabilities. We infer the most probable setting of surface and relation classes with belief propagation and estimate an optimal surface parametrization with constraints induced by inter-regional relations. The process is specifically designed to work on noisy data with outliers and a few exceptional freeform regions not describable with geometric primitives. It yields full 3D surface structures with watertightly connected surface primitives of different types. The performance of the proposed framework is experimentally evaluated on various data sets. On small synthetically generated meshes we analyze the accuracy of the estimated surface parameters, the sensitivity w.r.t. various properties of the input data and w.r.t. model assumptions as well as the computational complexity. Additionally we demonstrate the flexibility w.r.t. different acquisition techniques on real data sets. The proposed method turns out to be accurate, reasonably fast and little sensitive to defects in the data or imprecise model assumptions.Künstliche Oberflächenstrukturen aus triangulierten Punktwolken Ein Ziel der Photogrammetrie ist die Rekonstruktion der Form und Größe von Objekten, die mit Kameras, 3D-Laserscannern und anderern räumlichen Erfassungssystemen aufgenommen wurden. Während viele Aufnahmetechniken innerhalb von Sekunden triangulierte Punktwolken mit Millionen von Punkten liefern, ist deren Interpretation gewöhnlicherweise dem Nutzer überlassen. Besonders bei der Rekonstruktion künstlicher Objekte (i.S.v. engl. man-made = „von Menschenhand gemacht“ ist man an der zugrunde liegenden Oberflächenstruktur interessiert, welche nicht inhärent in den Daten enthalten ist. Diese umfasst die geometrische Form des Objekts, z.B. quaderförmig oder zylindrisch, als auch die zugehörigen Oberflächenparameter, z.B. Breite, Höhe oder Radius. Die Anwendungen sind vielfältig und reichen von industriellen Fertigungskontrollen über architektonische Raumaufmaße bis hin zu großmaßstäbigen Stadtmodellen. Das Ziel dieser Arbeit ist es, solche Oberflächenstrukturen automatisch aus triangulierten Punktwolken von künstlichen Objekten abzuleiten. Sie sind definiert als ein Verbund ebener und gekrümmter geometrischer Primitive. Modellwissen über typische Primitive und Relationen zwischen Paaren von ihnen soll die Rekonstruktion positiv beeinflussen. Nachdem wir ein parametrisiertes Modell für künstliche Oberflächenstrukturen formuliert haben, entwickeln wir ein Rekonstruktionsverfahren mit drei Verarbeitungsschritten: Im Rahmen einer schnellen Vorsegmentierung, die lokale Oberflächeneigenschaften berücksichtigt, teilen wir die gegebene vermaschte Oberfläche in ebene Regionen. Unter Verwendung eines Schemas zur Modellauswahl, das auf der Minimierung der Beschreibungslänge beruht, ist diese Oberflächensegmentierung unabhängig von Kontrollparametern und liefert automatisch eine optimale Anzahl an Regionen. Eine anschließende Verbesserung führt eine Menge von ebenen und gekrümmten geometrischen Primitiven ein und fusioniert benachbarte Regionen hierarchisch basierend auf ihrer gemeinsamen Beschreibungslänge. Eine globale Klassifikation und bedingte Parameterschätzung verbindet die datengetriebene Segmentierung mit hochrangigem Modellwissen. Dazu stellen wir die Oberflächenstruktur in Form eines graphischen Modells dar und formulieren Faktoren basierend auf der Likelihood sowie auf apriori Wissen über die Parameterverteilungen und Klassenwahrscheinlichkeiten. Wir leiten die wahrscheinlichste Konfiguration von Flächen- und Relationsklassen mit Hilfe von Belief-Propagation ab und schätzen eine optimale Oberflächenparametrisierung mit Bedingungen, die durch die Relationen zwischen benachbarten Primitiven induziert werden. Der Prozess ist eigens für verrauschte Daten mit Ausreißern und wenigen Ausnahmeregionen konzipiert, die nicht durch geometrische Primitive beschreibbar sind. Er liefert wasserdichte 3D-Oberflächenstrukturen mit Oberflächenprimitiven verschiedener Art. Die Leistungsfähigkeit des vorgestellten Verfahrens wird an verschiedenen Datensätzen experimentell evaluiert. Auf kleinen, synthetisch generierten Oberflächen untersuchen wir die Genauigkeit der geschätzten Oberflächenparameter, die Sensitivität bzgl. verschiedener Eigenschaften der Eingangsdaten und bzgl. Modellannahmen sowie die Rechenkomplexität. Außerdem demonstrieren wir die Flexibilität bzgl. verschiedener Aufnahmetechniken anhand realer Datensätze. Das vorgestellte Rekonstruktionsverfahren erweist sich als genau, hinreichend schnell und wenig anfällig für Defekte in den Daten oder falsche Modellannahmen

