Modern database systems are increasingly expected to support hybrid queries that combine traditional relational operators with vector-based similarity search enabling applications such as semantic search, contextual recommendations, and multimodal analytics. However, existing benchmarks target either purely relational workloads or isolated similarity search, leaving a gap in evaluating database systems that aim to integrate both. In this paper, we present RVBench , a benchmarking framework for evaluating hybrid relational–vector workloads. RVBench comes with a relational data model that adapts the real-world MediaWiki schema to include vector columns and provides a suite of parameterized SQL templates that interleave similarity search with traditional SQL operations. The framework supports multiple similarity semantics (neighbors based on top-$k$, rank intervals, and sampled ranks) and allows generating hybrid workloads to evaluate database systems on both performance and retrieval quality. We demonstrate RVBench by benchmarking and comparing PostgreSQL and other commercial databases with a reference implementation of the workloads to highlight key trade-offs in query execution strategies and accuracy.

High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional space while preserving important relationships. TopoMap is another technique that excels at preserving the underlying structure of the data, leading to interpretable visualizations. In particular, TopoMap maps the high-dimensional data into a visual space, guaranteeing that the 0-dimensional persistence diagram of the Rips filtration of the visual space matches the one from the high-dimensional data. However, the original TopoMap algorithm can be slow and its layout can be too sparse for large and complex datasets. In this paper, we propose three improvements to TopoMap: 1) a more space-efficient layout, 2) a significantly faster implementation, and 3) a novel TreeMap-based representation that makes use of the topological hierarchy to aid the exploration of the projections. These advancements make TopoMap, now referred to as TopoMap++, a more powerful tool for visualizing high-dimensional data which we demonstrate through different use case scenarios.

Over the past decade, the database research community has directed considerable attention towards harnessing the power of GPUs in query processing engines. The proposed techniques have primarily focused on devising customized low-level mechanisms that utilize the raw hardware parallelism provided abundantly by GPU compute kernels. In this paper, we advocate a radically different approach - instead of dealing directly with hardware idiosyncrasies, to leverage the well-established graphics pipeline architecture baked into the GPU hardware. A variety of advantages accrue from this high-level abstraction: (a) Extracting the power of GPUs is outsourced to highly-optimized graphics drivers, thereby providing hardware-consciousness for free; (b) Query processing becomes agnostic to changes in GPU architectures (e.g. integrated vs discrete) and vendors, requiring only a change of drivers; (c) Contemporary graphics APIs also support a compute element, facilitating query operator designs that seamlessly straddle the compute and graphics worlds. As a proof of concept of the above vision, we implement here the workhorse Join and GroupBy operators using core graphics primitives. These implementations, based on the Vulkan API, have been evaluated over large benchmark databases on vanilla hybrid computing platforms. The experimental results indicate both substantive performance benefits (typically, around 2X faster) over existing approaches, as well as auto-tuned portability to new hardware platforms.

Given the massive growth in the volume of spatial data, there is a great need for systems that can efficiently evaluate spatial queries over large data sets. These queries are notoriously expensive using traditional database solutions. While faster response times can be attained through powerful clusters or servers with large main-memory, these options, due to cost and complexity, are out of reach to many data scientists and analysts making up the long tail. Graphics Processing Units (GPUs), which are now widely available even in commodity desktops and laptops, provide a cost-effective alternative to support high-performance computing, opening up new opportunities to the efficient evaluation of spatial queries. While GPU-based approaches proposed in the literature have shown great improvements in performance, they are tied to specific GPU hardware and only handle specific queries over fixed geometry types. In this paper we present SPADE, a GPU-powered spatial database engine that supports a rich set of spatial queries. We discuss the challenges involved in attaining efficient query evaluation over large datasets as well as portability across different GPU hardware, and how these are addressed in SPADE. We performed a detailed experimental evaluation to assess the effectiveness of the system for wide range of queries and datasets, and report results which show that SPADE is scalable and able to handle data larger than main-memory, and its performance on a laptop is on par with that other systems that require clusters or large-memory servers.

