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data-ga-category="save_share"
data-ga-action="email"
data-ga-label="send">
Send email
</button>
<button class="action-panel-cancel"
aria-label="Close 'Email citations' panel"
ref="linksrc=close_email_panel"
aria-controls="email-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="email"
data-ga-label="cancel">
Cancel
</button>
</div>
<input type="hidden" name="email-search-details" value="" />
<input type="hidden" name="email-search-details-hash" value="0e42663a6c3bd85498fcb88798998fed7bfdc45d457db35281e41afe13cc0524" />
</form>
</div>
</div>
<div id="collections-action-panel"
class="collections-action-panel action-panel in-progress-dots-panel"
aria-hidden="true"
data-collections-open-panel-enabled="false"
data-collections-open-panel-url-hash="#open-collections-panel">
<div class="inner-wrap">
<h3 class="action-panel-heading">
Add to Collections
</h3>
<form id="collections-action-panel-form"
class="collections-action-panel-form action-panel-content action-form action-panel-smaller-selectors"
data-existing-collections-url="/list-existing-collections/"
data-add-to-existing-collection-url="/add-to-existing-collection/"
data-create-and-add-to-new-collection-url="/create-and-add-to-new-collection/"
data-get-article-ids-by-search-url="/get-article-ids-by-search/"
data-myncbi-max-collection-name-length="100"
data-add-to-collection-max-amount="1000"
data-collections-root-url="https://www.ncbi.nlm.nih.gov/myncbi/collections/">
<input type="hidden" name="csrfmiddlewaretoken" value="XDZcdaX9O7YxdrfHoBBjYxtPUHyKnMVYeqJhQ0qvoIL17Slx1UelsFZtsLgWgnti">
<div class="choice-group" role="radiogroup">
<ul class="radio-group-items">
<li>
<input type="radio"
id="collections-action-panel-new"
class="collections-new"
name="collections"
value="new"
data-ga-category="save_share"
data-ga-action="collections"
data-ga-label="collections_radio_new">
<label for="collections-action-panel-new">Create a new collection</label>
</li>
<li>
<input type="radio"
id="collections-action-panel-existing"
class="collections-existing"
name="collections"
value="existing"
checked="true"
data-ga-category="save_share"
data-ga-action="collections"
data-ga-label="collections_radio_existing">
<label for="collections-action-panel-existing">Add to an existing collection</label>
</li>
</ul>
</div>
<div class="controls-wrapper">
<div class="action-panel-control-wrap new-collections-controls">
<label for="collections-action-panel-add-to-new" class="action-panel-label required-field-asterisk">
Name your collection:
</label>
<input
type="text"
name="add-to-new-collection"
id="collections-action-panel-add-to-new"
class="collections-action-add-to-new"
pattern="[^&quot;&amp;=&lt;&gt;\/]*" title="The following characters are not allowed in the Name field: &quot;&amp;=&lt;&gt;/"
maxlength="100"
data-ga-category="save_share"
data-ga-action="create_collection"
data-ga-label="non_favorties_collection">
<div class="collections-new-name-too-long usa-input-error-message selection-validation-message">
Name must be less than 100 characters
</div>
</div>
<div class="action-panel-control-wrap existing-collections-controls">
<label for="collections-action-panel-add-to-existing" class="action-panel-label">
Choose a collection:
</label>
<select id="collections-action-panel-add-to-existing"
class="action-panel-selector collections-action-add-to-existing"
data-ga-category="save_share"
data-ga-action="select_collection"
data-ga-label="($('#collections-action-add-to-existing').val() === 'Favorites') ? 'Favorites' : 'non_favorites_collection'">
</select>
<div class="collections-retry-load-on-error usa-input-error-message selection-validation-message">
Unable to load your collection due to an error<br>
<a href="#">Please try again</a>
</div>
</div>
</div>
<div class="action-panel-actions">
<button class="action-panel-submit"
type="submit"
data-loading-label="Adding..."
