{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69422"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69422","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Dynamic Data Structures for Two Dimensional Searching","abstract":"In this thesis we investigate dynamic data structures and algorithms for searching in a subdivision of the plane. Three specific problems have been addressed in this area. The first problem, dynamic point location, considers a geometric subdivision of the plane into polygonal regions, and asks for the region that contains a given query point. The second problem, dynamic planar embedding, considers a topological subdivision of the plane induced by a planar embedding of a graph, and asks for a region that contains two given query vertices on its boundary (if one exists). The third problem, dynamic transitive closure, considers a planar acyclic digraph embedded in the plane, and asks for testing the existence of and/or reporting a directed path between two query vertices. In all of the three problems the update operations consist of inserting/deleting vertices and edges. We present several dynamic techniques that improve previously published results in the area. The space requirement ranges from $O$($n$) to $O$($n$ log $n$), and the query and update times range from $O$(log $n$) to $O$(log$\\sp2 n$), where $n$ is the size of the subdivision. In addition to their good theoretical space/time performance, all the data structures and algorithms presented are also practical and easy to implement, and therefore suited for real-world applications.","abstract_html":"In this thesis we investigate dynamic data structures and algorithms for searching in a subdivision of the plane. Three specific problems have been addressed in this area. The first problem, dynamic point location, considers a geometric subdivision of the plane into polygonal regions, and asks for the region that contains a given query point. The second problem, dynamic planar embedding, considers a topological subdivision of the plane induced by a planar embedding of a graph, and asks for a region that contains two given query vertices on its boundary (if one exists). The third problem, dynamic transitive closure, considers a planar acyclic digraph embedded in the plane, and asks for testing the existence of and/or reporting a directed path between two query vertices. In all of the three problems the update operations consist of inserting/deleting vertices and edges. We present several dynamic techniques that improve previously published results in the area. The space requirement ranges from $O$($n$) to $O$($n$ log $n$), and the query and update times range from $O$(log $n$) to $O$(log$\\sp2 n$), where $n$ is the size of the subdivision. In addition to their good theoretical space/time performance, all the data structures and algorithms presented are also practical and easy to implement, and therefore suited for real-world applications.","abstract_has_math":true,"creators":["Tamassia, Roberto"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":["Preparata, Franco P."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-15T19:05:43Z","date_published":"2014-12-15T19:05:43Z","updated_at":"2026-07-22T22:26:00Z","subjects":["Computer Science"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8908863"],"render_values":[{"text":"(UMI)AAI8908863","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69422","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Preparata, Franco P."]},{"key":"dc:creator","label":"Author","values":["Tamassia, Roberto"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T19:05:43Z","10000-01-01","1988"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computer Science"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/69422","(UMI)AAI8908863"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we investigate dynamic data structures and algorithms for searching in a subdivision of the plane. Three specific problems have been addressed in this area. The first problem, dynamic point location, considers a geometric subdivision of the plane into polygonal regions, and asks for the region that contains a given query point. The second problem, dynamic planar embedding, considers a topological subdivision of the plane induced by a planar embedding of a graph, and asks for a region that contains two given query vertices on its boundary (if one exists). The third problem, dynamic transitive closure, considers a planar acyclic digraph embedded in the plane, and asks for testing the existence of and/or reporting a directed path between two query vertices. In all of the three problems the update operations consist of inserting/deleting vertices and edges. We present several dynamic techniques that improve previously published results in the area. The space requirement ranges from $O$($n$) to $O$($n$ log $n$), and the query and update times range from $O$(log $n$) to $O$(log$\\sp2 n$), where $n$ is the size of the subdivision. In addition to their good theoretical space/time performance, all the data structures and algorithms presented are also practical and easy to implement, and therefore suited for real-world applications.","Made available in DSpace on 2014-12-15T19:05:43Z (GMT). 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The first problem, dynamic point location, considers a geometric subdivision of the plane into polygonal regions, and asks for the region that contains a given query point. The second problem, dynamic planar embedding, considers a topological subdivision of the plane induced by a planar embedding of a graph, and asks for a region that contains two given query vertices on its boundary (if one exists). The third problem, dynamic transitive closure, considers a planar acyclic digraph embedded in the plane, and asks for testing the existence of and/or reporting a directed path between two query vertices. In all of the three problems the update operations consist of inserting/deleting vertices and edges. We present several dynamic techniques that improve previously published results in the area. The space requirement ranges from $O$($n$) to $O$($n$ log $n$), and the query and update times range from $O$(log $n$) to $O$(log$\\sp2 n$), where $n$ is the size of the subdivision. 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