151,424 research outputs found
Light Euclidean Spanners with Steiner Points
No full textThe FOCS'19 paper of Le and Solomon [Hung Le and Shay Solomon, 2019], culminating a long line of research on Euclidean spanners, proves that the lightness (normalized weight) of the greedy (1+ε)-spanner in ℝ^d is Õ(ε^{-d}) for any d = O(1) and any ε = Ω(n^{-1/(d-1)}) (where Õ hides polylogarithmic factors of 1/ε), and also shows the existence of point sets in ℝ^d for which any (1+ε)-spanner must have lightness Ω(ε^{-d}). Given this tight bound on the lightness, a natural arising question is whether a better lightness bound can be achieved using Steiner points.
Our first result is a construction of Steiner spanners in ℝ² with lightness O(ε^{-1} log Δ), where Δ is the spread of the point set. In the regime of Δ ≪ 2^(1/ε), this provides an improvement over the lightness bound of [Hung Le and Shay Solomon, 2019]; this regime of parameters is of practical interest, as point sets arising in real-life applications (e.g., for various random distributions) have polynomially bounded spread, while in spanner applications ε often controls the precision, and it sometimes needs to be much smaller than O(1/log n). Moreover, for spread polynomially bounded in 1/ε, this upper bound provides a quadratic improvement over the non-Steiner bound of [Hung Le and Shay Solomon, 2019], We then demonstrate that such a light spanner can be constructed in O_ε(n) time for polynomially bounded spread, where O_ε hides a factor of poly(1/(ε)). Finally, we extend the construction to higher dimensions, proving a lightness upper bound of Õ(ε^{-(d+1)/2} + ε^{-2} log Δ) for any 3 ≤ d = O(1) and any ε = Ω(n^{-1/(d-1)})
Ready Hung Door
No full textReady Hung Doorhttps://mavmatrix.uta.edu/specialcollections_wdsmithphotography/1125/thumbnail.jp
Ready Hung Door
No full textReady Hung Doorhttps://mavmatrix.uta.edu/specialcollections_wdsmithphotography/1126/thumbnail.jp
Ready Hung Door sales
No full textReady Hung Door saleshttps://mavmatrix.uta.edu/specialcollections_wdsmithphotography/1405/thumbnail.jp
Ready Hung Doors sale
No full textReady Hung Doors salehttps://mavmatrix.uta.edu/specialcollections_wdsmithphotography/1419/thumbnail.jp
Ready Hung Doors sale
No full textReady Hung Doors--model or salesmanhttps://mavmatrix.uta.edu/specialcollections_wdsmithphotography/1426/thumbnail.jp
Ready Hung Doors sale
No full textReady Hung Doors salehttps://mavmatrix.uta.edu/specialcollections_wdsmithphotography/1425/thumbnail.jp
Ready Hung Door
No full textReady Hung Doorhttps://mavmatrix.uta.edu/specialcollections_wdsmithphotography/1124/thumbnail.jp
Faculty concert: Hung-Kuan Chen, January 12, 1999
No full textThis is the concert program of the Faculty Concert of Hung-Kuan Chen performance on Tuesday, January 12, 1999 at 8:00 p.m., at the Tsai Performance Center, 685 Commonwealth Avenue, Boston, Massachusetts. Works performed were Le baiser de l'enfant Jesus by Oliver Messiaen, Sonata No. 29 in B-flat major, Op. 106 "Hammerklavier" by Ludwig van Beethoven, and Etude-tableau in D minor, Op. 39, No. 8 and Sonata No. 2 in B-flat minor, Op. 36 by Serge Rachmaninoff. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund
Ready Hung Doors sale
No full textReady Hung Doors salehttps://mavmatrix.uta.edu/specialcollections_wdsmithphotography/1411/thumbnail.jp
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