data-pinger-ignore
data-ga-category="save_share"
data-ga-action="collections"
data-ga-label="add">
Add
</button>
<button class="action-panel-cancel"
aria-label="Close 'Add to Collections' panel"
ref="linksrc=close_collections_panel"
aria-controls="collections-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="collections"
data-ga-label="cancel">
Cancel
</button>
</div>
</form>
</div>
</div>
<div id="bibliography-action-panel"
class="bibliography-action-panel action-panel in-progress-dots-panel"
aria-hidden="true"
data-bibliography-open-panel-enabled="false"
data-bibliography-open-panel-url-hash="#open-bibliography-panel">
<div class="inner-wrap">
<h3 class="action-panel-heading">
Add to My Bibliography
</h3>
<form id="bibliography-action-panel-form"
class="bibliography-action-panel-form action-panel-content action-form action-panel-smaller-selectors"
data-add-to-bibliography-max-amount="100"
data-add-to-bibliography-batch-size="10"
data-bibliography-delegates-url="/list-bibliography-delegates/"
data-add-to-bibliography-url="/add-to-bibliography/"
data-get-article-ids-by-search-url="/get-article-ids-by-search/"
data-mybib-root-url="https://www.ncbi.nlm.nih.gov/myncbi/collections/mybibliography/">
<input type="hidden" name="csrfmiddlewaretoken" value="XDZcdaX9O7YxdrfHoBBjYxtPUHyKnMVYeqJhQ0qvoIL17Slx1UelsFZtsLgWgnti">
<div class="action-panel-control-wrap bibliographies-controls">
<div class="choice-group">
<ul class="bibliographies-action-add radio-group-items">
<li>
<input name="bibliography" id="my-bibliography" class="my-bibliography" type="radio" checked/>
<label for="my-bibliography">My Bibliography</label>
</li>
</ul>
</div>
</div>
<div class="bibliographies-retry-load-on-error usa-input-error-message selection-validation-message">
Unable to load your delegates due to an error<br>
<a href="#">Please try again</a>
</div>
<div class="action-panel-actions">
<button class="action-panel-submit"
type="submit"
data-loading-label="Adding..."
data-pinger-ignore>
Add
</button>
<button class="action-panel-cancel"
aria-label="Close 'Add to bibliography' panel"
ref="linksrc=close_bibliography_panel"
aria-controls="bibliography-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="mybib"
data-ga-label="cancel">
Cancel
</button>
</div>
</form>
</div>
</div>
<div id="saved-search-action-panel" class="saved-search-action-panel action-panel " aria-hidden="true"
data-saved-search-open-panel-enabled="false"
data-saved-search-open-panel-url-hash="#open-saved-search-panel">
<div class="inner-wrap">
<h2 class="action-panel-heading">
Your saved search
</h2>
<form id="saved-search-action-panel-form"
class="saved-search-action-panel-form action-panel-content action-form"
data-create-saved-search-url="/create-saved-search/"
data-try-search-terms-url="/try-search-term/"
data-saved-search-root-url="https://www.ncbi.nlm.nih.gov/myncbi/searches/">
<input type="hidden" name="csrfmiddlewaretoken" value="XDZcdaX9O7YxdrfHoBBjYxtPUHyKnMVYeqJhQ0qvoIL17Slx1UelsFZtsLgWgnti">
<div class="action-panel-control-wrap">
<label for="saved-search-name" class="action-panel-label saved-search-name-label required-field-asterisk">
Name of saved search:
</label>
<input maxlength="200"
type="text"
name="saved-search-name"
id="saved-search-name"
class="saved-search-name"
value=""
required
pattern="[^&quot;&amp;=&lt;&gt;\/]*" title="The following characters are not allowed in the Name field: &quot;&amp;=&lt;&gt;/">
</div>
<div class="action-panel-control-wrap">
<label for="saved-search-term" class="action-panel-label required-field-asterisk">
Search terms:
</label>
<textarea name="saved-search-term" id="saved-search-term" class="saved-search-term" required></textarea>
</div>
<div class="test-search-term-wrap">
<a href="#" class="try-search-term">Test search terms</a>
</div>
<div class="choice-group action-panel-extra-margin-top">
<span class="action-panel-label" id="fieldset-label">
Would you like email updates of new search results?
