{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T03:48:14Z","timestamp":1790826494518,"version":"4.1.0"},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Bioinform. Comput. Biol."],"published-print":{"date-parts":[[2003,4]]},"abstract":"<jats:p> A central problem in genome rearrangement is finding a most parsimonious rearrangement scenario using certain rearrangement operations. An important problem of this type is sorting a signed genome by reversals and translocations (SBRT). Hannenhalli and Pevzner presented a duality theorem for SBRT which leads to a polynomial time algorithm for sorting a multi-chromosomal genome using a minimum number of reversals and translocations. However, there is one case for which their theorem and algorithm fail. We describe that case and suggest a correction to the theorem and the polynomial algorithm. <\/jats:p><jats:p> The solution of SBRT uses a reduction to the problem of sorting a signed permutation by reversals (SBR). The best extant algorithms for SBR require quadratic time. The common approach to solve SBR is by finding a safe reversal using the overlap graph or the interleaving graph of a permutation. We describe a family of signed permutations which proves a quadratic lower bound on the number of affected vertices in the overlap\/interleaving graph during any optimal sorting scenario. This implies, in particular, an \u03a9(n<jats:sup>3<\/jats:sup>) lower bound for Bergeron's algorithm. <\/jats:p>","DOI":"10.1142\/s0219720003000198","type":"journal-article","created":{"date-parts":[[2003,4,28]],"date-time":"2003-04-28T10:49:23Z","timestamp":1051526963000},"page":"71-94","source":"Crossref","is-referenced-by-count":54,"title":["TWO NOTES ON GENOME REARRANGEMENT"],"prefix":"10.1142","volume":"01","author":[{"given":"MICHAL","family":"OZERY-FLATO","sequence":"first","affiliation":[{"name":"School of Computer Science, Tel Aviv University, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"RON","family":"SHAMIR","sequence":"additional","affiliation":[{"name":"School of Computer Science, Tel Aviv University, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01459088"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793250627"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(96)00061-3"},{"key":"rf12","author":"Tesler G.","journal-title":"J. Comp. Syst. Sci."}],"container-title":["Journal of Bioinformatics and Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219720003000198","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:07:56Z","timestamp":1565132876000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219720003000198"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,4]]},"references-count":4,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[2003,4]]}},"alternative-id":["10.1142\/S0219720003000198"],"URL":"https:\/\/doi.org\/10.1142\/s0219720003000198","relation":{},"ISSN":["0219-7200","1757-6334"],"issn-type":[{"value":"0219-7200","type":"print"},{"value":"1757-6334","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,4]]}}}