Amortized efficiency of list update and paging rules
Communications of the ACM
Walking an unknown street with bounded detour
Computational Geometry: Theory and Applications
Piecemeal learning of an unknown environment
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Information and Computation
Competitive searching in a generalized street
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Searching for the kernel of a polygon—a competitive strategy
Proceedings of the eleventh annual symposium on Computational geometry
Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem
Information and Computation
Optimal constructions of hybrid algorithms
Journal of Algorithms
On-line search in a simple polygon
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Competitive searching in a generalized street
Computational Geometry: Theory and Applications
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
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Competitive Searching in Polygons - Beyond Generalised Streets
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
On the optimality of spiral search
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Competitive search in symmetric trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Survey: Online algorithms for searching and exploration in the plane
Computer Science Review
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We consider the problem of on-line searching on m rays. A point robot is assumed to stand at the origin of m concurrent rays one of which contains a goal g that the point robot has to find. Neither the ray containing g nor the distance to g are known to the robot. The only way the robot can detect g is by reaching its location. We use the competitive ratio as a measure of the performance of a search strategy, that is, the worst case ratio of the total distance DR traveled by the robot to find g to the distance D from the origin to g.We present a new proof of a tight lower bound of the competitive ratio for randomized strategies to search on m rays. Our proof allows us to obtain a lower bound on the optimal competitive ratio for a fixed m even if the distance of the goal to the origin is bounded from above.Finally, we show that the optimal competitive ratio converges to 1 +2(eα- 1)/α2 m ∼ 1 + 2.1.544 m, for large m where α minimizes the function(ex- 1)/x2.