</span>
<fieldset id="saved-search-alert" aria-describedby="fieldset-label">
<legend class="usa-sr-only">Saved Search Alert Radio Buttons</legend>
<ul class="radio-group-items">
<li>
<input type="radio" id="saved-search-alert-yes" class="saved-search-alert-yes" name="saved-search-alert" value="yes" checked>
<label for="saved-search-alert-yes" class="action-panel-label">Yes</label>
</li>
<li>
<input aria-label="No radio input" type="radio" id="saved-search-alert-no" class="saved-search-alert-no" name="saved-search-alert" value="no">
<label for="saved-search-alert-no" class="action-panel-label">No</label>
</li>
</ul>
</fieldset>
</div>
<div class="alert-schedule-wrap">
<div class="action-panel-control-wrap">
<label class="action-panel-label">
Email:
</label>
<span aria-label="Email address" id="saved-search-email" class="action-panel-label"><span class="action-panel-label-bold"></span> (<a class="myncbi-account-settings" href="https://www.ncbi.nlm.nih.gov/account/settings/">change</a>)</span>
</div>
<div class="action-panel-control-wrap action-panel-extra-margin-top">
<label for="saved-search-frequency" class="action-panel-label">
Frequency:
</label>
<select id="saved-search-frequency" class="no-border-panel-selector saved-search-frequency">
<option value="monthly">Monthly</option>
<option value="weekly">Weekly</option>
<option value="daily">Daily</option>
</select>
</div>
<div class="action-panel-control-wrap saved-search-monthly-additional">
<label for="saved-search-monthly-on-day" class="action-panel-label">
Which day?
</label>
<select id="saved-search-monthly-on-day" class="no-border-panel-selector">
<option value="Sunday">The first Sunday</option>
<option value="Monday">The first Monday</option>
<option value="Tuesday">The first Tuesday</option>
<option value="Wednesday">The first Wednesday</option>
<option value="Thursday">The first Thursday</option>
<option value="Friday">The first Friday</option>
<option value="Saturday">The first Saturday</option>
<option value="day">The first day</option>
<option value="weekday">The first weekday</option>
</select>
</div>
<div class="action-panel-control-wrap saved-search-weekly-additional">
<label for="saved-search-weekly-on-day" class="action-panel-label">
Which day?
</label>
<select id="saved-search-weekly-on-day" class="no-border-panel-selector saved-search-weekly-on-day">
<option value="Sunday">Sunday</option>
<option value="Monday">Monday</option>
<option value="Tuesday">Tuesday</option>
<option value="Wednesday">Wednesday</option>
<option value="Thursday">Thursday</option>
<option value="Friday">Friday</option>
<option value="Saturday">Saturday</option>
</select>
</div>
<div class="action-panel-control-wrap">
<label for="saved-search-report" class="action-panel-label">
Report format:
</label>
<select id="saved-search-report" class="no-border-panel-selector saved-search-report">
<option value="DocSum">Summary</option>
<option value="DocSumText">Summary (text)</option>
<option value="Abstract">Abstract</option>
<option value="AbstractText">Abstract (text)</option>
<option value="MEDLINE">PubMed</option>
</select>
</div>
<div class="action-panel-control-wrap">
<label for="saved-search-amount" class="action-panel-label">
Send at most:
</label>
<select id="saved-search-amount" class="no-border-panel-selector saved-search-amount">
<option value="1">1 item</option>
<option value="5" selected>5 items</option>
<option value="10">10 items</option>
<option value="20">20 items</option>
<option value="50">50 items</option>
<option value="100">100 items</option>
<option value="200">200 items</option>
</select>
</div>
<div>
<input type="checkbox" id="saved-search-send-if-no-result" class="saved-search-send-if-no-result" name="saved-search-send-if-no-result">
<label for="saved-search-send-if-no-result" class="action-panel-label smaller-checkbox">
Send even when there aren't any new results
</label>
</div>
<div class="action-panel-control-wrap option-text-in-email-wrap">
<label for="saved-search-email-text" class="action-panel-label">
Optional text in email:
</label>
<textarea name="saved-search-email-text"
id="saved-search-email-text"
class="saved-search-email-text"></textarea>
</div>
</div>
<div class="action-panel-actions">
<button class="action-panel-submit"
type="submit"
data-loading-label="Saving..."
