{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:37:47Z","timestamp":1787337467515,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:p>\n                    Weighted paths in directed grid graphs of dimension (m X n) can be used to model the string edit problem, which consists of obtaining optimal (weighted) alignments between substrings of A, |A|=m, and substrings of B, |B|=n. We build a data structure (in O(mn log m) time) that supports O(log m) time queries about the weight of any of the O(m\n                    <jats:sup>2<\/jats:sup>\n                    n) best paths from the vertices in column 0 of the graph to all other vertices. Using these techniques we present a simple O(n\n                    <jats:sup>2<\/jats:sup>\n                    log n) time and $\\Theta(n^2)$ space algorithm to find all (the locally optimal) approximate tandem (or nontandem) repeats xy within a string of size n. This improves (by a factor of log n) upon several previous algorithms for this problem and is the first algorithm to find all locally optimal repeats. For edit graphs with weights in {0, -1, 1}, a slight modification of our techniques yields an O(n\n                    <jats:sup>2<\/jats:sup>\n                    ) algorithm for the cyclic string comparison problem, as compared to O(n\n                    <jats:sup>2<\/jats:sup>\n                    log n) for the case of general weights.\n                  <\/jats:p>","DOI":"10.1137\/s0097539795288489","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"972-992","source":"Crossref","is-referenced-by-count":88,"title":["All Highest Scoring Paths in Weighted Grid Graphs and Their Application to Finding All Approximate Repeats in Strings"],"prefix":"10.1137","volume":"27","author":[{"given":"Jeanette P.","family":"Schmidt","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0219066"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01840359"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"A. Aggarwal and J. Park,\n                      Notes on searching in multidimensional monotone arrays\n                      , in Proc. 29th IEEE Symp. on Foundations of Computer Science, 1988, pp. 497\u2013512.","DOI":"10.1109\/SFCS.1988.21966"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(83)90109-3"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"Gary Benson, A space efficient algorithm for finding the best non\u2010overlapping alignment score, Lecture Notes in Comput. Sci., Vol. 807, Springer, Berlin, 1994, 1\u20131495d:92008","DOI":"10.1007\/3-540-58094-8_1"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(81)90024-7"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1145\/146637.146656"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1145\/146637.146650"},{"key":"R9","unstructured":"B. W. Erickson and P. H. Sellers,\n                      Recognition of patterns in genetic sequences\n                      , in Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, D. Sankoff and J. B. Kruskal, eds., Addison\u2010Wesley, Reading, MA, 1983, pp. 55\u201391."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(88)90220-7"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"Sampath Kannan, Eugene Myers, An algorithm for locating nonoverlapping regions of maximum alignment score, Lecture Notes in Comput. Sci., Vol. 684, Springer, Berlin, 1993, 74\u20138694k:68077","DOI":"10.1007\/BFb0029798"},{"key":"R12","first-page":"707","volume":"10","author":"Levenshtein V.","year":"1965","journal-title":"Soviet Physics Dokl."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539794264810"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"Gad Landau, Jeanette Schmidt, An algorithm for approximate tandem repeats, Lecture Notes in Comput. Sci., Vol. 684, Springer, Berlin, 1993, 120\u201313394i:68112","DOI":"10.1007\/BFb0029801"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(88)90045-1"},{"key":"R16","unstructured":"W. Miller,\n                      An Algorithm for Locating a Repeated Region\n                      , manuscript."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(90)90109-B"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(84)90021-X"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01586053"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/0022-2836(81)90087-5"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/0022-2836(87)90478-5"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539795288489","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:12:00Z","timestamp":1787335920000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539795288489"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1137\/S0097539795288489"],"URL":"https:\/\/doi.org\/10.1137\/s0097539795288489","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}