{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/116262"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/116262","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The art gallery problem in polyomino corridors","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","abstract_has_math":false,"creators":["Kaempen, Kieran"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Erickson, Jeff G"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-08","date_published":"2022-08","updated_at":"2026-07-22T22:24:56Z","subjects":["computational geometry","art gallery problem","polyomino"],"languages":["en","eng"],"rights":["Copyright 2022 Kieran Kaempen"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/116262","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Erickson, Jeff G"]},{"key":"dc:creator","label":"Author","values":["Kaempen, Kieran"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-08","2022-07-18"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["computational geometry","art gallery problem","polyomino"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2022 Kieran Kaempen"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/116262"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","The student, Kieran Kaempen, accepted the attached license on 2022-07-17 at 19:04.","The student, Kieran Kaempen, submitted this Thesis for approval on 2022-07-17 at 19:09.","This Thesis was approved for publication on 2022-07-18 at 15:17.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18359 on 2022-11-15 at 18:21:23","The classical Art Gallery Problem asks for a the smallest set of points, called guards, inside a given simple polygon P, such that every point in P is visible to at least one guard. This problem is known to be computationally hard, even in restricted cases. We consider a special case of this problem, where the input polygon P consists of a path of axis-aligned unit squares joined along edges; we call such a polygon a polyomino corridor. We show that an optimal guard set of a corridor can be computed in linear time if the corridor satisfies certain additional conditions. We also formulate (but do not prove) a natural structural conjecture; if this conjecture is true, an optimal guard set can be found in any corridor in linear time. Finally, we present several related geometric and combinatorial results."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The art gallery problem in polyomino corridors"]}]}],"canonical_facts":{"dc:contributor":["Erickson, Jeff G"],"dc:creator":["Kaempen, Kieran"],"dc:date":["2022-08","2022-07-18"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","The student, Kieran Kaempen, accepted the attached license on 2022-07-17 at 19:04.","The student, Kieran Kaempen, submitted this Thesis for approval on 2022-07-17 at 19:09.","This Thesis was approved for publication on 2022-07-18 at 15:17.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18359 on 2022-11-15 at 18:21:23","The classical Art Gallery Problem asks for a the smallest set of points, called guards, inside a given simple polygon P, such that every point in P is visible to at least one guard. This problem is known to be computationally hard, even in restricted cases. We consider a special case of this problem, where the input polygon P consists of a path of axis-aligned unit squares joined along edges; we call such a polygon a polyomino corridor. We show that an optimal guard set of a corridor can be computed in linear time if the corridor satisfies certain additional conditions. We also formulate (but do not prove) a natural structural conjecture; if this conjecture is true, an optimal guard set can be found in any corridor in linear time. Finally, we present several related geometric and combinatorial results."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/116262"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Kieran Kaempen"],"dc:subject":["computational geometry","art gallery problem","polyomino"],"dc:title":["The art gallery problem in polyomino corridors"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:56Z"}