{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T23:24:12Z","timestamp":1778887452948,"version":"3.51.4"},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2018,9,17]],"date-time":"2018-09-17T00:00:00Z","timestamp":1537142400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"H2020-MSCA-RISE","award":["734922- \u201cCONNECT\u201d"],"award-info":[{"award-number":["734922- \u201cCONNECT\u201d"]}]},{"name":"European Science Foundation as part of the EuroGIGA collaborative research program"},{"name":"MIUR-DAAD Joint Mobility Program","award":["34120 and 57397196"],"award-info":[{"award-number":["34120 and 57397196"]}]},{"name":"MIUR Project \u201cMODE\u201d","award":["PRIN 20157EFM5C"],"award-info":[{"award-number":["PRIN 20157EFM5C"]}]},{"name":"DFG","award":["Ka812\/17-1"],"award-info":[{"award-number":["Ka812\/17-1"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2018,10,31]]},"abstract":"<jats:p>\n            Given a planar graph\n            <jats:italic>G<\/jats:italic>\n            and a partition of the neighbors of each vertex\n            <jats:italic>v<\/jats:italic>\n            in four sets\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2197<\/jats:sup>\n            ,\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2196<\/jats:sup>\n            ,\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2199<\/jats:sup>\n            , and\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2198<\/jats:sup>\n            , the problem W\n            <jats:sc>indrose<\/jats:sc>\n            P\n            <jats:sc>lanarity<\/jats:sc>\n            asks to decide whether\n            <jats:italic>G<\/jats:italic>\n            admits a\n            <jats:italic>windrose-planar drawing<\/jats:italic>\n            , that is, a planar drawing in which (i) each neighbor\n            <jats:italic>u<\/jats:italic>\n            \u2208\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2197<\/jats:sup>\n            <jats:italic>v<\/jats:italic>\n            is above and to the right of\n            <jats:italic>v<\/jats:italic>\n            , (ii) each neighbor\n            <jats:italic>u<\/jats:italic>\n            \u2208\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2196<\/jats:sup>\n            is above and to the left of\n            <jats:italic>v<\/jats:italic>\n            , (iii) each neighbor\n            <jats:italic>u<\/jats:italic>\n            \u2208\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2199<\/jats:sup>\n            is below and to the left of\n            <jats:italic>v<\/jats:italic>\n            , (iv) each neighbor\n            <jats:italic>u<\/jats:italic>\n            \u2208\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2198<\/jats:sup>\n            is below and to the right of\n            <jats:italic>v<\/jats:italic>\n            , and (v) edges are represented by curves that are monotone with respect to each axis. By exploiting both the horizontal and the vertical relationship among vertices, windrose-planar drawings allow us to simultaneously visualize two partial orders defined by means of the edges of the graph.\n          <\/jats:p>\n          <jats:p>\n            Although the problem is\n            <jats:italic>NP<\/jats:italic>\n            -hard in the general case, we give a polynomial-time algorithm for testing whether there exists a windrose-planar drawing that respects a given combinatorial embedding. This algorithm is based on a characterization of the plane triangulations admitting a windrose-planar drawing. Furthermore, for any embedded graph with\n            <jats:italic>n<\/jats:italic>\n            vertices that has a windrose-planar drawing, we can construct one with at most one bend per edge and with at most 2\n            <jats:italic>n<\/jats:italic>\n            \u22125 bends in total, which lies on the 3\n            <jats:italic>n<\/jats:italic>\n            \u00d7 3\n            <jats:italic>n<\/jats:italic>\n            grid. The latter result contrasts with the fact that straight-line windrose-planar drawings may require exponential area.\n          <\/jats:p>","DOI":"10.1145\/3239561","type":"journal-article","created":{"date-parts":[[2018,9,17]],"date-time":"2018-09-17T12:14:54Z","timestamp":1537186494000},"page":"1-24","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Windrose Planarity"],"prefix":"10.1145","volume":"14","author":[{"given":"Patrizio","family":"Angelini","sequence":"first","affiliation":[{"name":"Wilhelm-Schickard-Institut f\u00fcr Informatik, Universit\u00e4t T\u00fcbingen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2396-5174","authenticated-orcid":false,"given":"Giordano Da","family":"Lozzo","sequence":"additional","affiliation":[{"name":"Department of Engineering, Roma Tre University, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giuseppe Di","family":"Battista","sequence":"additional","affiliation":[{"name":"Department of Engineering, Roma Tre University, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valentino Di","family":"Donato","sequence":"additional","affiliation":[{"name":"Department of Engineering, Roma Tre University, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Philipp","family":"Kindermann","sequence":"additional","affiliation":[{"name":"David R. Cheriton School of Computer Science, University of Waterloo, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G\u00fcnter","family":"Rote","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ignaz","family":"Rutter","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Mathematics, University of Passau, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,9,17]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.5555\/2884435.2884505"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-016-0128-9"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2014.08.001"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2014.12.019"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01188716"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2011.73"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-45803-7_35"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02122694"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.5555\/3116257.3116361"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(88)90123-5"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187850"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/IISA.2014.6878792"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-004-1144-8"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.5555\/647905.739634"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-25870-1_26"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539794277123"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jda.2012.04.012"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-45803-7_14"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-37623-2_17"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-11805-0_21"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-73915-1_34"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.5555\/320176.320191"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3239561","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3239561","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T01:08:20Z","timestamp":1750208900000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3239561"}},"subtitle":["Embedding Graphs with Direction-Constrained Edges"],"short-title":[],"issued":{"date-parts":[[2018,9,17]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,10,31]]}},"alternative-id":["10.1145\/3239561"],"URL":"https:\/\/doi.org\/10.1145\/3239561","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"value":"1549-6325","type":"print"},{"value":"1549-6333","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9,17]]},"assertion":[{"value":"2017-10-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-07-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-09-17","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}