[{"date_created":"2020-09-02T12:13:26Z","department":[{"_id":"63"}],"type":"journal_article","publication":"SIAM Journal on Computing","issue":"1","abstract":[{"text":"We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in $\\mathbb R^d$. We focus on the setting where the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within $1 + \\eps$ using only $\\widetilde{\\O}(\\sqrt{n} \\, \\text{poly} (1/\\eps))$ queries for constant d. The algorithm assumes that the input is supported by a minimal bounding cube enclosing it, by orthogonal range queries, and by cone approximate nearest neighbor queries.\r\n\r\n\r\nRead More: https://epubs.siam.org/doi/10.1137/S0097539703435297\r\n","lang":"eng"}],"language":[{"iso":"eng"}],"doi":"10.1137/s0097539703435297","author":[{"full_name":"Czumaj, Artur","first_name":"Artur","last_name":"Czumaj"},{"first_name":"Funda","last_name":"Ergün","full_name":"Ergün, Funda"},{"full_name":"Fortnow, Lance","last_name":"Fortnow","first_name":"Lance"},{"full_name":"Magen, Avner","last_name":"Magen","first_name":"Avner"},{"last_name":"Newman","first_name":"Ilan","full_name":"Newman, Ilan"},{"first_name":"Ronitt","last_name":"Rubinfeld","full_name":"Rubinfeld, Ronitt"},{"full_name":"Sohler, Christian","last_name":"Sohler","first_name":"Christian"}],"publication_identifier":{"issn":["0097-5397","1095-7111"]},"year":"2005","title":"Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time","intvolume":"        35","date_updated":"2022-01-06T06:53:53Z","publication_status":"published","citation":{"ama":"Czumaj A, Ergün F, Fortnow L, et al. Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time. <i>SIAM Journal on Computing</i>. 2005;35(1):91-109. doi:<a href=\"https://doi.org/10.1137/s0097539703435297\">10.1137/s0097539703435297</a>","bibtex":"@article{Czumaj_Ergün_Fortnow_Magen_Newman_Rubinfeld_Sohler_2005, title={Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time}, volume={35}, DOI={<a href=\"https://doi.org/10.1137/s0097539703435297\">10.1137/s0097539703435297</a>}, number={1}, journal={SIAM Journal on Computing}, author={Czumaj, Artur and Ergün, Funda and Fortnow, Lance and Magen, Avner and Newman, Ilan and Rubinfeld, Ronitt and Sohler, Christian}, year={2005}, pages={91–109} }","mla":"Czumaj, Artur, et al. “Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time.” <i>SIAM Journal on Computing</i>, vol. 35, no. 1, 2005, pp. 91–109, doi:<a href=\"https://doi.org/10.1137/s0097539703435297\">10.1137/s0097539703435297</a>.","chicago":"Czumaj, Artur, Funda Ergün, Lance Fortnow, Avner Magen, Ilan Newman, Ronitt Rubinfeld, and Christian Sohler. “Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time.” <i>SIAM Journal on Computing</i> 35, no. 1 (2005): 91–109. <a href=\"https://doi.org/10.1137/s0097539703435297\">https://doi.org/10.1137/s0097539703435297</a>.","short":"A. Czumaj, F. Ergün, L. Fortnow, A. Magen, I. Newman, R. Rubinfeld, C. Sohler, SIAM Journal on Computing 35 (2005) 91–109.","apa":"Czumaj, A., Ergün, F., Fortnow, L., Magen, A., Newman, I., Rubinfeld, R., &#38; Sohler, C. (2005). Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time. <i>SIAM Journal on Computing</i>, <i>35</i>(1), 91–109. <a href=\"https://doi.org/10.1137/s0097539703435297\">https://doi.org/10.1137/s0097539703435297</a>","ieee":"A. Czumaj <i>et al.</i>, “Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time,” <i>SIAM Journal on Computing</i>, vol. 35, no. 1, pp. 91–109, 2005."},"_id":"18855","page":"91-109","volume":35,"user_id":"15415","status":"public"}]