Almost-Linear Time Algorithms for Incremental Graphs: Cycle Detection, SCCs, ss-tt Shortest Path, and Minimum-Cost Flow

We give the first almost-linear time algorithms for several problems in incremental graphs including cycle detection, strongly connected component maintenance, $s$-$t$ shortest path, maximum flow, and minimum-cost flow. To solve these problems, we give a deterministic data structure that returns a $m^{o(1)}$-approximate minimum-ratio cycle in fully dynamic graphs in amortized $m^{o(1)}$ time per update. Combining this with the interior point method framework of Brand-Liu-Sidford (STOC 2023) gives the first almost-linear time algorithm for deciding the first update in an incremental graph after which the cost of the minimum-cost flow attains value at most some given threshold $F$. By rather direct reductions to minimum-cost flow, we are then able to solve the problems in incremental graphs mentioned above. At a high level, our algorithm dynamizes the $\ell_1$ oblivious routing of Rozho\v{n}-Grunau-Haeupler-Zuzic-Li (STOC 2022), and develops a method to extract an approximate minimum ratio cycle from the structure of the oblivious routing. To maintain the oblivious routing, we use tools from concurrent work of Kyng-Meierhans-Probst Gutenberg which designed vertex sparsifiers for shortest paths, in order to maintain a sparse neighborhood cover in fully dynamic graphs. To find a cycle, we first show that an approximate minimum ratio cycle can be represented as a fundamental cycle on a small set of trees resulting from the oblivious routing. Then, we find a cycle whose quality is comparable to the best tree cycle. This final cycle query step involves vertex and edge sparsification procedures reminiscent of previous works, but crucially requires a more powerful dynamic spanner which can handle far more edge insertions. We build such a spanner via a construction that hearkens back to the classic greedy spanner algorithm

DISTRIBUTED, PARALLEL AND DYNAMIC DISTANCE STRUCTURES

Many fundamental computational tasks can be modeled by distances on a graph. This has inspired studying various structures that preserve approximate distances, but trade off this approximation factor with size, running time, or the number of hops on the approximate shortest paths. Our focus is on three important objects involving preservation of graph distances: hopsets, in which our goal is to ensure that small-hop paths also provide approximate shortest paths; distance oracles, in which we build a small data structure that supports efficient distance queries; and spanners, in which we find a sparse subgraph that approximately preserves all distances. We study efficient constructions and applications of these structures in various models of computation that capture different aspects of computational systems. Specifically, we propose new algorithms for constructing hopsets and distance oracles in two modern distributed models: the Massively Parallel Computation (MPC) and the Congested Clique model. These models have received significant attention recently due to their close connection to present-day big data platforms. In a different direction, we consider a centralized dynamic model in which the input changes over time. We propose new dynamic algorithms for constructing hopsets and distance oracles that lead to state-of-the-art approximate single-source, multi-source and all-pairs shortest path algorithms with respect to update-time. Finally, we study the problem of finding optimal spanners in a different distributed model, the LOCAL model. Unlike our other results, for this problem our goal is to find the best solution for a specific input graph rather than giving a general guarantee that holds for all inputs. One contribution of this work is to emphasize the significance of the tools and the techniques used for these distance problems rather than heavily focusing on a specific model. In other words, we show that our techniques are broad enough that they can be extended to different models

