{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T20:35:22Z","timestamp":1648672522627},"reference-count":11,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A hotspot is an axis-aligned square of fixed side length <jats:italic>s<\/jats:italic>, where the amount of time a moving entity spends within it is maximised. An exact hotspot of a polygonal trajectory with <jats:italic>n<\/jats:italic> edges can be found with time complexity <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic>\n                  <jats:sup>2<\/jats:sup>). We define a <jats:italic>c<\/jats:italic>-approximate hotspot as an axis-aligned square of side length <jats:italic>cs<\/jats:italic>, in which the presence duration of the entity is no less than that of an exact hotspot. In this paper we present an algorithm to find a (1 + <jats:italic>\u03f5<\/jats:italic>)-approximate hotspot of a polygonal trajectory with time complexity <jats:inline-formula>\n                     <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_comp-2020-0176_eq_001.png\" \/>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>O<\/m:mi>\n                              <m:mrow>\n                                 <m:mo>(<\/m:mo>\n                                 <m:mrow>\n                                    <m:mfrac>\n                                       <m:mrow>\n                                          <m:mi>n<\/m:mi>\n                                          <m:mi>\u03d5<\/m:mi>\n                                       <\/m:mrow>\n                                       <m:mi>\u03f5<\/m:mi>\n                                    <\/m:mfrac>\n                                    <m:mo>log<\/m:mo>\n                                    <m:mfrac>\n                                       <m:mrow>\n                                          <m:mi>n<\/m:mi>\n                                          <m:mi>\u03d5<\/m:mi>\n                                       <\/m:mrow>\n                                       <m:mi>\u03f5<\/m:mi>\n                                    <\/m:mfrac>\n                                 <\/m:mrow>\n                                 <m:mo>)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:tex-math>O\\left( {{{n\\phi } \\over \\varepsilon }\\log {{n\\phi } \\over \\varepsilon }} \\right)<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, where \u03d5 is the ratio of average trajectory edge length to <jats:italic>s<\/jats:italic>.<\/jats:p>","DOI":"10.1515\/comp-2020-0176","type":"journal-article","created":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T08:41:40Z","timestamp":1614501700000},"page":"444-449","source":"Crossref","is-referenced-by-count":0,"title":["Approximate Discontinuous Trajectory Hotspots"],"prefix":"10.1515","volume":"10","author":[{"given":"Ali Gholami","family":"Rudi","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering , Babol Noshirvani University of Technology , Babol, Mazandaran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2020,11,18]]},"reference":[{"key":"2021022808284140868_j_comp-2020-0176_ref_001_w2aab3b7c59b1b6b1ab1ab1Aa","unstructured":"[1] van Kreveld M.J., L\u00f6ffler M., Wiratma L., On Optimal Polyline Simplification Using the Hausdorff and Fr\u00e9chet Distance, in International Symposium on Computational Geometry, 2018, 56:1\u201356:14, 10.4230\/LIPICS.SOCG.2018.56"},{"key":"2021022808284140868_j_comp-2020-0176_ref_002_w2aab3b7c59b1b6b1ab1ab2Aa","doi-asserted-by":"crossref","unstructured":"[2] Aronov B., Driemel A., van Kreveld M.J., L\u00f6ffler M., Staals F., Segmentation of Trajectories on Nonmonotone Criteria, ACM Transactions on Algorithms, 12(2), 2016, 26:1\u201326:28, 10.1145\/2660772","DOI":"10.1145\/2660772"},{"key":"2021022808284140868_j_comp-2020-0176_ref_003_w2aab3b7c59b1b6b1ab1ab3Aa","doi-asserted-by":"crossref","unstructured":"[3] Buchin