data-ga-category="save_share"
data-ga-action="alert"
data-ga-label="save">
Save
</button>
<button class="action-panel-cancel"
aria-label="Close 'Your saved search' panel"
ref="linksrc=close_saved_search_panel"
aria-controls="saved-search-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="alert"
data-ga-label="cancel">
Cancel
</button>
</div>
</form>
</div>
</div>
<div id="citation-manager-action-panel" class="citation-manager-action-panel action-panel" aria-hidden="true">
<div class="inner-wrap">
<h2 class="action-panel-heading">
Create a file for external citation management software
</h2>
<form id="citation-manager-action-panel-form"
class="action-panel-content action-form"
action="/results-export-ids/"
data-by-search-action="/results-export-search-data/"
data-by-ids-action="/results-export-ids/"
method="post"
data-by-search-method="post"
data-by-ids-method="post">
<input type="hidden" name="csrfmiddlewaretoken" value="XDZcdaX9O7YxdrfHoBBjYxtPUHyKnMVYeqJhQ0qvoIL17Slx1UelsFZtsLgWgnti">
<input name="results-format" type="hidden" value="pubmed"/>
<div class="action-panel-actions">
<button class="action-panel-submit"
type="submit"
data-loading-label="Sending..."
data-ga-category="save_share"
data-ga-action="citation_manager"
data-ga-label="save">
Create file
</button>
<button class="action-panel-cancel"
aria-label="Close 'Send citations to citation manager' panel"
ref="linksrc=close_citation_manager_panel"
aria-controls="citation-manager-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="citation_manager"
data-ga-label="cancel">
Cancel
</button>
</div>
</form>
</div>
</div>
<div id="rss-action-panel" class="rss-action-panel action-panel " aria-hidden="true">
<div class="inner-wrap">
<h2 class="action-panel-heading">
Your RSS Feed
</h2>
<form id="rss-action-panel-form"
class="rss-action-panel-form action-panel-content action-form"
data-create-rss-feed-url="/create-rss-feed-url/"
data-search-form-term-value="">
<input type="hidden" name="csrfmiddlewaretoken" value="XDZcdaX9O7YxdrfHoBBjYxtPUHyKnMVYeqJhQ0qvoIL17Slx1UelsFZtsLgWgnti">
<div class="action-panel-control-wrap">
<label for="rss-name" class="action-panel-label required-field-asterisk">
Name of RSS Feed:
</label>
<input maxlength="200"
placeholder="Name"
type="text"
name="rss-name"
id="rss-name"
class="rss-name"
value=''
required
pattern="[^&quot;&amp;=&lt;&gt;\/]*" title="The following characters are not allowed in the Name field: &quot;&amp;=&lt;&gt;/">
</div>
<div class="rss-limit-wrap">
<div class="action-panel-control-wrap action-panel-extra-margin-top">
<label for="rss-limit" class="action-panel-label">
Number of items displayed:
</label>
<select id="rss-limit" class="no-border-panel-selector rss-limit">
<option value="5">5</option>
<option value="10">10</option>
<option value="15" selected="selected">15</option>
<option value="20">20</option>
<option value="50">50</option>
<option value="100">100</option>
</select>
</div>
</div>
<div class="action-panel-actions">
<button class="action-panel-submit"
type="submit"
data-loading-label="Creating..."
