Publication Information

{'id': 'https://openalex.org/W1631414015', 'doi': 'https://doi.org/10.48550/arxiv.cs/0110030', 'title': 'Dense point sets have sparse Delaunay triangulations', 'display_name': 'Dense point sets have sparse Delaunay triangulations', 'publication_year': 2001, 'publication_date': '2001-01-01', 'ids': {'openalex': 'https://openalex.org/W1631414015', 'doi': 'https://doi.org/10.48550/arxiv.cs/0110030', 'mag': '1631414015'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/cs/0110030', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': ['datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/abs/cs/0110030', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5042187195', 'display_name': 'Jeff Erickson', 'orcid': 'https://orcid.org/0000-0002-5253-2282'}, 'institutions': [], 'countries': [], 'is_corresponding': True, 'raw_author_name': 'Jeff Erickson', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': ['https://openalex.org/A5042187195'], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 36, 'citation_normalized_percentile': {'value': 0.857143, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 89, 'max': 90}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10996', 'display_name': 'Computational Geometry and Mesh Generation', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/1704', 'display_name': 'Computer Graphics and Computer-Aided Design'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10996', 'display_name': 'Computational Geometry and Mesh Generation', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/1704', 'display_name': 'Computer Graphics and Computer-Aided Design'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T12923', 'display_name': 'Digital Image Processing Techniques', 'score': 0.9942, 'subfield': {'id': 'https://openalex.org/subfields/1707', 'display_name': 'Computer Vision and Pattern Recognition'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10191', 'display_name': 'Robotics and Sensor-Based Localization', 'score': 0.9765, 'subfield': {'id': 'https://openalex.org/subfields/2202', 'display_name': 'Aerospace Engineering'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/point-set-triangulation', 'display_name': 'Point set triangulation', 'score': 0.4235812}], 'concepts': [{'id': 'https://openalex.org/C68010082', 'wikidata': 'https://www.wikidata.org/wiki/Q192445', 'display_name': 'Delaunay triangulation', 'level': 2, 'score': 0.9673674}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.78022826}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.69453377}, {'id': 'https://openalex.org/C135981907', 'wikidata': 'https://www.wikidata.org/wiki/Q188056', 'display_name': 'Triangulation', 'level': 2, 'score': 0.677075}, {'id': 'https://openalex.org/C77553402', 'wikidata': 'https://www.wikidata.org/wiki/Q13222579', 'display_name': 'Upper and lower bounds', 'level': 2, 'score': 0.5295739}, {'id': 'https://openalex.org/C28719098', 'wikidata': 'https://www.wikidata.org/wiki/Q44946', 'display_name': 'Point (geometry)', 'level': 2, 'score': 0.49583277}, {'id': 'https://openalex.org/C184898388', 'wikidata': 'https://www.wikidata.org/wiki/Q1435712', 'display_name': 'Pairwise comparison', 'level': 2, 'score': 0.46424803}, {'id': 'https://openalex.org/C177264268', 'wikidata': 'https://www.wikidata.org/wiki/Q1514741', 'display_name': 'Set (abstract data type)', 'level': 2, 'score': 0.45864326}, {'id': 'https://openalex.org/C121198538', 'wikidata': 'https://www.wikidata.org/wiki/Q4951461', 'display_name': 'Bowyer–Watson algorithm', 'level': 3, 'score': 0.4404521}, {'id': 'https://openalex.org/C167117609', 'wikidata': 'https://www.wikidata.org/wiki/Q17078161', 'display_name': 'Point set triangulation', 'level': 3, 'score': 0.4235812}, {'id': 'https://openalex.org/C128321387', 'wikidata': 'https://www.wikidata.org/wiki/Q5164356', 'display_name': 'Constrained Delaunay triangulation', 'level': 3, 'score': 0.4170278}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.34427702}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.1443969}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.13211843}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.090099424}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C199360897', 'wikidata': 'https://www.wikidata.org/wiki/Q9143', 'display_name': 'Programming language', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/cs/0110030', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.cs/0110030', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/cs/0110030', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [{'score': 0.45, 'display_name': 'Sustainable cities and communities', 'id': 'https://metadata.un.org/sdg/11'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 86, 'referenced_works': ['https://openalex.org/W1497536023', 'https://openalex.org/W1502669108', 'https://openalex.org/W1517297551', 'https://openalex.org/W1528737170', 'https://openalex.org/W1530501787', 