{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101550"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101550","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Linear search problem with low sensing on two rays","abstract":"We consider a generalization of the linear search problem where the searcher has low sensing capabilities on two rays. We first show the necessary conditions for an optimal search plan to exist. We then investigate properties of optimal search plans and show that optimal search plans are defined by an underlying fourth order recurrence relation. We then develop numerical methods that aid in estimating and finding optimal search plans. In Chapter 4, we present an algorithm that produces a search plan that approximates the minimum expected cost up to any desired accuracy for any probability density distribution. In Chapter 5, for specific distributions, properties of the underlying dynamics are used to numerically find optimal search plans.","abstract_html":"We consider a generalization of the linear search problem where the searcher has low sensing capabilities on two rays. We first show the necessary conditions for an optimal search plan to exist. We then investigate properties of optimal search plans and show that optimal search plans are defined by an underlying fourth order recurrence relation. We then develop numerical methods that aid in estimating and finding optimal search plans. In Chapter 4, we present an algorithm that produces a search plan that approximates the minimum expected cost up to any desired accuracy for any probability density distribution. In Chapter 5, for specific distributions, properties of the underlying dynamics are used to numerically find optimal search plans.","abstract_has_math":false,"creators":["West, Argen McAllister"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Zharnitsky, Vadim","DeVille, Lee","Bronski, Jared","Rapti, Zoi"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-27T16:17:45Z","date_published":"2018-09-27T16:17:45Z","updated_at":"2026-07-22T22:24:40Z","subjects":["Linear Search Problem, Search Games"],"languages":["en"],"rights":["Copyright 2018 Argen West"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101550","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Zharnitsky, Vadim","DeVille, Lee","Bronski, Jared","Rapti, Zoi"]},{"key":"dc:creator","label":"Author","values":["West, Argen McAllister"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-27T16:17:45Z","2018-07-10","2018-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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":["Linear Search Problem, Search Games"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Argen West"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101550"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We consider a generalization of the linear search problem where the searcher has low sensing capabilities on two rays. We first show the necessary conditions for an optimal search plan to exist. We then investigate properties of optimal search plans and show that optimal search plans are defined by an underlying fourth order recurrence relation. We then develop numerical methods that aid in estimating and finding optimal search plans. In Chapter 4, we present an algorithm that produces a search plan that approximates the minimum expected cost up to any desired accuracy for any probability density distribution. In Chapter 5, for specific distributions, properties of the underlying dynamics are used to numerically find optimal search plans.","Submission original under an indefinite embargo labeled 'Open Access'. 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We then develop numerical methods that aid in estimating and finding optimal search plans. In Chapter 4, we present an algorithm that produces a search plan that approximates the minimum expected cost up to any desired accuracy for any probability density distribution. In Chapter 5, for specific distributions, properties of the underlying dynamics are used to numerically find optimal search plans.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Argen West, accepted the attached license on 2018-07-09 at 20:19.","The student, Argen West, submitted this Dissertation for approval on 2018-07-09 at 20:27.","This Dissertation was approved for publication on 2018-07-10 at 08:48.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12787 on 2018-09-27 at 10:47:31","Made available in DSpace on 2018-09-27T16:17:45Z (GMT). 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