Inference Maximizing Point Configurations for Parsimonious Algorithms

Inference Maximizing Point Configurations for Parsimonious Algorithms | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Inference Maximizing Point Configurations for Parsimonious Algorithms Shivam Sharma, John Keyser This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8691338/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract We present an exploration of inferring orientations for point configurations. We can compute the orientation of every triple of points by a combination of direct calculation and inference from prior computations. This ''parsimonious'' approach was suggested by Knuth in 1992, and aims to minimize calculation by maximizing inference. We wish to investigate the efficacy of this approach by investigating the minimum and maximum number of inferences that are possible for a point set configuration. To find the configurations which yield maximum inferences, there is no direct formula and hence two constructive approaches are suggested. A basic analysis of sequences that achieve those maximum inferences is also presented and some properties have been proved regarding their existence. Our problem is found to be related to the famous ''Empty Triangle'' problem, an Erdős-class problem in Discrete Geometry. Hence our work could potentially shed light on this problem. Combinatorial Geometry Order Types Robust Geometric Computation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 05 Feb, 2026 Editor assigned by journal 29 Jan, 2026 Submission checks completed at journal 27 Jan, 2026 First submitted to journal 25 Jan, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8691338","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":586580517,"identity":"448670ed-6fcd-443d-9eb2-c844a79fdc41","order_by":0,"name":"Shivam Sharma","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArklEQVRIiWNgGAWjYDACCcYGIGkD5bERryVNghQtYPIwCVrkZze3SfzMOV/HP+2MAcOHssOEtRjcOdgm2bvttoTE7RwDxhnniNEikdhswAvUwgDUwszbRoQW+RmJzYZ/t52TkAdp+UuMFoYbiY2PebcdkDAAaWEkRosBSIvstmTJjbfTCg72nEsnxmHpDw6+3WbHL3c7eeODH2XWRDgMGRwgUf0oGAWjYBSMAlwAAGMeO/vU7Sw2AAAAAElFTkSuQmCC","orcid":"","institution":"Texas A\u0026M University","correspondingAuthor":true,"prefix":"","firstName":"Shivam","middleName":"","lastName":"Sharma","suffix":""},{"id":586580519,"identity":"64e2dcda-e310-4588-9eee-305c236ef76e","order_by":1,"name":"John Keyser","email":"","orcid":"","institution":"Texas A\u0026M University","correspondingAuthor":false,"prefix":"","firstName":"John","middleName":"","lastName":"Keyser","suffix":""}],"badges":[],"createdAt":"2026-01-25 09:08:42","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8691338/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8691338/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102962046,"identity":"5f77c6c6-53e9-455b-9c04-fa577d03ddcd","added_by":"auto","created_at":"2026-02-19 03:57:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":592965,"visible":true,"origin":"","legend":"","description":"","filename":"SharmaKeyserAMAI2026Submitted.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8691338/v1_covered_5a5bd3fa-67d9-4268-96bf-ff59b17cfbcc.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Inference Maximizing Point Configurations for Parsimonious Algorithms","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"annals-of-mathematics-and-artificial-intelligence","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"amai","sideBox":"Learn more about [Annals of Mathematics and Artificial Intelligence](https://www.springer.com/journal/10472)","snPcode":"10472","submissionUrl":"https://submission.springernature.com/new-submission/10472/3","title":"Annals of Mathematics and Artificial Intelligence","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Combinatorial Geometry, Order Types, Robust Geometric Computation","lastPublishedDoi":"10.21203/rs.3.rs-8691338/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8691338/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We present an exploration of inferring orientations for point configurations. 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