Matches in SemOpenAlex for { <https://semopenalex.org/work/W4300993368> ?p ?o ?g. }
Showing items 1 to 58 of
58
with 100 items per page.
- W4300993368 abstract "In this paper we provide faster algorithms for solving the geometric median problem: given $n$ points in $mathbb{R}^{d}$ compute a point that minimizes the sum of Euclidean distances to the points. This is one of the oldest non-trivial problems in computational geometry yet despite an abundance of research the previous fastest algorithms for computing a $(1+epsilon)$-approximate geometric median were $O(dcdot n^{4/3}epsilon^{-8/3})$ by Chin et. al, $tilde{O}(dexp{epsilon^{-4}logepsilon^{-1}})$ by Badoiu et. al, $O(nd+mathrm{poly}(d,epsilon^{-1})$ by Feldman and Langberg, and $O((nd)^{O(1)}logfrac{1}{epsilon})$ by Parrilo and Sturmfels and Xue and Ye. In this paper we show how to compute a $(1+epsilon)$-approximate geometric median in time $O(ndlog^{3}frac{1}{epsilon})$ and $O(depsilon^{-2})$. While our $O(depsilon^{-2})$ is a fairly straightforward application of stochastic subgradient descent, our $O(ndlog^{3}frac{1}{epsilon})$ time algorithm is a novel long step interior point method. To achieve this running time we start with a simple $O((nd)^{O(1)}logfrac{1}{epsilon})$ time interior point method and show how to improve it, ultimately building an algorithm that is quite non-standard from the perspective of interior point literature. Our result is one of very few cases we are aware of outperforming traditional interior point theory and the only we are aware of using interior point methods to obtain a nearly linear time algorithm for a canonical optimization problem that traditionally requires superlinear time. We hope our work leads to further improvements in this line of research." @default.
- W4300993368 created "2022-10-04" @default.
- W4300993368 creator A5010457003 @default.
- W4300993368 creator A5011053473 @default.
- W4300993368 creator A5024980585 @default.
- W4300993368 creator A5059735243 @default.
- W4300993368 creator A5086787265 @default.
- W4300993368 date "2016-06-16" @default.
- W4300993368 modified "2023-10-18" @default.
- W4300993368 title "Geometric Median in Nearly Linear Time" @default.
- W4300993368 doi "https://doi.org/10.48550/arxiv.1606.05225" @default.
- W4300993368 hasPublicationYear "2016" @default.
- W4300993368 type Work @default.
- W4300993368 citedByCount "0" @default.
- W4300993368 crossrefType "posted-content" @default.
- W4300993368 hasAuthorship W4300993368A5010457003 @default.
- W4300993368 hasAuthorship W4300993368A5011053473 @default.
- W4300993368 hasAuthorship W4300993368A5024980585 @default.
- W4300993368 hasAuthorship W4300993368A5059735243 @default.
- W4300993368 hasAuthorship W4300993368A5086787265 @default.
- W4300993368 hasBestOaLocation W43009933681 @default.
- W4300993368 hasConcept C11413529 @default.
- W4300993368 hasConcept C114614502 @default.
- W4300993368 hasConcept C126255220 @default.
- W4300993368 hasConcept C129782007 @default.
- W4300993368 hasConcept C155253501 @default.
- W4300993368 hasConcept C158968445 @default.
- W4300993368 hasConcept C2524010 @default.
- W4300993368 hasConcept C28719098 @default.
- W4300993368 hasConcept C33923547 @default.
- W4300993368 hasConcept C63553672 @default.
- W4300993368 hasConceptScore W4300993368C11413529 @default.
- W4300993368 hasConceptScore W4300993368C114614502 @default.
- W4300993368 hasConceptScore W4300993368C126255220 @default.
- W4300993368 hasConceptScore W4300993368C129782007 @default.
- W4300993368 hasConceptScore W4300993368C155253501 @default.
- W4300993368 hasConceptScore W4300993368C158968445 @default.
- W4300993368 hasConceptScore W4300993368C2524010 @default.
- W4300993368 hasConceptScore W4300993368C28719098 @default.
- W4300993368 hasConceptScore W4300993368C33923547 @default.
- W4300993368 hasConceptScore W4300993368C63553672 @default.
- W4300993368 hasLocation W43009933681 @default.
- W4300993368 hasLocation W43009933682 @default.
- W4300993368 hasOpenAccess W4300993368 @default.
- W4300993368 hasPrimaryLocation W43009933681 @default.
- W4300993368 hasRelatedWork W1503069380 @default.
- W4300993368 hasRelatedWork W1963589315 @default.
- W4300993368 hasRelatedWork W1978042415 @default.
- W4300993368 hasRelatedWork W1992753230 @default.
- W4300993368 hasRelatedWork W2009569868 @default.
- W4300993368 hasRelatedWork W2012893123 @default.
- W4300993368 hasRelatedWork W2171604177 @default.
- W4300993368 hasRelatedWork W2314329970 @default.
- W4300993368 hasRelatedWork W2787766011 @default.
- W4300993368 hasRelatedWork W4235392810 @default.
- W4300993368 isParatext "false" @default.
- W4300993368 isRetracted "false" @default.
- W4300993368 workType "article" @default.