{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22735"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22735","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Degeneracy control in geometric programs","abstract":"Degenerate geometric data (e.g., three points on a line, four points on a circle) is known to create all sorts of special cases, some easy and some complicated, that have to be considered in implementations of geometric algorithms. Traditionally, the designers of algorithms coped with these difficulties by assuming special cases away, and left it to the unfortunate implementer to deal with data that would not satisfy the assumption.","abstract_html":"Degenerate geometric data (e.g., three points on a line, four points on a circle) is known to create all sorts of special cases, some easy and some complicated, that have to be considered in implementations of geometric algorithms. Traditionally, the designers of algorithms coped with these difficulties by assuming special cases away, and left it to the unfortunate implementer to deal with data that would not satisfy the assumption.","abstract_has_math":false,"creators":["Rosenberger, Harald"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Edelsbrunner, Herbert"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:49:43Z","date_published":"2011-05-07T13:49:43Z","updated_at":"2026-07-22T22:25:20Z","subjects":["Computer Science"],"languages":["eng"],"rights":["Copyright 1990 Rosenberger, Harald"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9026308","(UMI)AAI9026308"],"render_values":[{"text":"AAI9026308","href":null,"code":true},{"text":"(UMI)AAI9026308","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/22735","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Edelsbrunner, Herbert"]},{"key":"dc:creator","label":"Author","values":["Rosenberger, Harald"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:49:43Z","10000-01-01","1990"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"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":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1990 Rosenberger, Harald"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9026308","(UMI)AAI9026308","http://hdl.handle.net/2142/22735"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Degenerate geometric data (e.g., three points on a line, four points on a circle) is known to create all sorts of special cases, some easy and some complicated, that have to be considered in implementations of geometric algorithms. Traditionally, the designers of algorithms coped with these difficulties by assuming special cases away, and left it to the unfortunate implementer to deal with data that would not satisfy the assumption.","This thesis discusses several issues related to the phenomenon of degeneracy itself, and a symbolic perturbation scheme that allows programs to work on degenerate data as if it were nondegenerate. The topics covered are the likelihood of a special case, the computational overhead induced by the symbolic perturbation scheme and ways to reduce it, examples of applications, extensions and modifications of the scheme.","Made available in DSpace on 2011-05-07T13:49:43Z (GMT). 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Traditionally, the designers of algorithms coped with these difficulties by assuming special cases away, and left it to the unfortunate implementer to deal with data that would not satisfy the assumption.","This thesis discusses several issues related to the phenomenon of degeneracy itself, and a symbolic perturbation scheme that allows programs to work on degenerate data as if it were nondegenerate. The topics covered are the likelihood of a special case, the computational overhead induced by the symbolic perturbation scheme and ways to reduce it, examples of applications, extensions and modifications of the scheme.","Made available in DSpace on 2011-05-07T13:49:43Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9026308.pdf: 4006399 bytes, checksum: 6e93c0a7249d44b9c0d5e8ffb12208b5 (MD5) Previous issue date: 1990","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:59:38Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:28:09-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9026308","(UMI)AAI9026308","http://hdl.handle.net/2142/22735"],"dc:language":["eng"],"dc:rights":["Copyright 1990 Rosenberger, Harald"],"dc:subject":["Computer Science"],"dc:title":["Degeneracy control in geometric programs"],"dc:type":["text"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:20Z"}