Approximation Algorithms for the Minimum Bends Traveling Salesman Problem
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Computational Geometry: Theory and Applications
On covering points with minimum turns
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Maximizing maximal angles for plane straight-line graphs
Computational Geometry: Theory and Applications
Maximizing maximal angles for plane straight-line graphs
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Discrete Applied Mathematics
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Motivated by applications in robotics, we formulate the problem of minimizing the total angle cost of a TSP tour for a set of points in Euclidean space, where the angle cost of a tour is the sum of the direction changes at the points. We establish the NP-hardness of both this problem and its relaxation to the cycle cover problem. We then consider the issue of designing approximation algorithms for these problems and show that both problems can be approximated to within a ratio of O(log n) in polynomial time. We also consider the problem of simultaneously approximating both the angle and the length measure for a TSP tour. In studying the resulting tradeoff, we choose to focus on the sum of the two performance ratios and provide tight bounds on the sum. Finally, we consider the extremal value of the angle measure and obtain essentially tight bounds for it. In this paper we restrict our attention to the planar setting, but all our results are easily extended to higher dimensions.