No. 318 on SWAT 88: 1st Scandinavian workshop on algorithm theory
Information and Computation
Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem
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
Optimal covering tours with turn costs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Lower bounds in on-line geometric searching
Computational Geometry: Theory and Applications
The ultimate strategy to search on m rays?
Theoretical Computer Science
The Polygon Exploration Problem
SIAM Journal on Computing
Position-Independent Near Optimal Searching and On-line Recognition in Star Polygons
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Pure Strategy Asymmetric Rendezvous on the Line with an Unknown Initial Distance
Operations Research
Operations Research
On-line target searching in bounded and unbounded domains
On-line target searching in bounded and unbounded domains
Searching with an autonomous robot
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Online searching with an autonomous robot
Computational Geometry: Theory and Applications
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Polygon exploration with time-discrete vision
Computational Geometry: Theory and Applications
A Shadow Simplex Method for Infinite Linear Programs
Operations Research
Multi-target ray searching problems
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Competitive search in symmetric trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Optimal competitive online ray search with an error-prone robot
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Survey: Online algorithms for searching and exploration in the plane
Computer Science Review
Collaborative search on the plane without communication
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
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We consider the problem of searching for an object on a line at an unknown distance OPT from the original position of the searcher, in the presence of a cost of d for each time the searcher changes direction. This is a generalization of the well-studied linear-search problem. We describe a strategy that is guaranteed to find the object at a cost of at most 9 ċ OPT + 2d, which has the optimal competitive ratio 9 with respect to OPT plus the minimum corresponding additive term. Our argument for upper and lower bound uses an infinite linear program, which we solve by experimental solution of an infinite series of approximating finite linear programs, estimating the limits, and solving the resulting recurrences for an explicit proof of optimality. We feel that this technique is interesting in its own right and should help solve other searching problems. In particular, we consider the star search or cowpath problem with turn cost, where the hidden object is placed on one of m rays emanating from the original position of the searcher. For this problem we give a tight bound of (1 + 2mm/(m - 1)m-1)OPT + m((m/(m - 1))m-1 - 1)d. We also discuss tradeoffs between the corresponding coefficients and we consider randomized strategies on the line.