8 research outputs found

    On Compatible Matchings

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    A matching is compatible to two or more labeled point sets of size nn with labels {1,,n}\{1,\dots,n\} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of nn points there exists a compatible matching with 2n\lfloor \sqrt {2n}\rfloor edges. More generally, for any \ell labeled point sets we construct compatible matchings of size Ω(n1/)\Omega(n^{1/\ell}). As a corresponding upper bound, we use probabilistic arguments to show that for any \ell given sets of nn points there exists a labeling of each set such that the largest compatible matching has O(n2/(+1)){\mathcal{O}}(n^{2/({\ell}+1)}) edges. Finally, we show that Θ(logn)\Theta(\log n) copies of any set of nn points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge

    Improved Bounds for Covering Paths and Trees in the Plane

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    An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants

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    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    State of Utah v. Heather Jo Rodriguez : Brief of Amici Curiae

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    ON WRIT OF CERTIORARI TO THE UTAH COURT OF APPEAL

    Six Decades of Flight Research: An Annotated Bibliography of Technical Publications of NASA Dryden Flight Research Center, 1946-2006

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    Titles, authors, report numbers, and abstracts are given for nearly 2900 unclassified and unrestricted technical reports and papers published from September 1946 to December 2006 by the NASA Dryden Flight Research Center and its predecessor organizations. These technical reports and papers describe and give the results of 60 years of flight research performed by the NACA and NASA, from the X-1 and other early X-airplanes, to the X-15, Space Shuttle, X-29 Forward Swept Wing, X-31, and X-43 aircraft. Some of the other research airplanes tested were the D-558, phase 1 and 2; M-2, HL-10 and X-24 lifting bodies; Digital Fly-By-Wire and Supercritical Wing F-8; XB-70; YF-12; AFTI F-111 TACT and MAW; F-15 HiDEC; F-18 High Alpha Research Vehicle, F-18 Systems Research Aircraft and the NASA Landing Systems Research aircraft. The citations of reports and papers are listed in chronological order, with author and aircraft indices. In addition, in the appendices, citations of 270 contractor reports, more than 200 UCLA Flight System Research Center reports, nearly 200 Tech Briefs, 30 Dryden Historical Publications, and over 30 videotapes are included
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