Improved bounds on the average length of longest common subsequences
GS Lueker - Journal of the ACM (JACM), 2009 - dl.acm.org
It has long been known [Chvátal and Sankoff 1975] that the average length of the longest
common subsequence of two random strings of length n over an alphabet of size k is …
common subsequence of two random strings of length n over an alphabet of size k is …
Improved Lower Bounds on the Expected Length of Longest Common Subsequences
GT Heineman, C Miller, D Reichman, A Salls… - arXiv preprint arXiv …, 2024 - arxiv.org
It has been proven that, when normalized by $ n $, the expected length of a longest common
subsequence of $ d $ random strings of length $ n $ over an alphabet of size $\sigma …
subsequence of $ d $ random strings of length $ n $ over an alphabet of size $\sigma …
On complexity of 1-center in various metrics
We consider the classic 1-center problem: Given a set $ P $ of $ n $ points in a metric space
find the point in $ P $ that minimizes the maximum distance to the other points of $ P $. We …
find the point in $ P $ that minimizes the maximum distance to the other points of $ P $. We …
$ LCSk $++: Practical similarity metric for long strings
In this paper we present $ LCSk $++: a new metric for measuring the similarity of long
strings, and provide an algorithm for its efficient computation. With ever increasing size of …
strings, and provide an algorithm for its efficient computation. With ever increasing size of …
Upper bounds on the average edit distance between two random strings
M Rosenfeld - arXiv preprint arXiv:2407.18113, 2024 - arxiv.org
We study the average edit distance between two random strings. More precisely, we adapt a
technique introduced by Lueker in the context of the average longest common subsequence …
technique introduced by Lueker in the context of the average longest common subsequence …
Simulations, computations, and statistics for longest common subsequences
Q Liu, C Houdré - arXiv preprint arXiv:1705.06826, 2017 - arxiv.org
The length of the longest common subsequences (LCSs) is often used as a similarity
measurement to compare two (or more) random words. Below we study its statistical …
measurement to compare two (or more) random words. Below we study its statistical …
Bounds and Estimates on the Average Edit Distance
The edit distance is a metric of dissimilarity between strings, widely applied in computational
biology, speech recognition, and machine learning. Let $ e_k (n) $ denote the average edit …
biology, speech recognition, and machine learning. Let $ e_k (n) $ denote the average edit …
On the variance of the length of the longest common subsequences in random words with an omitted letter
C Houdré, Q Liu - arXiv preprint arXiv:1812.09552, 2018 - arxiv.org
We investigate the variance of the length of the longest common subsequences of two
independent random words of size $ n $, where the letters of one word are iid uniformly …
independent random words of size $ n $, where the letters of one word are iid uniformly …
Longest common subsequences between words of very unequal length
B Bukh, Z Dong - arXiv preprint arXiv:2009.05869, 2020 - arxiv.org
We consider the expected length of the longest common subsequence between two random
words of lengths $ n $ and $(1-\varepsilon) kn $ over $ k $-symbol alphabet. It is well-known …
words of lengths $ n $ and $(1-\varepsilon) kn $ over $ k $-symbol alphabet. It is well-known …
[PDF][PDF] Several problems in extremal combinatorics
Z Dong - 2023 - kilthub.cmu.edu
In this thesis, we study several problems from combinatorial probability theory, discrete
geometry and extremal graph theory. We establish several extremal results towards our …
geometry and extremal graph theory. We establish several extremal results towards our …