{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T14:12:37Z","timestamp":1761401557151},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2011,3,25]],"date-time":"2011-03-25T00:00:00Z","timestamp":1301011200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2011,9]]},"DOI":"10.1007\/s00454-011-9338-8","type":"journal-article","created":{"date-parts":[[2011,3,24]],"date-time":"2011-03-24T14:53:20Z","timestamp":1300978400000},"page":"334-360","source":"Crossref","is-referenced-by-count":14,"title":["Representing a Functional Curve by Curves with Fewer Peaks"],"prefix":"10.1007","volume":"46","author":[{"given":"Danny Z.","family":"Chen","sequence":"first","affiliation":[]},{"given":"Chao","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Haitao","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,3,25]]},"reference":[{"key":"9338_CR1","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/11830924_5","volume-title":"Proc. of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems","author":"N. Bansal","year":"2006","unstructured":"Bansal, N., Coppersmith, D., Schieber, B.: Minimizing setup and beam-on times in radiation therapy. In: Proc. of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, pp. 27\u201338 (2006)"},{"issue":"2","key":"9338_CR2","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1007\/s00453-001-0096-5","volume":"33","author":"G. Barequet","year":"2002","unstructured":"Barequet, G., Chen, D.Z., Daescu, O., Goodrich, M., Snoeyink, J.: Efficiently approximating polygonal paths in three and higher dimensions. Algorithmica 33(2), 150\u2013167 (2002)","journal-title":"Algorithmica"},{"key":"9338_CR3","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1142\/S0218195996000058","volume":"6","author":"S. Chan","year":"1996","unstructured":"Chan, S., Chin, F.: Approximation of polygonal curves with minimum number of line segments or minimum error. Int. J. Comput. Geom. Appl. 6, 59\u201377 (1996)","journal-title":"Int. J. Comput. Geom. Appl."},{"key":"9338_CR4","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/BF02574703","volume":"6","author":"B. Chazelle","year":"1991","unstructured":"Chazelle, B.: Triangulating a simple polygon in linear time. Discrete Comput. Geom. 6, 485\u2013524 (1991)","journal-title":"Discrete Comput. Geom."},{"issue":"2","key":"9338_CR5","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1142\/S0218195903001086","volume":"13","author":"D.Z. Chen","year":"2003","unstructured":"Chen, D.Z., Daescu, O.: Space-efficient algorithms for approximating polygonal curves in two dimensional space. Int. J. Comput. Geom. Appl. 13(2), 95\u2013111 (2003)","journal-title":"Int. J. Comput. Geom. Appl."},{"key":"9338_CR6","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1007\/978-3-540-27798-9_27","volume-title":"Proc. of the 10th Annual International Computing and Combinatorics Conference","author":"D.Z. Chen","year":"2004","unstructured":"Chen, D.Z., Chun, J., Katoh, N., Tokuyama, T.: Efficient algorithms for approximating a multi-dimensional voxel terrain by a unimodal terrain. In: Proc. of the 10th Annual International Computing and Combinatorics Conference, pp. 238\u2013248 (2004)"},{"key":"9338_CR7","first-page":"701","volume-title":"Proc. of the 12th Annual Int. Symp. on Algorithms and Computation","author":"D.Z. Chen","year":"2006","unstructured":"Chen, D.Z., Hu, X.S., Luan, S., Misiolek, E., Wang, C.: Shape rectangularization problems in intensity-modulated radiation therapy. In: Proc. of the 12th Annual Int. Symp. on Algorithms and Computation, pp. 701\u2013711 (2006)"},{"issue":"2\u20133","key":"9338_CR8","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1142\/S0218195906001999","volume":"16","author":"D.Z. Chen","year":"2006","unstructured":"Chen, D.Z., Hu, X.S., Luan, S., Naqvi, S.A., Wang, C., Yu, C.X.: Generalized geometric approaches for leaf sequencing problems in radiation therapy. Int. J. Comput. Geom. Appl. 16(2\u20133), 175\u2013204 (2006)","journal-title":"Int. J. Comput. Geom. Appl."},{"issue":"2","key":"9338_CR9","first-page":"191","volume":"11","author":"J. Chun","year":"2005","unstructured":"Chun, J., Sadakane, K., Tokuyama, T., Yuki, M.: Peak-reducing fitting of a curve under the L p metric. Interdiscip. Inf. Sci. 11(2), 191\u2013198 (2005)","journal-title":"Interdiscip. Inf. Sci."