Algorithms for Sequence Similarity Measures

Given two sets of points $A$ and $B$ ($|A| = m$, $|B| = n$), we seek to find a minimum-weight many-to-many matching which seeks to match each point in $A$ to at least one point in $B$ and vice versa. Each matched pair (an edge) has a weight. The goal is to find the matching that minimizes the tota...

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Main Author: MOHAMAD, Mustafa Amid
Other Authors: Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))
Language:en
en
Published: 2010
Subjects:
Online Access:http://hdl.handle.net/1974/6202
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spelling ndltd-LACETR-oai-collectionscanada.gc.ca-OKQ.1974-62022013-12-20T03:40:01ZAlgorithms for Sequence Similarity MeasuresMOHAMAD, Mustafa Amidmany-to-many matchingalgorithmmatchingminimum costcirclelinetranslationrotationsequence alignmentGiven two sets of points $A$ and $B$ ($|A| = m$, $|B| = n$), we seek to find a minimum-weight many-to-many matching which seeks to match each point in $A$ to at least one point in $B$ and vice versa. Each matched pair (an edge) has a weight. The goal is to find the matching that minimizes the total weight. We study two kinds of problems depending on the edge weight used. The first edge weight is the Euclidean distance, $d_1$. The second is edge weight is the square of the Euclidean distance, $d_2$. There already exists an $O(k\log k)$ algorithm for $d_1$, where $k=m+n$. We provide an $O(mn)$ algorithm for the $d_2$ problem. We also solve the problem of finding the minimum-weight matching when the sets $A$ and $B$ are allowed to be translated on the real line. We present an $O(mnk \log k)$ algorithm for the $d_1$ problem and an $O(3^{mn})$ algorithm for the $d_2$. Furthermore, we also deal with the special case where $A$ and $B$ lie on a circle of a specific circumference. We present an $O(k^2 \log k)$ algorithm and $O(kmn)$ algorithm for solving the minimum-weight matching for the $d_1$, and $d_2$ weights respectively. Much like the problem on the real line, we extend this problem to allow the sets $A$ and $B$ to be rotated on the circle. We try to find the minimum-weight many-to-many matching when rotations are allowed. For $d_1$ we present an $O(k^2mn \log k)$ algorithm and a $O(3^{mn})$ algorithm for $d_2$.Thesis (Master, Computing) -- Queen's University, 2010-11-08 20:48:18.968Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))2010-11-08 20:48:18.9682010-11-17T17:16:20Z2010-11-17T17:16:20Z2010-11-17T17:16:20ZThesishttp://hdl.handle.net/1974/6202enenCanadian thesesThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
collection NDLTD
language en
en
sources NDLTD
topic many-to-many matching
algorithm
matching
minimum cost
circle
line
translation
rotation
sequence alignment
spellingShingle many-to-many matching
algorithm
matching
minimum cost
circle
line
translation
rotation
sequence alignment
MOHAMAD, Mustafa Amid
Algorithms for Sequence Similarity Measures
description Given two sets of points $A$ and $B$ ($|A| = m$, $|B| = n$), we seek to find a minimum-weight many-to-many matching which seeks to match each point in $A$ to at least one point in $B$ and vice versa. Each matched pair (an edge) has a weight. The goal is to find the matching that minimizes the total weight. We study two kinds of problems depending on the edge weight used. The first edge weight is the Euclidean distance, $d_1$. The second is edge weight is the square of the Euclidean distance, $d_2$. There already exists an $O(k\log k)$ algorithm for $d_1$, where $k=m+n$. We provide an $O(mn)$ algorithm for the $d_2$ problem. We also solve the problem of finding the minimum-weight matching when the sets $A$ and $B$ are allowed to be translated on the real line. We present an $O(mnk \log k)$ algorithm for the $d_1$ problem and an $O(3^{mn})$ algorithm for the $d_2$. Furthermore, we also deal with the special case where $A$ and $B$ lie on a circle of a specific circumference. We present an $O(k^2 \log k)$ algorithm and $O(kmn)$ algorithm for solving the minimum-weight matching for the $d_1$, and $d_2$ weights respectively. Much like the problem on the real line, we extend this problem to allow the sets $A$ and $B$ to be rotated on the circle. We try to find the minimum-weight many-to-many matching when rotations are allowed. For $d_1$ we present an $O(k^2mn \log k)$ algorithm and a $O(3^{mn})$ algorithm for $d_2$. === Thesis (Master, Computing) -- Queen's University, 2010-11-08 20:48:18.968
author2 Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))
author_facet Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))
MOHAMAD, Mustafa Amid
author MOHAMAD, Mustafa Amid
author_sort MOHAMAD, Mustafa Amid
title Algorithms for Sequence Similarity Measures
title_short Algorithms for Sequence Similarity Measures
title_full Algorithms for Sequence Similarity Measures
title_fullStr Algorithms for Sequence Similarity Measures
title_full_unstemmed Algorithms for Sequence Similarity Measures
title_sort algorithms for sequence similarity measures
publishDate 2010
url http://hdl.handle.net/1974/6202
work_keys_str_mv AT mohamadmustafaamid algorithmsforsequencesimilaritymeasures
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