Adaptive scheduling for adaptive sampling in pos taggers construction

We introduce an adaptive scheduling for adaptive sampling as a novel way of machine learning in the construction of part-of-speech taggers. The goal is to speed up the training on large data sets, without significant loss of performance with regard to an optimal configuration. In contrast to previous methods using a random, fixed or regularly rising spacing between the instances, ours analyzes the shape of the learning curve geometrically in conjunction with a functional model to increase or decrease it at any time. The algorithm proves to be formally correct regarding our working hypotheses. Namely, given a case, the following one is the nearest ensuring a net gain of learning ability from the former, it being possible to modulate the level of requirement for this condition. We also improve the robustness of sampling by paying greater attention to those regions of the training data base subject to a temporary inflation in performance, thus preventing the learning from stopping prematurely. The proposal has been evaluated on the basis of its reliability to identify the convergence of models, corroborating our expectations. While a concrete halting condition is used for testing, users can choose any condition whatsoever to suit their own specific needs.Agencia Estatal de Investigación | Ref. TIN2017-85160-C2-1-RAgencia Estatal de Investigación | Ref. TIN2017-85160-C2-2-RXunta de Galicia | Ref. ED431C 2018/50Xunta de Galicia | Ref. ED431D 2017/1

A Dynamic Shortest Paths Toolbox: Low-Congestion Vertex Sparsifiers and their Applications

We present a general toolbox, based on new vertex sparsifiers, for designing data structures to maintain shortest paths in dynamic graphs. In an $m$-edge graph undergoing edge insertions and deletions, our data structures give the first algorithms for maintaining (a) $m^{o(1)}$-approximate all-pairs shortest paths (APSP) with \emph{worst-case} update time $m^{o(1)}$ and query time $\tilde{O}(1)$, and (b) a tree $T$ that has diameter no larger than a subpolynomial factor times the diameter of the underlying graph, where each update is handled in amortized subpolynomial time. In graphs undergoing only edge deletions, we develop a simpler and more efficient data structure to maintain a $(1+\epsilon)$-approximate single-source shortest paths (SSSP) tree $T$ in a graph undergoing edge deletions in amortized time $m^{o(1)}$ per update. Our data structures are deterministic. The trees we can maintain are not subgraphs of $G$, but embed with small edge congestion into $G$. This is in stark contrast to previous approaches and is useful for algorithms that internally use trees to route flow. To illustrate the power of our new toolbox, we show that our SSSP data structure gives simple deterministic implementations of flow-routing MWU methods in several contexts, where previously only randomized methods had been known. To obtain our toolbox, we give the first algorithm that, given a graph $G$ undergoing edge insertions and deletions and a dynamic terminal set $A$, maintains a vertex sparsifier $H$ that approximately preserves distances between terminals in $A$, consists of at most $|A|m^{o(1)}$ vertices and edges, and can be updated in worst-case time $m^{o(1)}$. Crucially, our vertex sparsifier construction allows us to maintain a low edge-congestion embedding of $H$ into $G$, which is needed for our applications

Sociodemographic Factors Predicting Exclusive Breastfeeding in Ethiopia:Evidence from a Meta-analysis of Studies Conducted in the Past 10 Years

OBJECTIVES: To investigate the association between EBF and educational status, household income, marital status, media exposure, and parity in Ethiopia.METHODS: PubMed, EMBASE, Web of Science, SCOPUS, CINAHL and WHO Global health library databases were searched using key terms for all studies published in English between September 2009 and March 2019. The methodological quality of studies was examined using the Newcastle-Ottawa Scale (NOS) for cross-sectional studies. To obtain the pooled odds ratio (OR), extracted data were fitted in a random-effects meta-analysis model. Statistical heterogeneity was quantified using Cochran's Q test, τ2, and I2 statistics. In addition, Jackknife sensitivity analysis, cumulative meta-analysis, and meta-regression analysis were conducted.RESULTS: Out of 553 studies retrieved, 31 studies fulfilled our inclusion criteria. Almost all included studies were conducted among mothers with newborn less than 23 months old. Maternal primary school education (OR 1.39; 95% CI 1.03-1.89; I2 = 86.11%), medium household income (OR 1.27; 95% CI 1.05-1.55; I2 = 60.9%) and being married (OR 1.39; 95% CI 1.05-1.83; I2 = 76.96%) were found to be significantly associated with EBF. We also observed an inverse dose-response relationship of EBF with educational status and income. However, EBF was not significantly associated with parity, media exposure, and paternal educational status.CONCLUSIONS: In this meta-analysis, we showed the relevant effect of maternal education, income, and marital status on EBF. Therefore, multifaceted, effective, and evidence-based efforts are needed to increase the national level of exclusive breastfeeding in Ethiopia.</p

