{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T22:21:00Z","timestamp":1770070860466,"version":"3.49.0"},"reference-count":0,"publisher":"Journal of Graph Algorithms and Applications","issue":"1","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JGAA"],"abstract":"<jats:p>We investigate the problem of finding a spanning tree of a set of $n$ moving points in $\\mathbb{R}^{\\dim}$ that minimizes the maximum total weight (under any convex distance function) or the maximum bottleneck throughout the motion.\nThe output is a single tree, i.e., it does not change combinatorially during the movement of the points.\nWe call these trees a minimum moving spanning tree, and a \nminimum bottleneck moving spanning tree, respectively.\nWe show that, although finding the minimum bottleneck moving spanning tree can be done in $O(n^2)$ time when $\\dim$ is a constant, it is NP-hard to compute the minimum moving spanning tree even for $\\dim=2$.\nWe provide a simple $O(n^2)$-time 2-approximation and a $O(n \\log n)$-time $(2+\\varepsilon)$-approximation for the latter problem, for any constant $\\dim$ and any constant $\\varepsilon&gt;0$.<\/jats:p>","DOI":"10.7155\/jgaa.00607","type":"journal-article","created":{"date-parts":[[2022,12,23]],"date-time":"2022-12-23T18:22:01Z","timestamp":1671819721000},"page":"1-18","source":"Crossref","is-referenced-by-count":1,"title":["The Minimum Moving Spanning Tree Problem"],"prefix":"10.7155","volume":"27","author":[{"given":"Hugo","family":"Akitaya","sequence":"first","affiliation":[]},{"given":"Ahmad","family":"Biniaz","sequence":"additional","affiliation":[]},{"given":"Prosenjit","family":"Bose","sequence":"additional","affiliation":[]},{"given":"Jean-Lou","family":"De Carufel","sequence":"additional","affiliation":[]},{"given":"Anil","family":"Maheshwari","sequence":"additional","affiliation":[]},{"given":"Lu\u00eds Fernando Schultz Xavier","family":"Da Silveira","sequence":"additional","affiliation":[]},{"given":"Michiel","family":"Smid","sequence":"additional","affiliation":[]}],"member":"4175","published-online":{"date-parts":[[2023,1,1]]},"container-title":["Journal of Graph Algorithms and Applications"],"original-title":[],"link":[{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/download\/paper607\/2342","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/download\/paper607\/2342","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T20:11:26Z","timestamp":1727467886000},"score":1,"resource":{"primary":{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/view\/paper607"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,1]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1,1]]}},"URL":"https:\/\/doi.org\/10.7155\/jgaa.00607","relation":{},"ISSN":["1526-1719"],"issn-type":[{"value":"1526-1719","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,1]]}}}