https://curiouscoding.nl/authors/pesho-ivanov/Recent content in Pesho Ivanov on CuriousCodingHugoenFri, 01 Apr 2022 00:00:00 +0200https://curiouscoding.nl/posts/pairwise-alignment-history/Fri, 01 Apr 2022 00:00:00 +0200https://curiouscoding.nl/posts/pairwise-alignment-history/<div class="ox-hugo-toc toc"> <div class="heading">Table of Contents</div> <ul> <li><a href="#variants-of-pairwise-alignment" >Variants of pairwise alignment</a> <ul> <li><a href="#cost-models" >Cost models</a></li> <li><a href="#alignment-types" >Alignment types</a></li> </ul> </li> <li><a href="#a-chronological-overview-of-global-pairwise-alignment" >A chronological overview of global pairwise alignment</a></li> <li><a href="#algorithms-in-detail" >Algorithms in detail</a> <ul> <li><a href="#classic-dp-algorithms" >Classic DP algorithms</a> <ul> <li><a href="#cubic-dp" >Cubic algorithm of Needleman and Wunsch (<a href="#citeproc_bib_item_25">1970</a>)</a></li> <li><a href="#quadratic-dp" >A quadratic DP</a></li> <li><a href="#local-alignment" >Local alignment</a></li> <li><a href="#affine-costs" >Affine costs</a></li> </ul> </li> <li><a href="#minimizing-vs-dot-maximizing-duality" >Minimizing vs. maximizing duality</a></li> <li><a href="#four-russians" >Four Russians method</a></li> <li><a href="#o--ns--methods" ><span class="org-todo todo TODO">TODO</span> \(O(ns)\) methods</a> <ul> <li><a href="#exponential-band" ><span class="org-todo todo TODO">TODO</span> Exponential search on band</a></li> <li><a href="#thresholds" ><span class="org-todo todo TODO">TODO</span> LCS: thresholds, $k$-candidates and contours</a></li> <li><a href="#diagonal-transition" ><span class="org-todo todo TODO">TODO</span> Diagonal transition: furthest reaching and wavefronts</a></li> </ul> </li> <li><a href="#ns2" ><span class="org-todo todo TODO">TODO</span> Suffixtree for \(O(n+s^2)\) expected runtime</a></li> <li><a href="#using-less-memory" >Using less memory</a> <ul> <li><a href="#computing-the-score-in-linear-space" >Computing the score in linear space</a></li> <li><a href="#divide-and-conquer" >Divide-and-conquer</a></li> </ul> </li> <li><a href="#lcsk-plus-plus-algorithms" ><span class="org-todo todo TODO">TODO</span> LCSk[++] algorithms</a></li> <li><a href="#theoretical-lower-bound" >Theoretical lower bound</a></li> <li><a href="#a-note-on-dp--toposort--vs-dijkstra-vs-a" ><span class="org-todo todo TODO">TODO</span> A note on DP (toposort) vs Dijkstra vs A*</a></li> </ul> </li> <li><a href="#tools" ><span class="org-todo todo TODO">TODO</span> Tools</a></li> <li><a href="#notes-for-other-posts" ><span class="org-todo todo TODO">TODO</span> Notes for other posts</a> <ul> <li><a href="#semi-global-alignment-papers" >Semi-global alignment papers</a></li> <li><a href="#approximate-pairwise-aligners" >Approximate pairwise aligners</a></li> <li><a href="#old-vs-new-papers" >Old vs new papers</a></li> </ul> </li> </ul> </div> <!--endtoc--> <p>This post explains the many variants of pairwise alignment, and covers papers defining and exploring the topic.</p>