Dynamic Data Mining: Methodology and Algorithms

Supervised data stream mining has become an important and challenging data mining task in modern organizations. The key challenges are threefold: (1) a possibly infinite number of streaming examples and time-critical analysis constraints; (2) concept drift; and (3) skewed data distributions. To address these three challenges, this thesis proposes the novel dynamic data mining (DDM) methodology by effectively applying supervised ensemble models to data stream mining. DDM can be loosely defined as categorization-organization-selection of supervised ensemble models. It is inspired by the idea that although the underlying concepts in a data stream are time-varying, their distinctions can be identified. Therefore, the models trained on the distinct concepts can be dynamically selected in order to classify incoming examples of similar concepts. First, following the general paradigm of DDM, we examine the different concept-drifting stream mining scenarios and propose corresponding effective and efficient data mining algorithms. • To address concept drift caused merely by changes of variable distributions, which we term pseudo concept drift, base models built on categorized streaming data are organized and selected in line with their corresponding variable distribution characteristics. • To address concept drift caused by changes of variable and class joint distributions, which we term true concept drift, an effective data categorization scheme is introduced. A group of working models is dynamically organized and selected for reacting to the drifting concept. Secondly, we introduce an integration stream mining framework, enabling the paradigm advocated by DDM to be widely applicable for other stream mining problems. Therefore, we are able to introduce easily six effective algorithms for mining data streams with skewed class distributions. In addition, we also introduce a new ensemble model approach for batch learning, following the same methodology. Both theoretical and empirical studies demonstrate its effectiveness. Future work would be targeted at improving the effectiveness and efficiency of the proposed algorithms. Meantime, we would explore the possibilities of using the integration framework to solve other open stream mining research problems

Adherence to prenatal iron-folic acid supplementation in low- and middle-income countries (LMIC):A protocol for systematic review and meta-analysis

BACKGROUND: Daily iron-folic acid supplementation reduces anemia and various adverse obstetric outcomes such as preterm delivery, low birthweight, hemorrhage, and perinatal and maternal morbidity and mortality. However, its supplementation has not been successful that attributed to several determinants including poor adherence. Therefore, we aimed to conduct a systematic review and meta-analysis on the prevalence and determinants of adherence to prenatal iron-folic acid supplementation in low- and middle-income countries. In addition, we will develop a conceptual framework in the context of low- and middle-income countries (LMIC). METHODS/DESIGN: We will search PubMed, MEDLINE, EMBASE, EBSCO, Web of Science, SCOPUS, WHO Global Index Medicus, and African Journals Online (AJOL) databases to retrieve relevant literatures. Observational (i.e., case-control, cohort, cross-sectional, survey, and surveillance reports) and quasi-randomized and randomized controlled trial studies conducted in LMIC will be included. The Newcastle-Ottawa Scale (NOS) and Joanna Briggs Institute (JBI) critical appraisal checklist will be used to assess the quality of observational and randomized controlled trial studies respectively. The pooled prevalence and odds ratio of determinants of adherence will be generated using a weighted inverse-variance meta-analysis model. Statistical heterogeneity among studies will be assessed by Cochran's Q χ2 statistics and Higgins (I2 statistics) method. The result will be presented using forest plots and Harvest plots when necessary. Furthermore, we will perform Jackknife sensitivity and subgroup analysis. Data will be analyzed using comprehensive meta-analysis software (version 2). DISCUSSION: Contemporary evidence about the prevalence and determinants of adherence in LMIC will be synthesized to generate up-to-date knowledge. To our knowledge, this is the first systematic review. It would have substantial implications for researchers, clinicians, and policymakers for optimizing maternal and child health outcomes in LMIC. SYSTEMATIC REVIEW REGISTRATION: The protocol has been registered on International Prospective Register of Systematic Review (PROSPERO), University of York Center for Reviews and Dissemination ( https://www.crd.york.ac.uk/ ), registration number CRD42017080245