'https://openalex.org/W1570805656', 'https://openalex.org/W1578468649', 'https://openalex.org/W1586068580', 'https://openalex.org/W1593563200', 'https://openalex.org/W1604081952', 'https://openalex.org/W178783221', 'https://openalex.org/W1907649404', 'https://openalex.org/W1965167217', 'https://openalex.org/W1968045065', 'https://openalex.org/W1968264007', 'https://openalex.org/W1974393517', 'https://openalex.org/W1978600082', 'https://openalex.org/W1983067644', 'https://openalex.org/W1983932604', 'https://openalex.org/W1984406695', 'https://openalex.org/W1984732102', 'https://openalex.org/W1994242911', 'https://openalex.org/W1994621439', 'https://openalex.org/W1997596515', 'https://openalex.org/W2000332739', 'https://openalex.org/W2008497801', 'https://openalex.org/W2009919199', 'https://openalex.org/W2012774596', 'https://openalex.org/W2014754855', 'https://openalex.org/W2017155445', 'https://openalex.org/W2024766881', 'https://openalex.org/W2027387410', 'https://openalex.org/W2029041800', 'https://openalex.org/W2038636610', 'https://openalex.org/W2038722889', 'https://openalex.org/W2043867171', 'https://openalex.org/W2045672216', 'https://openalex.org/W2050167630', 'https://openalex.org/W2050230854', 'https://openalex.org/W2050753006', 'https://openalex.org/W2052793762', 'https://openalex.org/W2054011861', 'https://openalex.org/W2057512681', 'https://openalex.org/W2058432138', 'https://openalex.org/W2059155916', 'https://openalex.org/W2059217294', 'https://openalex.org/W2060633701', 'https://openalex.org/W2061344951', 'https://openalex.org/W2061845601', 'https://openalex.org/W2064436582', 'https://openalex.org/W2065078485', 'https://openalex.org/W2065345805', 'https://openalex.org/W2068019092', 'https://openalex.org/W2069585823', 'https://openalex.org/W2070143657', 'https://openalex.org/W2075010828', 'https://openalex.org/W2075013407', 'https://openalex.org/W2087585583', 'https://openalex.org/W2088352159', 'https://openalex.org/W2093241092', 'https://openalex.org/W2097944783', 'https://openalex.org/W2101730225', 'https://openalex.org/W2103264684', 'https://openalex.org/W2113692647', 'https://openalex.org/W2113830395', 'https://openalex.org/W2120018535', 'https://openalex.org/W2123869145', 'https://openalex.org/W2130470231', 'https://openalex.org/W2151631165', 'https://openalex.org/W2158905481', 'https://openalex.org/W2164950960', 'https://openalex.org/W2176679876', 'https://openalex.org/W2215813021', 'https://openalex.org/W2219767408', 'https://openalex.org/W2294424216', 'https://openalex.org/W2295428206', 'https://openalex.org/W2405619811', 'https://openalex.org/W2579405108', 'https://openalex.org/W2609482647', 'https://openalex.org/W2791449915', 'https://openalex.org/W2796138255', 'https://openalex.org/W3043060850', 'https://openalex.org/W3139495523', 'https://openalex.org/W34894234', 'https://openalex.org/W48500573', 'https://openalex.org/W76808627'], 'related_works': ['https://openalex.org/W4302417997', 'https://openalex.org/W2386266321', 'https://openalex.org/W2367036512', 'https://openalex.org/W2350914983', 'https://openalex.org/W2001351033', 'https://openalex.org/W1996934342', 'https://openalex.org/W1979362696', 'https://openalex.org/W1972369894', 'https://openalex.org/W1529719486', 'https://openalex.org/W109258179'], 'abstract_inverted_index': {'The': [0], 'spread': [1, 33, 111], 'of': [2, 6, 24, 27, 56, 73, 76, 79, 87, 104], 'a': [3, 101], 'finite': [4], 'set': [5, 26, 60], 'points': [7, 29], 'is': [8, 40], 'the': [9, 12, 21, 43, 53, 91], 'ratio': [10], 'between': [11], 'longest': [13], 'and': [14, 84, 97], 'shortest': [15], 'pairwise': [16], 'distances.': [17], 'We': [18, 64], 'prove': [19], 'that': [20], 'Delaunay': [22, 54], 'triangulation': [23, 55, 103], 'any': [25, 57, 95], 'n': [28, 96, 108], 'in': [30, 42], 'R^3': [31], 'with': [32], 'D': [34, 48], 'has': [35, 61], 'complexity': [36, 105], 'O(D^3).': [37], 'This': [38], 'bound': [39, 69], 'tight': [41], 'worst': [44], 'case': [45], 'for': [46, 94], 'all': [47], '=': [49], 'O(sqrt{n}).': [50], 'In': [51], 'particular,': [52], 'dense': [58, 81], 'point': [59, 82], 'linear': [62], 'complexity.': [63], 'also': [65], 'generalize': [66], 'this': [67], 'upper': [68], 'to': [70], 'regular': [71, 102], 'triangulations': [72], 'k-ply': [74], 'systems': [75], 'balls,': [77], 'unions': [78], 'several': [80], 'sets,': [83], 'uniform': [85], 'samples': [86], 'smooth': [88], 'surfaces.': [89], 'On': [90], 'other': [92], 'hand,': [93], 'D=O(n),': [98], 'we': [99], 'construct': [100], 'Omega(nD)': [106], 'whose': [107], 'vertices': [109], 'have': [110], 'D.': [112]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1631414015', 'counts_by_year': [{'year': 2019, 'cited_by_count': 1}, {'year': 2017, 'cited_by_count': 1}, {'year': 2015, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 3}, {'year': 2012, 'cited_by_count': 2}], 'updated_date': '2024-12-12T17:49:39.544666', 'created_date': '2016-06-24'}