{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,5]],"date-time":"2026-09-05T20:56:23Z","timestamp":1788641783881,"version":"build-2803163510"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:p>We deal with the problem of constructing the orthogonal drawing of a graph with the minimum number of bends along the edges. The problem has been recently shown to be NP-complete in the general case. In this paper we introduce and study the new concept of spirality, which is a measure of how an orthogonal drawing is \"rolled up,\" and develop a theory on the interplay between spirality and number of bends of orthogonal drawings. We exploit this theory to present polynomial time algorithms for two significant classes of graphs: series-parallel graphs and 3-planar graphs. Series-parallel graphs arise in a variety ofproblems such as scheduling, electrical networks, data-flow analysis, database logic programs, and circuit layout. Also, they play a central role in planarity problems. Furthermore, drawings of 3-planar graphs are a classical field of investigation.<\/jats:p>","DOI":"10.1137\/s0097539794262847","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1764-1811","source":"Crossref","is-referenced-by-count":75,"title":["Spirality and Optimal Orthogonal Drawings"],"prefix":"10.1137","volume":"27","author":[{"given":"Giuseppe","family":"Di Battista","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giuseppe","family":"Liotta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Vargiu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","unstructured":"R. K. Ahuja, T. L. Magnanti, and J. B. 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