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We study the dictionary problem in the compressed setting, where the pattern strings and the text string are compressed using run-length encoding, and the goal is to solve the problem without decompression and achieve efficient time and space in the size of the compressed strings. Let\n m<\/jats:italic>\n and\n n<\/jats:italic>\n be the total length of the patterns\n \n \n $$\\mathcal {P}$$<\/jats:tex-math>\n \n P<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and the length of the text string\n S<\/jats:italic>\n , respectively, and let\n \n \n $$\\overline{m}$$<\/jats:tex-math>\n \n \n m<\/mml:mi>\n \u00af<\/mml:mo>\n <\/mml:mover>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and\n \n \n $$\\overline{n}$$<\/jats:tex-math>\n \n \n n<\/mml:mi>\n \u00af<\/mml:mo>\n <\/mml:mover>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n be the total number of runs in the run-length encoding of the patterns in\n \n \n $$\\mathcal {P}$$<\/jats:tex-math>\n \n P<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and\n S<\/jats:italic>\n , respectively. Our main result is an algorithm that achieves\n \n \n $$O( (\\overline{m} + \\overline{n})\\log \\log m + \\textrm{occ})$$<\/jats:tex-math>\n \n \n O<\/mml:mi>\n (<\/mml:mo>\n \n (<\/mml:mo>\n \n m<\/mml:mi>\n \u00af<\/mml:mo>\n <\/mml:mover>\n +<\/mml:mo>\n \n n<\/mml:mi>\n \u00af<\/mml:mo>\n <\/mml:mover>\n )<\/mml:mo>\n <\/mml:mrow>\n log<\/mml:mo>\n log<\/mml:mo>\n m<\/mml:mi>\n +<\/mml:mo>\n occ<\/mml:mtext>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n expected time, and\n \n \n $$O(\\overline{m})$$<\/jats:tex-math>\n \n \n O<\/mml:mi>\n (<\/mml:mo>\n \n m<\/mml:mi>\n \u00af<\/mml:mo>\n <\/mml:mover>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n space, where\n \n \n $$\\textrm{occ}$$<\/jats:tex-math>\n \n occ<\/mml:mtext>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is the total number of occurrences of patterns in\n S<\/jats:italic>\n . This is the first non-trivial solution to the problem. Since any solution must read the input, our time bound is optimal within a\n \n \n $$\\log \\log m$$<\/jats:tex-math>\n \n \n log<\/mml:mo>\n log<\/mml:mo>\n m<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n factor. We introduce several new techniques to achieve our bounds, including a new compressed representation of the classic Aho-Corasick automaton and a new efficient string index that supports fast queries in run-length encoded strings.\n <\/jats:p>","DOI":"10.1007\/s00453-026-01398-0","type":"journal-article","created":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T04:01:37Z","timestamp":1779940897000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Compressed Dictionary Matching on Run-Length Encoded Strings"],"prefix":"10.1007","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1120-5154","authenticated-orcid":false,"given":"Philip","family":"Bille","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8322-4952","authenticated-orcid":false,"given":"Inge Li","family":"G\u00f8rtz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7668-7636","authenticated-orcid":false,"given":"Simon J.","family":"Puglisi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-4293-6475","authenticated-orcid":false,"given":"Simon Rumle","family":"Tarnow","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,28]]},"reference":[{"issue":"6","key":"1398_CR1","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1145\/360825.360855","volume":"18","author":"AV Aho","year":"1975","unstructured":"Aho, A.V., Corasick, M.J.: Efficient string matching: An aid to bibliographic search. 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