},{"issue":"2","key":"9338_CR10","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1093\/ietisy\/e89-d.2.783","volume":"E89-D","author":"J. Chun","year":"2006","unstructured":"Chun, J., Sadakane, K., Tokuyama, T.: Efficient algorithms for constructing a pyramid from a terrain. IEICE Trans. Inf. Syst. E89-D(2), 783\u2013788 (2006)","journal-title":"IEICE Trans. Inf. Syst."},{"issue":"2","key":"9338_CR11","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s00453-005-1201-y","volume":"44","author":"J. Chun","year":"2006","unstructured":"Chun, J., Sadakane, K., Tokuyama, T.: Linear time algorithm for approximating a curve by a single-peaked curve. Algorithmica 44(2), 103\u2013115 (2006)","journal-title":"Algorithmica"},{"key":"9338_CR12","volume-title":"Introduction to Algorithms","author":"T. Cormen","year":"2001","unstructured":"Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)","edition":"2"},{"key":"9338_CR13","volume-title":"Twenty Years After","author":"H. Edelsbrunner","year":"2007","unstructured":"Edelsbrunner, H., Harer, J.: Persistent homology\u2014a survey. In: Goodman, J.E., Pach, J., Pollack, R. (eds.) Twenty Years After. AMS, Providence (2007)"},{"issue":"2","key":"9338_CR14","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0022-0000(82)90048-4","volume":"24","author":"G. Frederickson","year":"1982","unstructured":"Frederickson, G., Johnson, D.: The complexity of selection and ranking in X+Y and matrices with sorted columns. J. Comput. Syst. Sci. 24(2), 197\u2013208 (1982)","journal-title":"J. Comput. Syst. Sci."},{"key":"9338_CR15","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1023\/A:1009755828992","volume":"2","author":"T. Fukuda","year":"1997","unstructured":"Fukuda, T., Morimoto, Y., Morishita, S., Tokuyama, T.: Implementation and evaluation of decision trees with range and region splitting. Constraints 2, 401\u2013427 (1997)","journal-title":"Constraints"},{"key":"9338_CR16","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1145\/383891.383893","volume":"26","author":"T. Fukuda","year":"2001","unstructured":"Fukuda, T., Morimoto, Y., Morishita, S., Tokuyama, T.: Data mining with optimized two-dimensional association. ACM Trans. Database Syst. 26, 179\u2013213 (2001)","journal-title":"ACM Trans. Database Syst."},{"key":"9338_CR17","first-page":"135","volume-title":"Proc. of the 16th Annual ACM Symposium on Theory of Computing (STOC)","author":"H. Gabow","year":"1984","unstructured":"Gabow, H., Bentley, J., Tarjan, R.: Scaling and related techniques for geometry problems. In: Proc. of the 16th Annual ACM Symposium on Theory of Computing (STOC), pp. 135\u2013143 (1984)"},{"key":"9338_CR18","first-page":"322","volume-title":"Proc. of the 10th Annual ACM Symposium on Computational Geometry","author":"M. Goodrich","year":"1994","unstructured":"Goodrich, M.: Efficient piecewise-linear function approximation using the uniform metric. In: Proc. of the 10th Annual ACM Symposium on Computational Geometry, pp. 322\u2013331 (1994)"},{"issue":"7","key":"9338_CR19","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1109\/TKDE.2007.1039","volume":"19","author":"S. Guha","year":"2007","unstructured":"Guha, S., Shim, K.: A note on linear time algorithms for maximum error histograms. IEEE Trans. Knowl. Data Eng. 19(7), 993\u2013997 (2007)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"9338_CR20","first-page":"195","volume-title":"Optimum Design","author":"J. Hardwick","year":"2000","unstructured":"Hardwick, J., Stout, Q.F.: Optimizing a unimodal response function for binary variables. In: Atkinson, A., Bogacka, B., Zhigljavsky, A. (eds.) Optimum Design, pp. 195\u2013208 (2000)"},{"key":"9338_CR21","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/S0734-189X(86)80027-5","volume":"36","author":"H. Imai","year":"1986","unstructured":"Imai, H., Iri, M.: Computational-geometric methods for polygonal approximations of a curve. Comput. Vis. Graph. Image Process. 36, 31\u201341 (1986)","journal-title":"Comput. Vis. Graph. Image Process."},{"issue":"1","key":"9338_CR22","first-page":"1","volume":"12","author":"D. Krizanc","year":"2005","unstructured":"Krizanc, D., Morin, P., Smid, M.: Range mode and range median queries on lists and trees. Nord. J. Comput. 