A Combinatorial Lower Bound of the Storage Cost of Shared Memory Emulation

A Combinatorial Lower Bound of the Storage Cost of Shared Memory Emulation | 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 A Combinatorial Lower Bound of the Storage Cost of Shared Memory Emulation Yusong Shi, Weidong Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5737346/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper aims to obtain a lower bound of the storage cost of emulating an atomic shared memory over an asynchronous distributed message passing system using topological techniques. Previous literature has developed several shared memory emulation algorithms based on replication and erasure coding techniques. A common insight that applies to all the algorithms is that the worst-case storage cost of implementing an atomic shared memory object grows with the number of concurrent active writes. A natural question is whether the growth of storage complexity is intrinsic to any algorithm that implements an atomic shared-memory object. It was known that the storage cost cannot be lower than $\frac{N}{N - f}log_{2}|V|$ using the classic coding theoretic result. Previous literature gives a result approximately twice as strong as $\frac{N}{N - f}log_{2}|V|$, and partially answers this question in the positive when the write protocol has certain restrictions. We develop a lower bound using combinatorial techniques to answer this question without restrictions on the algorithm. Our topological structure provides a modeling of the client-server architecture which is widely used in modern distributed systems. Distributed Storage Shared Memory Emulation Storage Cost Combinatorial topology Client-Server architecture Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-5737346","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":396169994,"identity":"afa403b9-97fd-4609-81ce-9016a420072a","order_by":0,"name":"Yusong Shi","email":"data:image/png;base64,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","orcid":"","institution":"Tsinghua University","correspondingAuthor":true,"prefix":"","firstName":"Yusong","middleName":"","lastName":"Shi","suffix":""},{"id":396169995,"identity":"e8d51ade-f0d0-4a26-9306-86d590d0652f","order_by":1,"name":"Weidong Liu","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"prefix":"","firstName":"Weidong","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2024-12-30 18:08:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5737346/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5737346/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91865955,"identity":"f72d6b5d-6222-4fe4-89d3-36c5b7bb0d1a","added_by":"auto","created_at":"2025-09-22 13:18:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":955730,"visible":true,"origin":"","legend":"","description":"","filename":"SpringACombinatorialLowerBoundoftheStorageCostofSharedMemoryEmulation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5737346/v1_covered_5fbf1aa4-33b2-4304-bc8f-fc1e2810f3fc.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Combinatorial Lower Bound of the Storage Cost of Shared Memory Emulation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Distributed Storage, Shared Memory Emulation, Storage Cost, Combinatorial topology, Client-Server architecture","lastPublishedDoi":"10.21203/rs.3.rs-5737346/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5737346/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper aims to obtain a lower bound of the storage cost of emulating an atomic shared memory over an asynchronous distributed message passing system using topological techniques. 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