Improved FPT algorithms for rectilinear k-links spanning path

  • Authors:

  • Jianxin Wang;Jinyi Yao;Qilong Feng;Jianer Chen

  • Affiliations:

  • School of Information Science and Engineering, Central South University, Changsha, P.R. China;School of Information Science and Engineering, Central South University, Changsha, P.R. China;School of Information Science and Engineering, Central South University, Changsha, P.R. China;School of Information Science and Engineering, Central South University, Changsha, P.R. China,Department of Computer Science and Engineering, Texas A&M University, College Station, Texas

  • Venue:
  • TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

Given n points in ℝd and a positive integer k , the Rectilinear k -Links Spanning Path problem is to find a piecewise linear path through these n points having at most k line-segments (Links) where these line-segments are axis-parallel. This problem is known to be NP-complete when d ≥3, we first prove that it is also NP-complete in 2-dimensions. Under the assumption that one line-segment in the spanning path covers all the points on the same line, we propose a new FPT algorithm with running time O (d k +12k k 2+d k n ), which greatly improves the previous best result and is the first FPT algorithm that runs in O *(2O (k )). When d =2, we further improve this result to O (3.24k k 2+1.62k n ). For the Rectilinear k -Bends TSP problem, the NP-completeness proof in 2-dimensions and FPT algorithms are also given.