12(1), 1\u201317 (2005)","journal-title":"Nord. J. Comput."},{"key":"9338_CR23","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1145\/358746.358758","volume":"24","author":"J. O\u2019Rourke","year":"1981","unstructured":"O\u2019Rourke, J.: An on-line algorithm for fitting straight lines between data ranges. Commun. ACM 24, 574\u2013578 (1981)","journal-title":"Commun. ACM"},{"issue":"4","key":"9338_CR24","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.2307\/2532850","volume":"52","author":"G. Pan","year":"1996","unstructured":"Pan, G.: Subset selection with additional order information. Biometrics 52(4), 1363\u20131374 (1996)","journal-title":"Biometrics"},{"issue":"2","key":"9338_CR25","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.csda.2008.08.005","volume":"53","author":"Q.F. Stout","year":"2008","unstructured":"Stout, Q.F.: Unimodal regression via prefix isotonic regression. Comput. Stat. Data Anal. 53(2), 289\u2013297 (2008)","journal-title":"Comput. Stat. Data Anal."},{"issue":"3","key":"9338_CR26","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/S0167-9473(97)00009-1","volume":"25","author":"T.R. Turner","year":"1997","unstructured":"Turner, T.R., Wollan, P.C.: Locating a maximum using isotonic regression. Comput. Stat. Data Anal. 25(3), 305\u2013320 (1997)","journal-title":"Comput. Stat. Data Anal."},{"key":"9338_CR27","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1145\/237218.237400","volume-title":"Proc. of the 12th Annual ACM Symposium on Computational Geometry","author":"K. Varadarajan","year":"1996","unstructured":"Varadarajan, K.: Approximating monotone polygonal curves using the uniform metric. In: Proc. of the 12th Annual ACM Symposium on Computational Geometry, pp. 311\u2013318 (1996)"},{"key":"9338_CR28","first-page":"515","volume-title":"Proc. of the 4th International Symposium on Algorithms and Computation (ISAAC)","author":"D. Wang","year":"1993","unstructured":"Wang, D., Huang, N., Chao, H., Lee, R.: Plane sweep algorithms for the polynomial approximation problems with applications. In: Proc. of the 4th International Symposium on Algorithms and Computation (ISAAC), pp. 515\u2013522 (1993)"},{"issue":"22","key":"9338_CR29","doi-asserted-by":"crossref","first-page":"6291","DOI":"10.1088\/0031-9155\/53\/22\/002","volume":"53","author":"C. Wang","year":"2008","unstructured":"Wang, C., Luan, S., Tang, G., Chen, D.Z., Earl, M.A., Yu, C.X.: Arc-modulated radiation therapy (AMRT): A single-arc form of intensity-modulated arc therapy. Phys. Med. Biol. 53(22), 6291\u20136303 (2008)","journal-title":"Phys. Med. Biol."},{"key":"9338_CR30","doi-asserted-by":"crossref","DOI":"10.1887\/0750302542","volume-title":"The Physics of Three-Dimensional Radiation Therapy","author":"S. Webb","year":"1993","unstructured":"Webb, S.: The Physics of Three-Dimensional Radiation Therapy. Institute of Physics, Bristol (1993)"},{"key":"9338_CR31","doi-asserted-by":"crossref","DOI":"10.1887\/0750303972","volume-title":"The Physics of Conformal Radiotherapy\u2014Advances in Technology","author":"S. Webb","year":"1997","unstructured":"Webb, S.: The Physics of Conformal Radiotherapy\u2014Advances in Technology. Institute of Physics, Bristol (1997)"},{"issue":"2","key":"9338_CR32","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s00454-004-1146-y","volume":"33","author":"A. Zomorodian","year":"2005","unstructured":"Zomorodian, A., Carlsson, G.: Computing persistent homology. Discrete Comput. Geom. 33(2), 249\u2013274 (2005)","journal-title":"Discrete Comput. Geom."}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-011-9338-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-011-9338-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-011-9338-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T11:30:56Z","timestamp":1712316656000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-011-9338-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,25]]},"references-count":32,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,9]]}},"alternative-id":["9338"],"URL":"https:\/\/doi.org\/10.1007\/s00454-011-9338-8","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3,25]]}}}