Exploring large virtual environments, such as cities, is a central task in several domains, such as gaming and urban planning. VR systems can greatly help this task by providing an immersive experience; however, a common issue with viewing and navigating a city in the traditional sense is that users can either obtain a local or a global view, but not both at the same time, requiring them to continuously switch between perspectives, losing context and distracting them from their analysis. In this article, our goal is to allow users to navigate to points of interest without changing perspectives. To accomplish this, we design an intuitive navigation interface that takes advantage of the strong sense of spatial presence provided by VR. We supplement this interface with a perspective that warps the environment, called UrbanRama, based on a cylindrical projection, providing a mix of local and global views. The design of this interface was performed as an iterative process in collaboration with architects and urban planners. We conducted a qualitative and a quantitative pilot user study to evaluate UrbanRama and the results indicate the effectiveness of our system in reducing perspective changes, while ensuring that the warping doesn't affect distance and orientation perception.

Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to preserve some dissimilarity (similarity) measure, such as the Euclidean distance for example. In fact, although adopting distinct mathematical formulations designed to favor different aspects of the data, most multidimensional projection methods strive to preserve dissimilarity measures that encapsulate geometric properties such as distances or the proximity relation between data objects. However, geometric relations are not the only interesting property to be preserved in a projection. For instance, the analysis of particular structures such as clusters and outliers could be more reliably performed if the mapping process gives some guarantee as to topological invariants such as connected components and loops. This paper introduces TopoMap, a novel projection technique which provides topological guarantees during the mapping process. In particular, the proposed method performs the mapping from a high-dimensional space to a visual space, while preserving the 0-dimensional persistence diagram of the Rips filtration of the high-dimensional data, ensuring that the filtrations generate the same connected components when applied to the original as well as projected data. The presented case studies show that the topological guarantee provided by TopoMap not only brings confidence to the visual analytic process but also can be used to assist in the assessment of other projection methods.

Esports, despite its expanding interest, lacks fundamental sports analytics resources such as accessible data or proven and reproducible analytical frameworks. Even Counter-Strike: Global Offensive (CSGO), the second most popular esport, suffers from these problems. Thus, quantitative evaluation of CSGO players, a task important to teams, media, bettors and fans, is difficult. To address this, we introduce (1) a data model for CSGO with an open-source implementation; (2) a graph distance measure for defining distances in CSGO; and (3) a context-aware framework to value players' actions based on changes in their team's chances of winning. Using over 70 million in-game CSGO events, we demonstrate our framework's consistency and independence compared to existing valuation frameworks. We also provide use cases demonstrating high-impact play identification and uncertainty estimation.

Urban planning is increasingly data driven, yet the challenge of designing with data at a city scale and remaining sensitive to the impact at a human scale is as important today as it was for Jane Jacobs. We address this challenge with Urban Mosaic, a tool for exploring the urban fabric through a spatially and temporally dense data set of 7.7 million street-level images from New York City, captured over the period of a year. Working in collaboration with professional practitioners, we use Urban Mosaic to investigate questions of accessibility and mobility, and preservation and retrofitting. In doing so, we demonstrate how tools such as this might provide a bridge between the city and the street, by supporting activities such as visual comparison of geographically distant neighborhoods, and temporal analysis of unfolding urban development.

The ScanAllFish project is a large-scale effort to scan all the world's 33,100 known species of fishes. It has already generated thousands of volumetric CT scans of fish species which are available on open access platforms such as the Open Science Framework. To achieve a scanning rate required for a project of this magnitude, many specimens are grouped together into a single tube and scanned all at once. The resulting data contain many fish which are often bent and twisted to fit into the scanner. Our system, Unwind, is a novel interactive visualization and processing tool which extracts, unbends, and untwists volumetric images of fish with minimal user interaction. Our approach enables scientists to interactively unwarp these volumes to remove the undesired torque and bending using a piecewise-linear skeleton extracted by averaging isosurfaces of a harmonic function connecting the head and tail of each fish. The result is a volumetric dataset of a individual, straight fish in a canonical pose defined by the marine biologist expert user. We have developed Unwind in collaboration with a team of marine biologists: Our system has been deployed in their labs, and is presently being used for dataset construction, biomechanical analysis, and the generation of figures for scientific publication.

