Efficient Many-To-Many Point Matching in One Dimension

Colannino, Justin; Damian, Mirela; Hurtado, Ferrán; Langerman, Stefan; Meijer, Henk; Ramaswami, Suneeta; Souvaine, Diane L.; Toussaint, Godfried T.

doi:10.1007/s00373-007-0714-3

Cited by 22 publications

(48 citation statements)

References 9 publications

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“…We review the O(N log N ) algorithm for solving the minimum-weight many-to-many matching problem using the d 1 measure due to Colannino et al [4], and then show why properties that are used to gain efficiencies do not hold when using the d 2 measure. Without loss of generality, the set A is assumed to have the leftmost element in A ∪ B.…”

Section: Computing a Minimum-weight Many-to-many Matchingmentioning

confidence: 99%

“…Lemma 2 implies that an optimal many-to-many minimum weight matching allowing translations can be found in O(mn) time by applying the algorithm due to Colannino et al [4] to each alignment of A and B that realizes a coincident pair.…”

Section: Finding the Minimum-weight Many-to-many Matching Under Transmentioning

confidence: 99%

“…There is an O(N ω ) algorithm for optimal weighted matching in bipartite graphs due to Mucha and Sankowski [9], where ω is the exponent in the best matrix multiplication algorithm (currently ω = 2.38). For the special case where A and B are points on the real line and using the d 1 weight, Colannino et al [4] provide an O(N log N ) algorithm.…”

mentioning

confidence: 99%

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Minimum Many-to-Many Matchings for Computing the Distance Between Two Sequences

Mohamad

Rappaport

Toussaint

2014

Graphs and Combinatorics

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Motivated by a problem in music theory of measuring the distance between chords and scales we consider algorithms for obtaining a minimum-weight many-to-many matching between two sets of points on the real line. Given sets A and B, we want to find the best rigid translation of B and a many-to-many matching that minimizes the sum of the squares of the distances between matched points. We provide a discrete algorithm that solves this continuous optimization problem, and discuss other related matters.

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Section: Computing a Minimum-weight Many-to-many Matchingmentioning

confidence: 99%

Section: Finding the Minimum-weight Many-to-many Matching Under Transmentioning

confidence: 99%

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Minimum Many-to-Many Matchings for Computing the Distance Between Two Sequences

Mohamad

Rappaport

Toussaint

2014

Graphs and Combinatorics

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“…In an ODMLM, a point matching to its capacity number of points is called a saturated point. Now, we briefly explain the dynamic programming matching algorithm presented by Colannino et al [4] which determines a minimum-cost many-to-many matching between S and T . The time complexity of their algorithm is O(n log n) for the unsorted point sets S and T .…”

Section: Introductionmentioning

confidence: 99%

“…Lemma 1 Let b < c be two points in S, and a < d be two points in T such that a ≤ b < c ≤ d. Then a minimum cost many-to-many matching that contains (a, c) does not contain (b, d), and vice versa (Fig. 2a) [4]. Lemma 2 Let b, d ∈ T and a, c ∈ S with a < b < c < d. Then, a minimum cost many-to-many matching contains no pairs (a, d) (Fig.…”

Section: Introductionmentioning

confidence: 99%

An $$O(n^2)$$ O ( n 2 ) Algorithm for the Limited-Capacity Many-to-Many Point Matching in One Dimension

Rajabi-Alni

Bagheri

2015

Algorithmica

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Given two point sets S and T , in a many-to-many matching between S and T each point in S is assigned to one or more points in T and vice versa. A generalization of the many-to-many matching problem is the limited capacity many-to-many matching problem, where the number of points that can be matched to each point (the capacity of each point) is limited. In this paper, we provide an O n 2 time algorithm for the one dimensional minimum-cost limited capacity many-to-many matching problem, where |S| + |T | = n. Our algorithm improves the best previous time complexity of O(kn 2 ), that in which k is the largest capacity of the points in S ∪ T . In this problem, both S and T lie on the real line and the cost of matching s ∈ S to t ∈ T is equal to the distance between s and t.

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Evaluating individualized treatment effect predictions: A model‐based perspective on discrimination and calibration assessment

Hoogland,

Efthimiou,

Nguyen

et al. 2024

Statistics in Medicine

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In recent years, there has been a growing interest in the prediction of individualized treatment effects. While there is a rapidly growing literature on the development of such models, there is little literature on the evaluation of their performance. In this paper, we aim to facilitate the validation of prediction models for individualized treatment effects. The estimands of interest are defined based on the potential outcomes framework, which facilitates a comparison of existing and novel measures. In particular, we examine existing measures of discrimination for benefit (variations of the c‐for‐benefit), and propose model‐based extensions to the treatment effect setting for discrimination and calibration metrics that have a strong basis in outcome risk prediction. The main focus is on randomized trial data with binary endpoints and on models that provide individualized treatment effect predictions and potential outcome predictions. We use simulated data to provide insight into the characteristics of the examined discrimination and calibration statistics under consideration, and further illustrate all methods in a trial of acute ischemic stroke treatment. The results show that the proposed model‐based statistics had the best characteristics in terms of bias and accuracy. While resampling methods adjusted for the optimism of performance estimates in the development data, they had a high variance across replications that limited their accuracy. Therefore, individualized treatment effect models are best validated in independent data. To aid implementation, a software implementation of the proposed methods was made available in R.

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Efficient Many-To-Many Point Matching in One Dimension

Cited by 22 publications

References 9 publications

Minimum Many-to-Many Matchings for Computing the Distance Between Two Sequences

Minimum Many-to-Many Matchings for Computing the Distance Between Two Sequences

An $$O(n^2)$$ O ( n 2 ) Algorithm for the Limited-Capacity Many-to-Many Point Matching in One Dimension

Evaluating individualized treatment effect predictions: A model‐based perspective on discrimination and calibration assessment

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