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Articles

On approximations to minimum link visibility paths in simple polygons

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Pages 300-307 | Received 17 Jun 2020, Accepted 21 Sep 2020, Published online: 16 Oct 2020

References

  • M.H. Alsuwaiyel, D.T. Lee, Minimal link visibility paths inside a simple polygon. Comput. Geom. Theory Appl. 3(1) (1993), pp. 1–25. doi: 10.1016/0925-7721(93)90027-4
  • M.H. Alsuwaiyel and D.T. Lee, Finding an approximate minimum-link visibility path inside a simple polygon, Inform. Process. Lett. 55(2) (1995), pp. 75–79. doi: 10.1016/0020-0190(95)00072-K
  • E.M. Arkin, J.S.B. Mitchell, and S. Suri, Logarithmic-time link path queries in a simple polygon, Int. J. Comput. Geom. Appl. 5(4) (1995), pp. 369–395. doi: 10.1142/S0218195995000234
  • E.M. Arkin, J.S.B. Mitchell, and C.D. Piatko, Minimum-link watchman tour, Inform. Process. Lett.86(4) (2003), pp. 203–207. doi: 10.1016/S0020-0190(02)00502-1
  • B. Chazelle, Triangulating a simple polygon in linear time, Discrete Comput. Geom. 6(3) (1991), pp. 485–524. doi: 10.1007/BF02574703
  • N. Christofides, Worst case analysis of a new heuristic for the traveling salesman problem, Tech. Rep., Graduate School of Industrial Administration, CMU (388), 1976.
  • H. Edelsbrunner, L.J. Guibas, and J. Stolfi, Optimal point location in a monotone subdivision, SIAM J. Comput. 15(2) (1986), pp. 317–340. doi: 10.1137/0215023
  • L.J. Guibas and J. Hershberger, Optimal shortest path queries in a simple polygon, J. Comput. Syst. Sci. 39(2) (1989), pp. 126–152. doi: 10.1016/0022-0000(89)90041-X
  • J.A. Hoogeveen, Analysis of Christofides' heuristic: Some paths are more difficult than cycles, Oper. Res. Lett. 10(5) (1991), pp. 291–295. doi: 10.1016/0167-6377(91)90016-I
  • A. Sebo and J. Vygen, Shorter tours by nicer ears: 7/5-approximation for graphic TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs, Combinatorica 34(5) (2014), pp. 597–629. doi: 10.1007/s00493-014-2960-3
  • S. Suri, On some link distance problems in a simple polygon, IEEE Trans. Robot. Autom. 6(1) (1990), pp. 108–113. doi: 10.1109/70.88124
  • X. Tan, A linear-time 2-approximation algorithm for the watchman route problem for simple polygons, Theor. Comput. Sci. 384(1) (2007), pp. 92–103. doi: 10.1016/j.tcs.2007.05.021
  • M.R. Zarrabi and N.M. Charkari, A simple proof for visibility paths in simple polygons, preprint (2020). Available at arXiv:2004.02227.
  • M.R. Zarrabi and N.M. Charkari, Query-points visibility constraint minimum link paths in simple polygons, preprint (2020). Available at arXiv:2004.02220.

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