data-ga-category="save_share"
data-ga-action="alert"
data-ga-label="save">
Create RSS
</button>
<button class="action-panel-cancel"
aria-label="Close 'Your RSS' panel"
ref="linksrc=close_rss_panel"
aria-controls="rss-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="alert"
data-ga-label="cancel">
Cancel
</button>
</div>
<div class="action-panel-control-wrap rss-link-copy-wrap">
<label for="rss-link" class="usa-sr-only">RSS Link</label>
<input placeholder="Your RSS Feed Link" type="text" name="rss-link" id="rss-link" class="rss-link" title="RSS Link">
<button
type="button"
disabled
class="rss-link-copy-button disabled"
data-ga-category="save_share"
data-ga-action="rss"
data-ga-label="copy">
Copy
</button>
</div>
</form>
</div>
</div>
</div>
</div>
<div class="article-page" id="article-page" data-article-pmid="29206392">
<aside class="page-sidebar">
<div class="inner-wrap">
<div class="full-text-links">
<div class="full-view">
<h3 class="title">
Full text links
</h3>
<div class="full-text-links-list">
<a class="link-item
book
dialog-focus"
href="https://www.ncbi.nlm.nih.gov/books/NBK464187"
target="_blank"
rel="noopener"
ref="linksrc=fulltextorjournal_fulltext&amp;is_pmc=False&amp;PrId=3057&amp;itool=Abstract-def&amp;log$=linkouticon&amp;uid=29206392&amp;db=pubmed"
title="See full text options at NCBI Bookshelf"
data-ga-category="full_text"
data-ga-action="NCBI Bookshelf"
data-ga-label="29206392"
><img class="book-icon" src="https://cdn.ncbi.nlm.nih.gov/corehtml/pmc/pmcgifs/bookshelf/thumbs/th-hbkdiscombmath.png" alt="book cover photo"><div class="book-icon-label"><div class="book-icon-label-subtitle">20.1</div><div class="book-icon-label-title">Handbook of Discrete and Combinatorial Mathematics</div></div><span class="text">
NCBI Bookshelf
</span></a>
</div>
</div>
<div class="short-view">
<a href="#" class="full-text-links-button full-text-links-dialog-trigger">
Full text links
</a>
</div>
</div>
<div class="actions-buttons sidebar"><h3 class="title">Actions</h3><div class="inner-wrap"><button class="citation-button citation-dialog-trigger"
aria-label="Open dialog with citation text in different styles"
data-ga-category="save_share"
data-ga-action="cite"
data-ga-label="open"
data-all-citations-url="/29206392/citations/"
data-citation-style="nlm"
data-pubmed-format-link="/29206392/export/"><span class="button-label">Cite</span></button><link type="text/css" href="ncbi-overlay-block/src/overlay-block.css"><div class="collections-button-container" data-article-id="29206392" data-article-db="pubmed"><button class="collections-button collections-dialog-trigger"
aria-label="Save article in MyNCBI collections."
data-ga-category="collections_button"
data-ga-action="click"
data-ga-label="collections_button"
data-collections-open-dialog-enabled="false"
data-collections-open-dialog-url="https://account.ncbi.nlm.nih.gov/?back_url=https%3A%2F%2Fpubmed.ncbi.nlm.nih.gov%2F29206392%2F%23open-collections-dialog"
data-in-collections="false"><span class="button-label">Collections</span></button><div class="overlay" role="dialog"><div id="collections-action-dialog"
class="dialog collections-dialog"
aria-hidden="true"><div class="title">Add to Collections</div><div class="collections-action-panel action-panel"><form id="collections-action-dialog-form"
class="collections-action-panel-form action-panel-content action-form action-panel-smaller-selectors"
data-existing-collections-url="/list-existing-collections/"
data-add-to-existing-collection-url="/add-to-existing-collection/"
data-create-and-add-to-new-collection-url="/create-and-add-to-new-collection/"
data-myncbi-max-collection-name-length="100"
data-collections-root-url="https://www.ncbi.nlm.nih.gov/myncbi/collections/"><input type="hidden" name="csrfmiddlewaretoken" value="XDZcdaX9O7YxdrfHoBBjYxtPUHyKnMVYeqJhQ0qvoIL17Slx1UelsFZtsLgWgnti"><div class="choice-group" role="radiogroup"><ul class="radio-group-items"><li><input type="radio"
id="collections-action-dialog-new"
class="collections-new"
name="collections"
value="new"
data-ga-category="collections_button"
data-ga-action="click"
data-ga-label="collections_radio_new"><label for="collections-action-dialog-new">Create a new collection</label></li><li><input type="radio"
id="collections-action-dialog-existing"
class="collections-existing"
name="collections"
value="existing"
checked="true"
data-ga-category="collections_button"
data-ga-action="click"
data-ga-label="collections_radio_existing"><label for="collections-action-dialog-existing">Add to an existing collection</label></li></ul></div><div class="controls-wrapper"><div class="action-panel-control-wrap new-collections-controls"><label for="collections-action-dialog-add-to-new" class="action-panel-label required-field-asterisk">