Connected mobility applications rely heavily on geospatial joins that associate point data, such as locations of Uber cars, to static polygonal regions, such as city neighborhoods. These joins typically involve expensive geometric computations, which makes it hard to provide an interactive user experience. In this paper, we propose an adaptive polygon index that leverages true hit fltering to avoid expensive geometric computations in most cases. In particular, our approach closely approximates polygons by combining quadtrees with true hit filtering, and stores these approximations in a query-effcient radix tree. Based on this index, we introduce two geospatial join algorithms: an approximate one that guarantees a user-defined precision, and an exact one that adapts to the expected point distribution. In summary, our technique outperforms existing CPU-based joins by up to two orders of magnitude and is competitive with state-of-the-art GPU implementations.

The availability of low cost sensors has led to an unprecedented growth in the volume of spatial data. Unfortunately, the time required to evaluate even simple spatial queries over large data sets greatly hampers our ability to interactively explore these data sets and extract actionable insights. While Graphics Processing Units~(GPUs) are increasingly being used to speed up spatial queries, existing solutions have two important drawbacks: they are often tightly coupled to the specific query types they target, making it hard to adapt them for other queries; and since their design is based on CPU-based approaches, it can be difficult to effectively utilize all the benefits provided by the GPU. As a first step towards making GPU spatial query processing mainstream, we propose a new model that represents spatial data as geometric objects and define an algebra consisting of GPU-friendly composable operators that operate over these objects. We demonstrate the expressiveness of the proposed algebra and present a proof-of-concept prototype that supports a subset of the operators, which shows that it is orders of magnitude faster than a CPU-based implementation and outperforms custom GPU-based approaches.

Large scale shadows from buildings in a city play an important role in determining the environmental quality of public spaces. They can be both beneficial, such as for pedestrians during summer, and detrimental, by impacting vegetation and by blocking direct sunlight. Determining the effects of shadows requires the accumulation of shadows over time across different periods in a year. In this paper, we propose a simple yet efficient class of approach that uses the properties of sun movement to track the changing position of shadows within a fixed time interval. We use this approach to extend two commonly used shadow techniques, shadow maps and ray tracing, and demonstrate the efficiency of our approach. Our technique is used to develop an interactive visual analysis system, Shadow Profiler, targeted at city planners and architects that allows them to test the impact of shadows for different development scenarios. We validate the usefulness of this system through case studies set in Manhattan, a dense borough of New York City.

The recent explosion in the number and size of spatio-temporal data sets from urban environments and social sensors creates new opportunities for data-driven approaches to understand and improve cities. Visual analytics systems like Urbane aim to empower domain experts to explore multiple data sets, at different time and space resolutions. Since these systems rely on computationally-intensive spatial aggregation queries that slice and summarize the data over different regions, an important challenge is how to attain interactivity. While traditional pre-aggregation approaches support interactive exploration, they are unsuitable in this setting because they do not support ad-hoc query constraints or polygons of arbitrary shapes. To address this limitation, we have recently proposed Raster Join, an approach that converts a spatial aggregation query into a set of drawing operations on a canvas and leverages the rendering pipeline of the graphics hardware (GPU). By doing so, Raster Join evaluates queries on the fly at interactive speeds on commodity laptops and desktops. In this demonstration, we showcase the efficiency of Raster Join by integrating it with Urbane and enabling interactivity. Demo visitors will interact with Urbane to filter and visualize several urban data sets over multiple resolutions.

