{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T08:00:10Z","timestamp":1649145610034},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:p> In this paper, we provide an algorithm for traversing geometric graphs which visits all vertices and reports every vertex and edge exactly once. To achieve this, we combine a given geometric graph G with the integer lattice, seen as a graph, in such a way that the resulting hypothetical graph can be traversed using a known algorithm which is based on face routing. To overcome the problem with hypothetical vertices and edges, we develop an algorithm for visiting any k-th neighborhood of a vertex in a graph straight-line drawn in the plane using O(k log k) memory. The memory needed to complete the traversal of a geometric graph then turns out to depend on the maximum graph distance among pairs of distinct vertices of G whose Euclidean distance is greater than one and less than [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219265919500087","type":"journal-article","created":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T07:25:03Z","timestamp":1576826703000},"page":"1950008","source":"Crossref","is-referenced-by-count":0,"title":["Traversal with Enumeration of Geometric Graphs in Bounded Space"],"prefix":"10.1142","volume":"19","author":[{"given":"SAHAND","family":"KHAKABIMAMAGHANI","sequence":"first","affiliation":[{"name":"Department of Computer Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MASOOD","family":"MASJOODY","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LADISLAV","family":"STACHO","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,12,19]]},"reference":[{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1080\/136588197242310"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195902000906"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1142\/S0219265904001234"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1137\/0209048"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01305237"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1998.1616"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265919500087","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T07:40:32Z","timestamp":1576827632000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219265919500087"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12]]},"references-count":6,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["10.1142\/S0219265919500087"],"URL":"https:\/\/doi.org\/10.1142\/s0219265919500087","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"value":"0219-2659","type":"print"},{"value":"1793-6713","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12]]}}}