{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T18:24:58Z","timestamp":1787509498666,"version":"build-2736575974"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>String comparison is a fundamental problem in computer science, with applications in areas such as computational biology, text processing and compression.  In this paper we address the minimum common string partition problem, a string comparison problem with tight connection to the problem of sorting by reversals with duplicates, a key problem in genome rearrangement. A partition of a string $A$ is a sequence ${\\cal P} = (P_1,P_2,\\dots,P_m)$ of strings, called the blocks, whose concatenation is equal to $A$.  Given a partition ${\\cal P}$ of a string $A$ and a partition ${\\cal Q}$ of a string $B$, we say that the pair $\\langle{{\\cal P},{\\cal Q}}\\rangle$ is a common partition of $A$ and $B$ if ${\\cal Q}$ is a permutation of ${\\cal P}$.  The minimum common string partition problem (MCSP) is to find a common partition of two strings $A$ and $B$ with the minimum number of blocks.  The restricted version of MCSP where each letter occurs at most $k$ times in each input string, is denoted by $k$-MCSP. In this paper, we show that $2$-MCSP (and therefore MCSP) is NP-hard and, moreover, even APX-hard. We describe a $1.1037$-approximation for $2$-MCSP and a linear time $4$-approximation algorithm for $3$-MCSP. We are not aware of any better approximations.<\/jats:p>","DOI":"10.37236\/1947","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:09:26Z","timestamp":1578701366000},"source":"Crossref","is-referenced-by-count":20,"title":["Minimum Common String Partition Problem: Hardness and Approximations"],"prefix":"10.37236","volume":"12","author":[{"given":"Avraham","family":"Goldstein","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Petr","family":"Kolman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2005,9,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r50\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r50\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:40:45Z","timestamp":1579304445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1947","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,9,29]]},"article-number":"R50"}}