Abstract Advances in technology coupled with the availability of low‐cost sensors have resulted in the continuous generation of large time series from several sources. In order to visually explore and compare these time series at different scales, analysts need to execute online analytical processing (OLAP) queries that include constraints and group‐by's at multiple temporal hierarchies. Effective visual analysis requires these queries to be interactive. However, while existing OLAP cube‐based structures can support interactive query rates, the exponential memory requirement to materialize the data cube is often unsuitable for large data sets. Moreover, none of the recent space‐efficient cube data structures allow for updates. Thus, the cube must be re‐computed whenever there is new data, making them impractical in a streaming scenario. We propose Time Lattice, a memory‐efficient data structure that makes use of the implicit temporal hierarchy to enable interactive OLAP queries over large time series. Time Lattice is a subset of a fully materialized cube and is designed to handle fast updates and streaming data. We perform an experimental evaluation which shows that the space efficiency of the data structure does not hamper its performance when compared to the state of the art. In collaboration with signal processing and acoustics research scientists, we use the Time Lattice data structure to design the Noise Profiler, a web‐based visualization framework that supports the analysis of noise from cities. We demonstrate the utility of Noise Profiler through a set of case studies.

We present TopoAngler, a visualization framework that enables an interactive user-guided segmentation of fishes contained in a micro-CT scan. The inherent noise in the CT scan coupled with the often disconnected (and sometimes broken) skeletal structure of fishes makes an automatic segmentation of the volume impractical. To overcome this, our framework combines techniques from computational topology with an interactive visual interface, enabling the human-in-the-Ioop to effectively extract fishes from the volume. In the first step, the join tree of the input is used to create a hierarchical segmentation of the volume. Through the use of linked views, the visual interface then allows users to interactively explore this hierarchy, and gather parts of individual fishes into a coherent sub-volume, thus reconstructing entire fishes. Our framework was primarily developed for its application to CT scans of fishes, generated as part of the ScanAllFish project, through close collaboration with their lead scientist. However, we expect it to also be applicable in other biological applications where a single dataset contains multiple specimen; a common routine that is now widely followed in laboratories to increase throughput of expensive CT scanners.

The Data Polygamy framework allows users to uncover interesting patterns and interactions in the data exhaust from different components of an urban environment. But analyzing the plethora of relationships derived by the framework is challenging. In this demo, we show how visualization can help in the discovery of relationships that are potentially interesting by allowing users to query and explore the relationship set in an intuitive way. We will demonstrate the effectiveness of the visual interface through case studies, and demo visitors will also interact with the polygamous relationships.

Visual exploration of spatial data relies heavily on spatial aggregation queries that slice and summarize the data over different regions. These queries comprise computationally-intensive point-in-polygon tests that associate data points to polygonal regions, challenging the responsiveness of visualization tools. This challenge is compounded by the sheer amounts of data, requiring a large number of such tests to be performed. Traditional pre-aggregation approaches are unsuitable in this setting since they fix the query constraints and support only rectangular regions. On the other hand, query constraints are defined interactively in visual analytics systems, and polygons can be of arbitrary shapes. In this paper, we convert a spatial aggregation query into a set of drawing operations on a canvas and leverage the rendering pipeline of the graphics hardware (GPU) to enable interactive response times. Our technique trades-off accuracy for response time by adjusting the canvas resolution, and can even provide accurate results when combined with a polygon index. We evaluate our technique on two large real-world data sets, exhibiting superior performance compared to index-based approaches.

Cities are inherently dynamic. Interesting patterns of behavior typically manifest at several key areas of a city over multiple temporal resolutions. Studying these patterns can greatly help a variety of experts ranging from city planners and architects to human behavioral experts. Recent technological innovations have enabled the collection of enormous amounts of data that can help in these studies. However, techniques using these data sets typically focus on understanding the data in the context of the city, thus failing to capture the dynamic aspects of the city. The goal of this work is to instead understand the city in the context of multiple urban data sets. To do so, we define the concept of an "urban pulse" which captures the spatio-temporal activity in a city across multiple temporal resolutions. The prominent pulses in a city are obtained using the topology of the data sets, and are characterized as a set of beats. The beats are then used to analyze and compare different pulses. We also design a visual exploration framework that allows users to explore the pulses within and across multiple cities under different conditions. Finally, we present three case studies carried out by experts from two different domains that demonstrate the utility of our framework.

