{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T16:51:14Z","timestamp":1649177474821},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[1996,3]]},"abstract":"<jats:p> The stereo-realization of a graph is the assignment of positions in Cartesian space to each of its vertices such that vertex density is bounded. A bound is derived on the average edge length in such a realization. It is similar to an earlier reported result, however the new bound can be applied to graphs for which the earlier result is not well suited. A more precise realization definition is also presented. The bound is applied to d-dimensional realizations of de Bruijn graphs, yielding an edge length of \u03a9((1\u22122<jats:sup>\u2212d<\/jats:sup>)r<jats:sup>n\/d<\/jats:sup>\/(2n)), where r is the radix (number of distinct symbols) and n is the number of graph dimensions (number of symbol positions). The bound is also applied to shuffle-exchange graphs; for such graphs with small radix the edge-length bound is [Formula: see text], where r is the radix, n is the number of graph dimensions, l<jats:sub>\u03c3<\/jats:sub> is the average length of shuffle edges, and l<jats:sub>\u03b5<\/jats:sub> is the average length of exchange edges. <\/jats:p>","DOI":"10.1142\/s0129626496000145","type":"journal-article","created":{"date-parts":[[2004,10,28]],"date-time":"2004-10-28T18:29:23Z","timestamp":1098988163000},"page":"137-143","source":"Crossref","is-referenced-by-count":0,"title":["A LOWER BOUND ON THE AVERAGE PHYSICAL LENGTH OF EDGES IN THE PHYSICAL REALIZATION OF GRAPHS"],"prefix":"10.1142","volume":"06","author":[{"given":"DAVID M.","family":"KOPPELMAN","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, Louisiana 70803, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626496000145","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:18:38Z","timestamp":1565108318000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626496000145"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[1996,3]]}},"alternative-id":["10.1142\/S0129626496000145"],"URL":"https:\/\/doi.org\/10.1142\/s0129626496000145","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"value":"0129-6264","type":"print"},{"value":"1793-642X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,3]]}}}