TY - JOUR

T1 - Approximating shortest path for the skew lines problem in time doubly logarithmic in 1/epsilon

AU - Burago, D.

AU - Grigoriev, D.

AU - Slissenko, A.

N1 - Funding Information:
∗Corresponding author. E-mail addresses: burago@math.psu.edu (D. Burago), dima@math.univ-rennes1.fr (D. Grigoriev), slissenko@univ-paris12.fr (A. Slissenko). 1Partially supported by an Alferd P. Sloan Fellowship and NSF Grant DMS-9803129. 2Member of St-Petersburg Steklov Mathematical Institute, Russian Academy of Sciences, St-Petersburg, Russia. 3Member of St-Petersburg Institute for Informatics, Russian Academy of Sciences, St-Petersburg, Russia.

PY - 2004/5/6

Y1 - 2004/5/6

N2 - The approximation of shortest path for skew line problems in time doubly logarithmic in 1/epsilon was studied. A three-dimensional situation was considered where a polytime algorithm for approximating a shortest path can be constructed. Very simple grid approximations were also analyzed by assuming that a parameter describing separability of obstacle is given. It was found that that there is a algorithm of time complexity, which finds a path whose length is bounded from above.

AB - The approximation of shortest path for skew line problems in time doubly logarithmic in 1/epsilon was studied. A three-dimensional situation was considered where a polytime algorithm for approximating a shortest path can be constructed. Very simple grid approximations were also analyzed by assuming that a parameter describing separability of obstacle is given. It was found that that there is a algorithm of time complexity, which finds a path whose length is bounded from above.

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U2 - 10.1016/j.tcs.2004.01.014

DO - 10.1016/j.tcs.2004.01.014

M3 - Article

AN - SCOPUS:2042536010

VL - 315

SP - 371

EP - 404

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 2-3

ER -