The widespread use of location-based services has led to an increasing availability of trajectory data from urban environments. These data carry rich information that are useful for improving cities through traffic management and city planning. Yet, it also contains information about individuals which can jeopardize their privacy. In this study, we work with the New York City (NYC) taxi trips data set publicly released by the Taxi and Limousine Commission (TLC). This data set contains information about every taxi cab ride that happened in NYC. A bad hashing of the medallion numbers (the ID corresponding to a taxi) allowed the recovery of all the medallion numbers and led to a privacy breach for the drivers, whose income could be easily extracted. In this work, we initiate a study to evaluate whether "perfect" anonymity is possible and if such an identity disclosure can be avoided given the availability of diverse sets of external data sets through which the hidden information can be recovered. This is accomplished through a spatio-temporal join based attack which matches the taxi data with an external medallion data that can be easily gathered by an adversary. Using a simulation of the medallion data, we show that our attack can re-identify over 91% of the taxis that ply in NYC even when using a perfect pseudonymization of medallion numbers. We also explore the effectiveness of trajectory anonymization strategies and demonstrate that our attack can still identify a significant fraction of the taxis in NYC. Given the restrictions in publishing the taxi data by TLC, our results indicate that unless the utility of the data set is significantly compromised, it will not be possible to maintain the privacy of taxi medallion owners and drivers.

There are increasing volumes of spatio-temporal data from various sources such as sensors, social networks and urban environments. Analysis of such data requires flexible exploration and visualizations, but queries that span multiple geographical regions over multiple time slices are expensive to compute, making it challenging to attain interactive speeds for large data sets. In this paper, we propose a new indexing scheme that makes use of modern GPUs to efficiently support spatio-temporal queries over point data. The index covers multiple dimensions, thus allowing simultaneous filtering of spatial and temporal attributes. It uses a block-based storage structure to speed up OLAP-type queries over historical data, and supports query processing over in-memory and disk-resident data. We present different query execution algorithms that we designed to allow the index to be used in different hardware configurations, including CPU-only, GPU-only, and a combination of CPU and GPU. To demonstrate the effectiveness of our techniques, we implemented them on top of MongoDB and performed an experimental evaluation using two real-world data sets: New York City's (NYC) taxi data - consisting of over 868 million taxi trips spanning a period of five years, and Twitter posts - over 1.1 billion tweets collected over a period of 14 months. Our results show that our GPU-based index obtains interactive, sub-second response times for queries over large data sets and leads to at least two orders of magnitude speedup over spatial indexes implemented in existing open-source and commercial database systems.

The increasing ability to collect data from urban environments, coupled with a push towards openness by governments, has resulted in the availability of numerous spatio-temporal data sets covering diverse aspects of a city. Discovering relationships between these data sets can produce new insights by enabling domain experts to not only test but also generate hypotheses. However, discovering these relationships is difficult. First, a relationship between two data sets may occur only at certain locations and/or time periods. Second, the sheer number and size of the data sets, coupled with the diverse spatial and temporal scales at which the data is available, presents computational challenges on all fronts, from indexing and querying to analyzing them. Finally, it is non-trivial to differentiate between meaningful and spurious relationships. To address these challenges, we propose Data Polygamy, a scalable topology-based framework that allows users to query for statistically significant relationships between spatio-temporal data sets. We have performed an experimental evaluation using over 300 spatial-temporal urban data sets which shows that our approach is scalable and effective at identifying interesting relationships.

