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Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal…

Combinatorics · Mathematics 2016-09-06 Herbert Edelsbrunner , Ernst Mücke

For a given point set $S$ in a plane, we develop a distributed algorithm to compute the $\alpha-$shape of $S$. $\alpha-$shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for…

Computational Geometry · Computer Science 2013-02-19 Harish Chintakunta , Hamid Krim

Temporal graphs arise when modeling interactions that evolve over time. They usually come in several flavors, depending on the number of parameters used to describe the temporal aspects of the interactions: time of appearance, duration,…

Data Structures and Algorithms · Computer Science 2026-01-26 Guillaume Aubian , Filippo Brunelli , Feodor F Dragan , Guillaume Ducoffe , Michel Habib , Allen Ibiapina , Laurent Viennot

Shapelet-based algorithms are widely used for time series classification because of their ease of interpretation, but they are currently outperformed by recent state-of-the-art approaches. We present a new formulation of time series…

Computer Vision and Pattern Recognition · Computer Science 2022-06-10 Antoine Guillaume , Christel Vrain , Elloumi Wael

A temporal graph is a graph in which the edge set can change from one time step to the next. The temporal graph exploration problem TEXP is the problem of computing a foremost exploration schedule for a temporal graph, i.e., a temporal walk…

Data Structures and Algorithms · Computer Science 2021-03-17 Thomas Erlebach , Michael Hoffmann , Frank Kammer

Temporal data is information measured in the context of time. This contextual structure provides components that need to be explored to understand the data and that can form the basis of interactions applied to the plots. In multivariate…

Computation · Statistics 2014-12-23 Xiaoyue Cheng , Dianne Cook , Heike Hofmann

SHAP (SHapley Additive exPlanations) has become a popular method to attribute the prediction of a machine learning model on an input to its features. One main challenge of SHAP is the computation time. An exact computation of Shapley values…

Machine Learning · Statistics 2023-09-06 Linwei Hu , Ke Wang

Unpacking and comprehending how black-box machine learning algorithms make decisions has been a persistent challenge for researchers and end-users. Explaining time-series predictive models is useful for clinical applications with high…

Machine Learning · Computer Science 2023-05-09 Amin Nayebi , Sindhu Tipirneni , Chandan K Reddy , Brandon Foreman , Vignesh Subbian

This paper introduces a Delaunay triangulation algorithm based on the external incremental method. Unlike traditional random incremental methods, this approach uses convex hull and points as basic operational units instead of triangles.…

Computational Geometry · Computer Science 2025-03-20 Yifeng Cai

We introduce the idea of temporal graphs, a representation that encodes temporal data into graphs while fully retaining the temporal information of the original data. This representation lets us explore the dynamic temporal properties of…

Physics and Society · Physics 2013-06-06 Vassilis Kostakos

The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry,…

Soft Condensed Matter · Physics 2009-04-30 Florencio Balboa Usabiaga , Daniel Duque

The appearance of the world varies dramatically not only from place to place but also from hour to hour and month to month. Every day billions of images capture this complex relationship, many of which are associated with precise time and…

Computer Vision and Pattern Recognition · Computer Science 2021-01-01 Tawfiq Salem , Scott Workman , Nathan Jacobs

Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of…

Statistical Mechanics · Physics 2013-10-23 Bruno Ribeiro , Nicola Perra , Andrea Baronchelli

Temporal graphs are graphs where the edge set can change in each time step, and the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been…

Data Structures and Algorithms · Computer Science 2024-07-19 Konstantinos Dogeas , Thomas Erlebach , Frank Kammer , Johannes Meintrup , William K. Moses

Word-representable graphs are a subset of graphs that may be represented by a word $w$ over an alphabet composed of the vertices in the graph. In such graphs, an edge exists if and only if the occurrences of the corresponding vertices…

Data Structures and Algorithms · Computer Science 2025-02-12 Duncan Adamson

Discovering shapelets -- i.e., discriminative temporal patterns within time series -- has been widely studied to address the inherent complexity of time-series classification (TSC) and to make model decision-making processes more…

Machine Learning · Computer Science 2026-05-20 Seongjun Lee , Seokhyun Lee , Changhee Lee

We present algorithms and data structures that support the interactive analysis of the grouping structure of one-, two-, or higher-dimensional time-varying data while varying all defining parameters. Grouping structures characterise…

Computational Geometry · Computer Science 2016-03-22 Arthur van Goethem , Marc van Kreveld , Maarten Löffler , Bettina Speckmann , Frank Staals

Graphs are commonly used to represent objects, such as images and text, for pattern classification. In a dynamic world, an object may continuously evolve over time, and so does the graph extracted from the underlying object. These changes…

Data Structures and Algorithms · Computer Science 2017-06-14 Haishuai Wang

Identifying trendline visualizations with desired patterns is a common and fundamental data exploration task. Existing visual analytics tools offer limited flexibility and expressiveness for such tasks, especially when the pattern of…

Databases · Computer Science 2020-01-31 Tarique Siddiqui , Zesheng Wang , Paul Luh , Karrie Karahalios , Aditya Parameswaran

Computing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes…

Discrete Mathematics · Computer Science 2021-05-27 Arnaud Casteigts , Anne-Sophie Himmel , Hendrik Molter , Philipp Zschoche
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