Finding Median and Center Strings for a Probability Distribution on a Set of Strings Under Levenshtein Distance Based on Integer Linear Programming

Hayashida, Morihiro; Koyano, Hitoshi

doi:10.1007/978-3-319-54717-6_7

Cited by 5 publications

(9 citation statements)

References 22 publications

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“…To evaluate our constraint propagator we also consider the median string problem, which has been thoroughly studied in the literature (e.g. (Kohonen 1985;Hayashida and Koyano 2016)).…”

Section: The Median String Problemmentioning

confidence: 99%

“…We generated a large number of instances following the instance generation procedure that has been proposed in (Hayashida and Koyano 2016) to evaluate the performance of different exact solution approaches: Our instance generation routine considered different numbers of strings n = [2,4,6,10,15] as well as different maximum string lengths k = [3,5,8,13,20]. We used a simple alphabet consisting of 4 different characters Σ = {1, 2, 3, 4} to randomly generate 10 different instances for each of the possible |n × k| configurations, totaling in 250 benchmark instances.…”

Section: The Median String Problemmentioning

confidence: 99%

“…We compare the performance of our edit distance constraint propagator (CP+global) on the median string problem with an existing mixed integer programming (MIP) formulation from (Hayashida and Koyano 2016) as well as a Constraint Programming (CP) model that uses the same edit distance constraint decomposition as for the paint shop scheduling to solve the median string problem. In our experiments we use the edit operations costs that are known as levensthein distance, as these costs have often been used for median string problems e.g.…”

Section: The Median String Problemmentioning

confidence: 99%

“…In our experiments we use the edit operations costs that are known as levensthein distance, as these costs have often been used for median string problems e.g. (Hayashida and Koyano 2016)…”

Section: The Median String Problemmentioning

confidence: 99%

“…(Hayashida and Koyano 2016;Jiang et al 2003;Olivares-Rodríguez and Oncina 2008). Although, most of these algorithms rely on approximations or heuristic techniques (Jiang et al 2003;Olivares-Rodríguez and Oncina 2008) an exact approach using integer linear programming has been recently proposed by Hayashida and Koyano (2016). An important open research question is if methods using constraint programming can improve the results of existing approaches.…”

Section: Introductionmentioning

confidence: 99%

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Explaining Propagators for String Edit Distance Constraints

Winter

Musliu

Stuckey³

2020

AAAI

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The computation of string similarity measures has been thoroughly studied in the scientific literature and has applications in a wide variety of different areas. One of the most widely used measures is the so called string edit distance which captures the number of required edit operations to transform a string into another given string. Although polynomial time algorithms are known for calculating the edit distance between two strings, there also exist NP-hard problems from practical applications like scheduling or computational biology that constrain the minimum edit distance between arrays of decision variables. In this work, we propose a novel global constraint to formulate restrictions on the minimum edit distance for such problems. Furthermore, we describe a propagation algorithm and investigate an explanation strategy for an edit distance constraint propagator that can be incorporated into state of the art lazy clause generation solvers. Experimental results show that the proposed propagator is able to significantly improve the performance of existing exact methods regarding solution quality and computation speed for benchmark problems from the literature.

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“…To evaluate our constraint propagator we also consider the median string problem, which has been thoroughly studied in the literature (e.g. (Kohonen 1985;Hayashida and Koyano 2016)).…”

Section: The Median String Problemmentioning

confidence: 99%

Section: The Median String Problemmentioning

confidence: 99%

Section: The Median String Problemmentioning

confidence: 99%

“…In our experiments we use the edit operations costs that are known as levensthein distance, as these costs have often been used for median string problems e.g. (Hayashida and Koyano 2016)…”

Section: The Median String Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Explaining Propagators for String Edit Distance Constraints

Winter

Musliu

Stuckey³

2020

AAAI

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Generalized Median Computation for Consensus Learning: A Brief Survey

Jiang,

Nienkötter

2023

Lecture Notes in Computer Science

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Computing a consensus object from a set of given objects is a core problem in machine learning and pattern recognition. A popular approach is the formulation of generalized median as an optimization problem. The concept of generalized median has been studied for numerous problem domains with a broad range of applications. Currently, the research is widely scattered in the literature and no comprehensive survey is available. This brief survey contributes to closing this gap and systematically discusses the relevant issues of generalized median computation. In particular, we present a taxonomy of computation frameworks and methods. We also outline a number of future research directions.

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Pivot Selection for Median String Problem

Mirabal

Abreu

Pedreira

2019

2019 38th International Conference of the Chilean Computer Science Society (SCCC)

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The Median String Problem is W[1]-Hard under the Levenshtein distance, thus, approximation heuristics are used. Perturbation-based heuristics have been proved to be very competitive as regards the ratio approximation accuracy/convergence speed. However, the computational burden increase with the size of the set. In this paper, we explore the idea of reducing the size of the problem by selecting a subset of representative elements, i.e. pivots, that are used to compute the approximate median instead of the whole set. We aim to reduce the computation time through a reduction of the problem size while achieving similar approximation accuracy. We explain how we find those pivots and how to compute the median string from them. Results on commonly used test data suggest that our approach can reduce the computational requirements (measured in computed edit distances) by 8% with approximation accuracy as good as the state of the art heuristic.

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Finding Median and Center Strings for a Probability Distribution on a Set of Strings Under Levenshtein Distance Based on Integer Linear Programming

Cited by 5 publications

References 22 publications

Explaining Propagators for String Edit Distance Constraints

Explaining Propagators for String Edit Distance Constraints

Generalized Median Computation for Consensus Learning: A Brief Survey

Pivot Selection for Median String Problem

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