Name your collection:
</label><input
type="text"
name="add-to-new-collection"
id="collections-action-dialog-add-to-new"
class="collections-action-add-to-new"
pattern="[^&quot;&amp;=&lt;&gt;\/]*" title="The following characters are not allowed in the Name field: &quot;&amp;=&lt;&gt;/"
maxlength="100"
data-ga-category="collections_button"
data-ga-action="create_collection"
data-ga-label="non_favorties_collection"><div class="collections-new-name-too-long usa-input-error-message selection-validation-message">
Name must be less than 100 characters
</div></div><div class="action-panel-control-wrap existing-collections-controls"><label for="collections-action-dialog-add-to-existing" class="action-panel-label">
Choose a collection:
</label><select id="collections-action-dialog-add-to-existing"
class="action-panel-selector collections-action-add-to-existing"
data-ga-category="collections_button"
data-ga-action="select_collection"
data-ga-label="($('.collections-action-add-to-existing').val() === 'Favorites') ? 'Favorites' : 'non_favorites_collection'"></select><div class="collections-retry-load-on-error usa-input-error-message selection-validation-message">
Unable to load your collection due to an error<br><a href="#">Please try again</a></div></div></div><div class="action-panel-actions"><button class="action-panel-submit"
type="submit"
data-loading-label="Adding..."
data-pinger-ignore
data-ga-category="collections_button"
data-ga-action="click"
data-ga-label="add">
Add
</button><button class="action-panel-cancel"
aria-label="Close 'Add to Collections' panel"
ref="linksrc=close_collections_panel"
aria-controls="collections-action-panel"
aria-expanded="false"
data-ga-category="collections_button"
data-ga-action="click"
data-ga-label="cancel">
Cancel
</button></div></form></div></div></div></div><button class="more-actions-button more-actions-dialog-trigger"
title="Open dialog with more actions to take"
ref="linksrc=more_actions_btn"></button><div class="display-options" data-format-key="format"
data-default-format-value="abstract"
data-current-format-value="abstract" role="region"><button
class="trigger usa-button"
title="Change format"
data-ga-category="display_options"
data-ga-action="display_options_dialog"><span class="button-label">Display options</span></button><div class="dropdown" hidden><div class="title">
Display options
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Alignments are a powerful way to compare related DNA or protein sequences. They can be used to capture various facts about the sequences aligned, such as common evolutionary descent or common structural function. We take the general view that the alignment of letters from two or multiple sequences represents the hypothesis that they are descended from a common ancestral sequence.
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DNA molecules are composed of chains of nucleotides, and protein molecules are composed of chains of amino acids. The specific order of nucleotides or amino acids within these chains are respectively called DNA and protein sequences. Perhaps chief among the various biological functions of DNA sequences is to encode protein sequences, because proteins are involved in most of the biological functions of living cells.
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DNA sequences, and the protein sequences they encode, evolve by mutation followed by natural selection. There are a variety of mechanisms for DNA mutation, but the most common result is the substitution of a single nucleotide for another, or the deletion or insertion of one or several adjacent nucleotides. At the protein level, the most common resulting mutations are the substitution of one amino acid for another, or the insertion or deletion of one or multiple adjacent amino acids. There is no simple biological mechanism for exchanging the order of two letters in a DNA or protein sequence, so an alignment representing the common descent of two DNA or protein sequences is co-linear, with no “crossovers” between corresponding letters.
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20.1.1. GLOBAL AND LOCAL PAIRWISE ALIGNMENTS
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20.1.2. PAIRWISE ALIGNMENT SCORES
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20.1.3. PATH GRAPHS AND OPTIMAL GLOBAL PAIRWISE ALIGNMENT
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20.1.4. OPTIMAL LOCAL PAIRWISE ALIGNMENT
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20.1.7. SEQUENCE ALIGNMENT HEURISTICS
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