Amortized efficiency of list update and paging rules
Communications of the ACM
Information and Computation
How to find a point on a line within a fixed distance
Discrete Applied Mathematics - Special issue on the 13th European workshop on computational geometry CG '97
Lower bounds in on-line geometric searching
Computational Geometry: Theory and Applications
The ultimate strategy to search on m rays?
Theoretical Computer Science
On the Competitive Complexity of Navigation Tasks
Revised Papers from the International Workshop on Sensor Based Intelligent Robots
Searching on m Bounded Rays Optimally
Searching on m Bounded Rays Optimally
A princess swimming in the fog looking for a monster cow
ACM SIGACT News
On the two-dimensional cow search problem
Information Processing Letters
On the optimality of spiral search
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Optimal competitive online ray search with an error-prone robot
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
| Hi-index | 5.23 |
We consider the problem of searching for an unknown horizontal or vertical line in a plane. A search path in the plane starts at the origin and detects the unknown line, if the path hits the line for the first time. The performance of the search path is measured by competitive analysis. That is, we compute the ratio of the length of the path until the line is detected over the shortest path from the origin to the given line. The competitive ratio of a given search path is the worst-case ratio of the path among all horizontal and vertical lines in the plane. In this paper, we design a search path that attains a competitive ratio of 12.53853842..., and slightly improves the current best-known search path. Furthermore, we prove that the search path is optimal among all paths that proceed in a cyclic manner. There is a strong conjecture that this path is the general optimal search path for searching axis-parallel lines.