Abstract The traffic infrastructure greatly impacts the quality of life in urban environments. To optimize this infrastructure, engineers and decision makers need to explore traffic data. In doing so, they face two important challenges: the sparseness of speed sensors that cover only a limited number of road segments, and the complexity of traffic patterns they need to analyze. In this paper we take a first step at addressing these challenges. We use New York City (NYC) taxi trips as sensors to capture traffic information. While taxis provide substantial coverage of the city, the data captured about taxi trips contain neither the location of taxis at frequent intervals nor their routes. We propose an efficient traffic model to derive speed and direction information from these data, and show that it provides reliable estimates. Using these estimates, we define a time‐varying vector‐valued function on a directed graph representing the road network, and adapt techniques used for vector fields to visualize the traffic dynamics. We demonstrate the utility of our technique in several case studies that reveal interesting mobility patterns in NYC's traffic. These patterns were validated by experts from NYC's Department of Transportation and the NYC Taxi & Limousine Commission, who also provided interesting insights into these results.

There is a growing expectation for high performance design in architecture which negotiates between the requirements of the client and the physical constraints of a building site. Clients for building projects often challenge architects to maximize view quality since it can significantly increase real estate value. To pursue this challenge, architects typically move through several design revision cycles to identify a set of design options which satisfy these view quality expectations in coordination with other goals of the project. However, reviewing a large quantity of design options within the practical time constraints is challenging due to the limitations of existing tools for view performance evaluation. These challenges include flexibility in the definition of view quality and the ability to handle the expensive computation involved in assessing both the view quality and the exploration of a large number of possible design options. To address these challenges, we propose a catalogue-based framework that enables the interactive exploration of conceptual building design options based on adjustable view preferences. We achieve this by integrating a flexible mechanism to combine different view measures with an indexing scheme for view computation that achieves high performance and precision. Furthermore, the combined view measures are then used to model the building design space as a high dimensional scalar function. The topological features of this function are then used as candidate building designs. Finally, we propose an interactive design catalogue for the exploration of potential building designs based on the given view preferences. We demonstrate the effectiveness of our approach through two use case scenarios to assess view potential and explore conceptual building designs on sites with high development likelihood in Manhattan, New York City.

Abstract Structured light scanning is ubiquituous in 3D acquisition. It is capable of capturing high geometric detail at a low cost under a variety of challenging scene conditions. Recent methods have demonstrated robustness in the presence of artifacts due to global illumination, such as inter‐reflections and sub‐surface scattering, as well as imperfections caused by projector defocus. For comparing approaches, however, the quantitative evaluation of structured lighting schemes is hindered by the challenges in obtaining ground truth data, resulting in a poor understanding for these methods across a wide range of shapes, materials, and lighting configurations. In this paper, we present a benchmark to study the performance of structured lighting algorithms in the presence of errors caused due to the above properties of the scene. In order to do this, we construct a synthetic structured lighting scanner that uses advanced physically based rendering techniques to simulate the point cloud acquisition process. We show that, under conditions similar to that of a real scanner, our synthetic scanner replicates the same artifacts found in the output of a real scanner. Using this synthetic scanner, we perform a quantitative evaluation of four different structured lighting techniques – gray‐code patterns, micro‐phase shifting, ensemble codes, and unstructured light scanning. The evaluation, performed on a variety of scenes, demonstrate that no one method is capable of adequately handling all sources of error – each method is appropriate for addressing distinct sources of error.

The explosion in the volume of data about urban environments has opened up opportunities to inform both policy and administration and thereby help governments improve the lives of their citizens, increase the efficiency of public services, and reduce the environmental harms of development. However, cities are complex systems and exploring the data they generate is challenging. The interaction between the various components in a city creates complex dynamics where interesting facts occur at multiple scales, requiring users to inspect a large number of data slices over time and space. Manual exploration of these slices is ineffective, time consuming, and in many cases impractical. In this paper, we propose a technique that supports event-guided exploration of large, spatio-temporal urban data. We model the data as time-varying scalar functions and use computational topology to automatically identify events in different data slices. To handle a potentially large number of events, we develop an algorithm to group and index them, thus allowing users to interactively explore and query event patterns on the fly. A visual exploration interface helps guide users towards data slices that display interesting events and trends. We demonstrate the effectiveness of our technique on two different data sets from New York City (NYC): data about taxi trips and subway service. We also report on the feedback we received from analysts at different NYC agencies.

