{"title":"A Lower Bound for the Shortest Path Problem","authors":"Ketan Mulmuley , Pradyut Shah","doi":"10.1006/jcss.2001.1766","DOIUrl":null,"url":null,"abstract":"<div><p>We show that the shortest path problem cannot be solved in <em>o</em>(log<!--> <em>n</em>) time on an unbounded fan-in PRAM without bit operations using poly(<em>n</em>) processors, even when the bit-lengths of the weights on the edges are restricted to be of size <em>O</em>(log<sup>3</sup> <em>n</em>). This shows that the matrix-based <em>repeated squaring</em> algorithm for the shortest path problem is optimal in the unbounded fan-in PRAM model without bit operations.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"63 2","pages":"Pages 253-267"},"PeriodicalIF":0.9000,"publicationDate":"2001-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1006/jcss.2001.1766","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computer and System Sciences","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022000001917660","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
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Abstract
We show that the shortest path problem cannot be solved in o(log n) time on an unbounded fan-in PRAM without bit operations using poly(n) processors, even when the bit-lengths of the weights on the edges are restricted to be of size O(log3n). This shows that the matrix-based repeated squaring algorithm for the shortest path problem is optimal in the unbounded fan-in PRAM model without bit operations.
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The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions.
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