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1. An O(n5/4) Time ∊-Approximation Algorithm for RMS Matching in a Plane

   https://doi.org/10.1137/1.9781611976465.55  

   Lahn, Nathaniel; Raghvendra, Sharath (January 2021, Proceedings of the Annual ACMSIAM Symposium on Discrete Algorithms)

   null (Ed.)

   The 2-Wasserstein distance (or RMS distance) is a useful measure of similarity between probability distributions with exciting applications in machine learning. For discrete distributions, the problem of computing this distance can be expressed in terms of finding a minimum-cost perfect matching on a complete bipartite graph given by two multisets of points A, B ⊂ ℝ2, with |A| = |B| = n, where the ground distance between any two points is the squared Euclidean distance between them. Although there is a near-linear time relative ∊-approximation algorithm for the case where the ground distance is Euclidean (Sharathkumar and Agarwal, JACM 2020), all existing relative ∊-approximation algorithms for the RMS distance take Ω(n3/2) time. This is primarily because, unlike Euclidean distance, squared Euclidean distance is not a metric. In this paper, for the RMS distance, we present a new ∊-approximation algorithm that runs in O(n^5/4 poly{log n, 1/∊}) time. Our algorithm is inspired by a recent approach for finding a minimum-cost perfect matching in bipartite planar graphs (Asathulla et al, TALG 2020). Their algorithm depends heavily on the existence of sublinear sized vertex separators as well as shortest path data structures that require planarity. Surprisingly, we are able to design a similar algorithm for a complete geometric graph that is far from planar and does not have any vertex separators. Central components of our algorithm include a quadtree-based distance that approximates the squared Euclidean distance and a data structure that supports both Hungarian search and augmentation in sublinear time. 

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2. Diverse Unionable Tuple Search: Novelty-Driven Discovery in Data Lakes. In EDBT 2026.

   https://doi.org/10.48786/edbt.2026.04  

   Khatiwada, Aamod; Shraga, Roee; Miller, Renée J (January 2026, OpenProceedings.org)

   EDBT (Ed.)

   Unionable table search techniques input a query table from a user and search for data lake tables that can contribute additional rows to the query table. The definition of unionability is gener- ally based on similarity measures which may include similarity between columns (e.g., value overlap or semantic similarity of the values in the columns) or tables (e.g., similarity of table embed- dings). Due to this and the large redundancy in many data lakes (which can contain many copies and versions of the same table), the most unionable tables may be identical or nearly identical to the query table and may contain little new information. Hence, we introduce the problem of identifying unionable tuples from a data lake that are diverse with respect to the tuples already present in a query table. We perform an extensive experimen- tal analysis of well-known diversity algorithms applied to this novel problem and identify a gap that we address with a novel, clustering-based tuple diversity algorithm called DUST. DUST uses a novel embedding model to represent unionable tuples that outperforms other tuple representation models by at least 15% when representing unionable tuples. Using real data lake bench- marks, we show that our diversification algorithm is more than six times faster than the most efficient diversification baseline. We also show that it is more effective in diversifying unionable tuples than existing diversification algorithms. 

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3. Introducing the contrast profile: a novel time series primitive that allows real world classification

   https://doi.org/https://doi.org/10.1007/s10618-022-00824-5  

   Ryan Mercer, Sara Alaee (March 2022, Data mining and knowledge discovery)

   Editor in Chief: Johannes Fürnkranz (Ed.)

   Time series data remains a perennially important datatype considered in data mining. In the last decade there has been an increasing realization that time series data can be best understood by reasoning about time series subsequences on the basis of their similarity to other subsequences: the two most familiar such time series concepts being motifs and discords. Time series motifs refer to two particularly close subsequences, whereas time series discords indicate subsequences that are far from their nearest neighbors. However, we argue that it can sometimes be useful to simultaneously reason about a subsequence’s closeness to certain data and its distance to other data. In this work we introduce a novel primitive called the Contrast Profile that allows us to efficiently compute such a definition in a principled way. As we will show, the Contrast Profile has many downstream uses, including anomaly detection, data exploration, and preprocessing unstructured data for classification. We demonstrate the utility of the Contrast Profile by showing how it allows end-to-end classification in datasets with tens of billions of datapoints, and how it can be used to explore datasets and reveal subtle patterns that might otherwise escape our attention. Moreover, we demonstrate the generality of the Contrast Profile by presenting detailed case studies in domains as diverse as seismology, animal behavior, and cardiology. 

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4. TS-MIoU: A Time Series Similarity Metric Without Mapping

   https://doi.org/10.1007/978-3-031-26422-1_6  

   Ahmadzadeh, A.; Chen, Y.; Puthucode, K.R.; Ma, R.; Angryk, R.A. (March 2023, Lecture notes in computer science)

   Amini, MR.; Canu, S.; Fischer, A.; Guns, T.; Kralj Novak, P.; Tsoumakas, G. (Ed.)

   Quantifying the similarity or distance between time series, processes, signals, and trajectories is a task-specific problem and remains a challenge for many applications. The simplest measure, meaning the Euclidean distance, is often dismissed because of its sensitivity to noise and the curse of dimensionality. Therefore, elastic mappings (such as DTW, LCSS, ED) are often utilized instead. However, these measures are not metric functions, and more importantly, they must deal with the challenges intrinsic to point-to-point mappings, such as pathological alignment. In this paper, we adopt an object-similarity measure, namely Multiscale Intersection over Union (MIoU), for measuring the distance/similarity between time series. We call the new measure TS-MIoU. Unlike the most popular time series similarity measures, TS-MIoU does not rely on a point-to-point mapping, and therefore, circumvents all respective challenges. We show that TS-MIoU is indeed a metric function, especially that it holds the triangle inequality axiom, and therefore can take advantage of indexing algorithms without a lower bounding. We further show that its sensitivity to noise is adjustable, which makes it a strong alternative to the Euclidean distance while not suffering from the curse of dimensionality. Our proof-of-concept experiments on over 100 UCR datasets show that TS-MIoU can fill the gap between the unforgiving strictness of the ℓp-norm measures, and the mapping challenges of elastic measures. 

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5. Similarity Search in Graph Databases: A Multi-Layered Indexing Approach

   Liang, Yongjiang; Zhao, Peixiang (January 2017, 33rd IEEE International Conference on Data Engineering, ICDE 2017)

   We consider in this paper the similarity search problem that retrieves relevant graphs from a graph database under the well-known graph edit distance (GED) constraint. Formally, given a graph database G = {g1, g2, . . . , gn} and a query graph q, we aim to search the graph gi ∈ g such that the graph edit distance between gi and q, GED(gi, q), is within a user-specified GED threshold, τ. In spite of its theoretical significance and wide applicability, the GED-based similarity search problem is challenging in large graph databases due in particular to a large amount of GED computation incurred, which has proven to be NP-hard. In this paper, we propose a parameterized, partition-based GED lower bound that can be instantiated into a series of tight lower bounds towards synergistically pruning false-positive graphs from before costly GED computation is performed. We design an efficient, selectivity-aware algorithm to partition graphs of into highly selective subgraphs. They are further incorporated in a cost-effective, multi-layered indexing structure, ML-Index (Multi-Layered Index), for GED lower bound cross-checking and false-positive graph filtering with theoretical performance guarantees. Experimental studies in real and synthetic graph databases validate the efficiency and effectiveness of ML-Index, which achieves up to an order of magnitude speedup over the state-of-the-art method for similarity search in graph databases. 

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