Elucidation of transcriptional regulatory networks (TRNs) is a fundamental goal in biology, and one of the most important components of TRNs are transcription factors (TFs), proteins that specifically bind to gene promoter and enhancer regions to alter target gene expression patterns. Advances in genomic technologies as well as advances in computational biology have led to multiple large regulatory network models (directed networks) each with a large corpus of supporting data and gene-annotation. There are multiple possible biological motivations for exploring large regulatory network models, including: validating TF-target gene relationships, figuring out co-regulation patterns, and exploring the coordination of cell processes in response to changes in cell state or environment. Here we focus on queries aimed at validating regulatory network models, and on coordinating visualization of primary data and directed weighted gene regulatory networks. The large size of both the network models and the primary data can make such coordinated queries cumbersome with existing tools and, in particular, inhibits the sharing of results between collaborators. In this work, we develop and demonstrate a web-based framework for coordinating visualization and exploration of expression data (RNA-seq, microarray), network models and gene-binding data (ChIP-seq). Using specialized data structures and multiple coordinated views, we design an efficient querying model to support interactive analysis of the data. Finally, we show the effectiveness of our framework through case studies for the mouse immune system (a dataset focused on a subset of key cellular functions) and a model bacteria (a small genome with high data-completeness).

The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. This paper describes a fast algorithm to compute the Reeb graph of a piecewise-linear (PL) function defined over manifolds and non-manifolds. The key idea in the proposed approach is to maximally leverage the efficient contour tree algorithm to compute the Reeb graph. The algorithm proceeds by dividing the input into a set of subvolumes that have loop-free Reeb graphs using the join tree of the scalar function and computes the Reeb graph by combining the contour trees of all the subvolumes. Since the key ingredient of this method is a series of union-find operations, the algorithm is fast in practice. Experimental results demonstrate that it outperforms current generic algorithms by a factor of up to two orders of magnitude, and has a performance on par with algorithms that are catered to restricted classes of input. The algorithm also extends to handle large data that do not fit in memory.

We describe a framework to explore and visualize the movement of cloud systems. Using techniques from computational topology and computer vision, our framework allows the user to study this movement at various scales in space and time. Such movements could have large temporal and spatial scales such as the Madden Julian Oscillation (MJO), which has a spatial scale ranging from 1000 km to 10000 km and time of oscillation of around 40 days. Embedded within these larger scale oscillations are a hierarchy of cloud clusters which could have smaller spatial and temporal scales such as the Nakazawa cloud clusters. These smaller cloud clusters, while being part of the equatorial MJO, sometimes move at speeds different from the larger scale and in a direction opposite to that of the MJO envelope. Hitherto, one could only speculate about such movements by selectively analysing data and a priori knowledge of such systems. Our framework automatically delineates such cloud clusters and does not depend on the prior experience of the user to define cloud clusters. Analysis using our framework also shows that most tropical systems such as cyclones also contain multi-scale interactions between clouds and cloud systems. We show the effectiveness of our framework to track organized cloud system during one such rainfall event which happened at Mumbai, India in July 2005 and for cyclone Aila which occurred in Bay of Bengal during May 2009.

The contour tree is a topological abstraction of a scalar field that captures evolution in level set connectivity. It is an effective representation for visual exploration and analysis of scientific data. We describe a work-efficient, output sensitive, and scalable parallel algorithm for computing the contour tree of a scalar field defined on a domain that is represented using either an unstructured mesh or a structured grid. A hybrid implementation of the algorithm using the GPU and multi-core CPU can compute the contour tree of an input containing 16 million vertices in less than ten seconds with a speedup factor of upto 13. Experiments based on an implementation in a multi-core CPU environment show near-linear speedup for large data sets.

