{"title":"An area-maximum edge length trade-off for VSLI layout","authors":"Norbert Blum","doi":"10.1016/S0019-9958(85)80011-5","DOIUrl":null,"url":null,"abstract":"<div><p>We construct an <em>N</em>-node graph <em>G</em> which has (i) a layout with area <em>O</em>(<em>N</em>) and maximum edge length <em>O</em>(<em>N</em><sup>1/2</sup>), (ii) a layout with area <em>O</em>(<em>N</em><sup>5/4</sup>) and maximum edge length <em>O</em>(<em>N</em><sup>1/4</sup>). We prove for 1 ≤ <em>f</em>(<em>N</em>) ≤ (<em>O</em>(<em>N</em><sup>1/8</sup>) that any layout for <em>G</em> with area <em>Nf</em>(<em>N</em>) has an edge of length <em>Ω</em>(<em>N</em><sup>1/2</sup>/<em>f</em>(<em>N</em>)·log <em>N</em>). Hence <em>G</em> has no layout which is optimal with respect to both measures.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":"66 1","pages":"Pages 45-52"},"PeriodicalIF":0.0000,"publicationDate":"1985-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(85)80011-5","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995885800115","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 4
Abstract
We construct an N-node graph G which has (i) a layout with area O(N) and maximum edge length O(N1/2), (ii) a layout with area O(N5/4) and maximum edge length O(N1/4). We prove for 1 ≤ f(N) ≤ (O(N1/8) that any layout for G with area Nf(N) has an edge of length Ω(N1/2/f(N)·log N). Hence G has no layout which is optimal with respect to both measures.
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