K., Buchin M., van Kreveld M.J., Speckmann B., Staals F., Trajectory grouping structure, Journal of Computational Geometry, 6(1), 2015, 75\u201398, 10.20382\/JOCG.V6I1A3","DOI":"10.1145\/2582112.2595646"},{"key":"2021022808284140868_j_comp-2020-0176_ref_004_w2aab3b7c59b1b6b1ab1ab4Aa","doi-asserted-by":"crossref","unstructured":"[4] Alewijnse S.P.A., Buchin K., Buchin M., Sijben S., Westenberg M.A., Model-Based Segmentation and Classification of Trajectories, Algorithmica, 80(8), 2018, 2422\u20132452, 10.1007\/S00453-017-0329-X","DOI":"10.1007\/s00453-017-0329-x"},{"key":"2021022808284140868_j_comp-2020-0176_ref_005_w2aab3b7c59b1b6b1ab1ab5Aa","doi-asserted-by":"crossref","unstructured":"[5] Benkert M., Djordjevic B., Gudmundsson J., Wolle T., Finding Popular Places, International Journal of Computational Geometry & Applications, 20(1), 2010, 19\u201342, 10.1142\/S02181959100 03189","DOI":"10.1142\/S0218195910003189"},{"key":"2021022808284140868_j_comp-2020-0176_ref_006_w2aab3b7c59b1b6b1ab1ab6Aa","doi-asserted-by":"crossref","unstructured":"[6] Gudmundsson J., van Kreveld M.J., Staals F., Algorithms for Hotspot Computation on Trajectory Data, in International Conference on Advances in Geographic Information Systems, 2013, 134\u2013143, 10.1145\/2525314.2525359","DOI":"10.1145\/2525314.2525359"},{"key":"2021022808284140868_j_comp-2020-0176_ref_007_w2aab3b7c59b1b6b1ab1ab7Aa","doi-asserted-by":"crossref","unstructured":"[7] Damiani M.L., I. H., Cagnacci F., Extracting stay regions with uncertain boundaries from GPS trajectories: a case study in animal ecology, in ACM International Conference on Advances in Geographic Information Systems (SIGSPATIAL), 2014, 253\u2013262, 10.1145\/2666310.2666417","DOI":"10.1145\/2666310.2666417"},{"key":"2021022808284140868_j_comp-2020-0176_ref_008_w2aab3b7c59b1b6b1ab1ab8Aa","unstructured":"[8] Rudi A.G., Looking for Bird Nests: Identifying Stay Points with Bounded Gaps, in The Canadian Conference on Computational Geometry, 2018, 334\u2013339"},{"key":"2021022808284140868_j_comp-2020-0176_ref_009_w2aab3b7c59b1b6b1ab1ab9Aa","doi-asserted-by":"crossref","unstructured":"[9] Rudi A.G., Approximate Hotspots of Orthogonal Trajectories, Fundamenta Informaticae, 167(4), 2019, 271\u2013285, 10.3233\/FI-2019-1818","DOI":"10.3233\/FI-2019-1818"},{"key":"2021022808284140868_j_comp-2020-0176_ref_010_w2aab3b7c59b1b6b1ab1ac10Aa","doi-asserted-by":"crossref","unstructured":"[10] de Berg M., Cheong O., van Kreveld M.J., Overmars M.H., Computational Geometry - Algorithms and Applications, Springer, third edition, 2008, 10.1007\/978-3-540-77974-2","DOI":"10.1007\/978-3-540-77974-2"},{"key":"2021022808284140868_j_comp-2020-0176_ref_011_w2aab3b7c59b1b6b1ab1ac11Aa","doi-asserted-by":"crossref","unstructured":"[11] Buchin M., Dodge S., Speckmann B., Similarity of trajectories taking into account geographic context, Journal of Spatial Information Science, 9(1), 2014, 101\u2013124, 10.5311\/JOSIS.2014.9.179","DOI":"10.5311\/JOSIS.2014.9.179"}],"container-title":["Open Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/comp-2020-0176\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/comp-2020-0176\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T08:42:06Z","timestamp":1614501726000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/comp-2020-0176\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,1]]},"references-count":11,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,11,18]]},"published-print":{"date-parts":[[2020,1,1]]}},"alternative-id":["10.1515\/comp-2020-0176"],"URL":"https:\/\/doi.org\/10.1515\/comp-2020-0176","relation":{},"ISSN":["2299-1093"],"issn-type":[{"value":"2299-1093","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,1]]}}}