{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T08:27:00Z","timestamp":1770539220113,"version":"3.49.0"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2006,4]]},"abstract":"<jats:p> We consider the problem BLOCK-SORTING: Given a permutation, sort it by using a minimum number of block moves, where a block is a maximal substring of the permutation which is also a substring of the identity permutation, and a block move repositions the chosen block so that it merges with another block. Although this problem has recently been shown to be NP-hard [3], nothing better than a trivial 3-approximation was known. We present here the first non-trivial approximation algorithm to this problem. For this purpose, we introduce the following optimization problem: Given a set of increasing sequences of distinct elements, merge them into one increasing sequence with a minimum number of block moves. We show that the merging problem has a polynomial time algorithm. Using this, we obtain an O(n<jats:sup>3<\/jats:sup>) time 2-approximation algorithm for BLOCK-SORTING. <\/jats:p><jats:p> We also observe that BLOCK-SORTING, as well as sorting by transpositions, are fixed-parameter-tractable in the framework of [6]. <\/jats:p>","DOI":"10.1142\/s0129054106003863","type":"journal-article","created":{"date-parts":[[2006,4,3]],"date-time":"2006-04-03T09:47:03Z","timestamp":1144057623000},"page":"337-355","source":"Crossref","is-referenced-by-count":16,"title":["APPROXIMATE BLOCK SORTING"],"prefix":"10.1142","volume":"17","author":[{"given":"MEENA","family":"MAHAJAN","sequence":"first","affiliation":[{"name":"The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"RAGHAVAN","family":"RAMA","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology, Madras, Chennai 600 036, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VENKATESH","family":"RAMAN","sequence":"additional","affiliation":[{"name":"The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"VIJAYKUMAR","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Anna University, Chennai 600 025, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793250627"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/S089548019528280X"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054103001820"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480197331995"},{"key":"rf6","volume-title":"Parameterized Complexity","author":"Downey R. 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