The Reeb graph of a scalar function represents the evolution of the topology of its level sets. This paper describes a near-optimal output-sensitive algorithm for computing the Reeb graph of scalar functions defined over manifolds or non-manifolds in any dimension. Key to the simplicity and efficiency of the algorithm is an alternate definition of the Reeb graph that considers equivalence classes of level sets instead of individual level sets. The algorithm works in two steps. The first step locates all critical points of the function in the domain. Critical points correspond to nodes in the Reeb graph. Arcs connecting the nodes are computed in the second step by a simple search procedure that works on a small subset of the domain that corresponds to a pair of critical points. The paper also describes a scheme for controlled simplification of the Reeb graph and two different graph layout schemes that help in the effective presentation of Reeb graphs for visual analysis of scalar fields. Finally, the Reeb graph is employed in four different applications-surface segmentation, spatially-aware transfer function design, visualization of interval volumes, and interactive exploration of time-varying data.

The Reeb graph of a scalar function represents the evolution of the topology of its level sets. In this video, we describe a near-optimal output-sensitive algorithm for computing the Reeb graph of scalar functions defined over manifolds. Key to the simplicity and efficiency of the algorithm is an alternate definition of the Reeb graph that considers equivalence classes of level sets instead of individual level sets. The algorithm works in two steps. The first step locates all critical points of the function in the domain. Arcs in the Reeb graph are computed in the second step using a simple search procedure that works on a small subset of the domain that corresponds to a pair of critical points. The algorithm is also able to handle non-manifold domains.

Estimates of predicate selectivities by database query optimizers often differ significantly from those actually encountered during query execution, leading to poor plan choices and inflated response times. In this paper, we investigate mitigating this problem by replacing selectivity error-sensitive plan choices with alternative plans that provide robust performance. Our approach is based on the recent observation that even the complex and dense "plan diagrams" associated with industrial-strength optimizers can be efficiently reduced to "anorexic" equivalents featuring only a few plans, without materially impacting query processing quality. Extensive experimentation with a rich set of TPC-H and TPC-DS-based query templates in a variety of database environments indicate that plan diagram reduction typically retains plans that are substantially resistant to selectivity errors on the base relations. However, it can sometimes also be severely counter-productive, with the replacements performing much worse. We address this problem through a generalized mathematical characterization of plan cost behavior over the parameter space, which lends itself to efficient criteria of when it is safe to reduce. Our strategies are fully non-invasive and have been implemented in the Picasso optimizer visualization tool.

Given a parametrized n-dimensional SQL query template and a choice of query optimizer, a plan diagram is a color-coded pictorial enumeration of the execution plan choices of the optimizer over the query parameter space. These diagrams have proved to be a powerful metaphor for the analysis and redesign of modern optimizers, and are gaining currency in diverse industrial and academic institutions. However, their utility is adversely impacted by the impractically large computational overheads incurred when standard brute-force exhaustive approaches are used for producing fine-grained diagrams on high-dimensional query templates. In this paper, we investigate strategies for efficiently producing close approximations to complex plan diagrams. Our techniques are customized to the features available in the optimizer's API, ranging from the generic optimizers that provide only the optimal plan for a query, to those that also support costing of sub-optimal plans and enumerating rank-ordered lists of plans. The techniques collectively feature both random and grid sampling, as well as inference techniques based on nearest-neighbor classifiers, parametric query optimization and plan cost monotonicity. Extensive experimentation with a representative set of TPC-H and TPC-DS-based query templates on industrial-strength optimizers indicates that our techniques are capable of delivering 90% accurate diagrams while incurring less than 15% of the computational overheads of the exhaustive approach. In fact, for full-featured optimizers, we can guarantee zero error with less than 10% overheads. These approximation techniques have been implemented in the publicly available Picasso optimizer visualization tool.