{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T05:58:06Z","timestamp":1775282286110,"version":"3.50.1"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2001,6]]},"abstract":"<jats:p> We show that the well-known random incremental construction of Clarkson and Shor<jats:sup>18<\/jats:sup> can be adapted to provide efficient external-memory algorithms for some geometric problems. In particular, as the main result, we obtain an optimal randomized algorithm for the problem of computing the trapezoidal decomposition determined by a set of N line segments in the plane with K pairwise intersections, that requires [Formula: see text] expected disk accesses, where M is the size of the available internal memory and B is the size of the block transfer. The approach is sufficiently general to derive algorithms for other geometric problems: 3-d half-space intersections, 2-d and 3-d convex hulls, 2-d abstract Voronoi diagrams and batched planar point location; these algorithms require an optimal expected number of disk accesses and are simpler than the ones previously known. The results extend to an external-memory model with multiple disks. <\/jats:p>","DOI":"10.1142\/s0218195901000523","type":"journal-article","created":{"date-parts":[[2003,5,7]],"date-time":"2003-05-07T08:18:55Z","timestamp":1052295535000},"page":"305-337","source":"Crossref","is-referenced-by-count":11,"title":["RANDOMIZED EXTERNAL-MEMORY ALGORITHMS FOR LINE SEGMENT INTERSECTION AND OTHER GEOMETRIC PROBLEMS"],"prefix":"10.1142","volume":"11","author":[{"given":"A.","family":"CRAUSER","sequence":"first","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Informatik, Stuhlsatzenhausweg 85, 66123 Saarbr\u00fccken, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"FERRAGINA","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Informatik, Stuhlsatzenhausweg 85, 66123 Saarbr\u00fccken, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K.","family":"MEHLHORN","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Informatik, Stuhlsatzenhausweg 85, 66123 Saarbr\u00fccken, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"U.","family":"MEYER","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Informatik, Stuhlsatzenhausweg 85, 66123 Saarbr\u00fccken, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E. 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