Shortest path is a fundamental graph problem with numerous applications. However, the concept of classic shortest path is insufficient or even flawed in a temporal graph, as the temporal information determines the order of activities along any path. In this paper, we show the shortcomings of classic shortest path in a temporal graph, and study various concepts of "shortest" path for temporal graphs. Computing these temporal paths is challenging as subpaths of a "shortest" path may not be "shortest" in a temporal graph. We investigate properties of the temporal paths and propose efficient algorithms to compute them. We tested our algorithms on real world temporal graphs to verify their efficiency, and also show that temporal paths are essential for studying temporal graphs by comparing shortest paths in normal static graphs.

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Data visualization is often used as the first step while performing a variety of analytical tasks. With the advent of large, high-dimensional datasets and strong interest in data science, there is a need for tools that can support rapid visual analysis. In this paper we describe our vision for a new class of visualization recommendation systems that can automatically identify and interactively recommend visualizations relevant to an analytical task.

The computation of Minimum Spanning Trees (MSTs) is a fundamental graph problem with important applications. However, there has been little study of MSTs for temporal graphs, which is becoming common as time information is collected for many existing networks. We define two types of MSTs for temporal graphs, MST a and MST w , based on the optimization of time and cost, respectively. We propose efficient linear time algorithms for computing MST a. We show that computing MST w is much harder. We design efficient approximation algorithms based on a transformation to the Directed Steiner Tree problem (DST). Our solution also solves the classical DST problem with a better time complexity and the same approximation factor compared to the state-of-the-art algorithm. Our experiments on real temporal networks further verify the effectiveness of our algorithms. For MST w , our solution is capable of shortening the runtime from 10 hours to 3 seconds.

In exploratory data analysis, analysts often have a need to identify histograms that possess a specific distribution, among a large class of candidate histograms, e.g., find countries whose income distribution is most similar to that of Greece. This distribution could be a new one that the user is curious about, or a known distribution from an existing histogram visualization. At present, this process of identification is brute-force, requiring the manual generation and evaluation of a large number of histograms. We present FastMatch: an end-to-end approach for interactively retrieving the histogram visualizations most similar to a user-specified target, from a large collection of histograms. The primary technical contribution underlying FastMatch is a probabilistic algorithm, HistSim, a theoretically sound sampling-based approach to identify the top-k closest histograms under 1 distance. While HistSim can be used independently, within FastMatch we couple HistSim with a novel system architecture that is aware of practical considerations, employing asynchronous block-based sampling policies, building on lightweight sampling engines developed in recent work [47]. Fast-Match obtains near-perfect accuracy with up to 35× speedup over approaches that do not use sampling on several real-world datasets. arXiv:1708.05918v3 [cs.DB] 8 May 2018 more than half of the queries issued one week completely absent in the following week, and more than 90% of the queries issued one week completely absent a month later [58]. In our case, based on the results for one matching query, Alice may be prompted to explore different (and arbitrary) slices of the same data, which can be exponential in the number of attributes in the dataset. Instead, we materialize samples on-the-fly, which doesn't suffer from the same limitations and has been employed for generating approximate visualizations incrementally [64], and while preserving ordering and perceptual guarantees [46,8]. To the best of our knowledge, however, on-demand approximate sampling techniques have not been applied to the problem of evaluating a large number of visualizations for matches in parallel.Key Research Challenges. In developing an approximation-based approach for rapid histogram matching we immediately encounter a number of theoretical and practical challenges. 1. Quantifying Importance. To benefit from approximation, we need to be able to quantify which samples are "important" to facilitate progress towards termination. It is not clear how to assess this importance: at one extreme, it may be preferable to sample more from candidate histograms that are more "uncertain", but these histograms may already be known to be rather far away from the target. Another approach is to sample more from candidate histograms at the "boundary" of top-k, but if these histograms are more "certain", refining them further may be useless. Another challenge is when we quantify the importance of samples: one approach would be to reassess importance every time new data become available, but this a...