TY - GEN

T1 - How to cover a point set with a V-shape of minimum width

AU - Aronov, Boris

AU - Dulieu, Muriel

N1 - Funding Information:
★ Work on this paper has been supported by grant No. 2006/194 from the U.S.-Israel Binational Science Foundation and by NSF Grant CCF-08-30691. Work by Boris
Funding Information:
A ronov has also been supported by NSA MSP Grant H98230-10-1-0210. 1 See [6] for a detailed survey of different notions of measuring similarity between geo-metric objects; is there a sensible (and relevant for our purposes) notion of closeness between a discrete unordered point set and a curve?

PY - 2011

Y1 - 2011

N2 - A balanced V-shape is a polygonal region in the plane contained in the union of two crossing equal-width strips. It is delimited by two pairs of parallel rays that emanate from two points x, y, are contained in the strip boundaries, and are mirror-symmetric with respect to the line xy. The width of a balanced V-shape is the width of the strips. We first present an O(n 2 log n) time algorithm to compute, given a set of n points P, a minimum-width balanced V-shape covering P. We then describe a PTAS for computing a (1 + ε)-approximation of this V-shape in time O((n/ε)log n + (n/ε3/2)log2(1/ε)).

AB - A balanced V-shape is a polygonal region in the plane contained in the union of two crossing equal-width strips. It is delimited by two pairs of parallel rays that emanate from two points x, y, are contained in the strip boundaries, and are mirror-symmetric with respect to the line xy. The width of a balanced V-shape is the width of the strips. We first present an O(n 2 log n) time algorithm to compute, given a set of n points P, a minimum-width balanced V-shape covering P. We then describe a PTAS for computing a (1 + ε)-approximation of this V-shape in time O((n/ε)log n + (n/ε3/2)log2(1/ε)).

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U2 - 10.1007/978-3-642-22300-6_6

DO - 10.1007/978-3-642-22300-6_6

M3 - Conference contribution

AN - SCOPUS:80052125797

SN - 9783642222993

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 61

EP - 72

BT - Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings

T2 - 12th International Symposium on Algorithms and Data Structures, WADS 2011

Y2 - 15 August 2011 through 17 August 2011

ER -