Amortized efficiency of list update and paging rules
Communications of the ACM
Theoretical Computer Science
How to learn an unknown environment (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Constructing competitive tours from local information
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
A competitive strategy for learning a polygon
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On-line search in a simple polygon
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Exploring Unknown Environments
SIAM Journal on Computing
The Polygon Exploration Problem
SIAM Journal on Computing
On-line Searching and Navigation
Developments from a June 1996 seminar on Online algorithms: the state of the art
Tree exploration with little memory
Journal of Algorithms
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Impact of memory size on graph exploration capability
Discrete Applied Mathematics
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Online graph exploration: new results on old and new algorithms
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Online graph exploration with advice
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Online graph exploration: New results on old and new algorithms
Theoretical Computer Science
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In the graph exploration problem, a searcher explores the whole set of nodes of an unknown graph. We assume that all the unknown graphs are undirected and connected. The searcher is not aware of the existence of an edge until he/she visits one of its endpoints. The searcher's task is to visit all the nodes and go back to the starting node by traveling a tour as short as possible. One of the simplest strategies is the nearest neighbor algorithm (NN), which always chooses the unvisited node nearest to the searcher's current position. The weighted NN (WNN) is an extension of NN, which chooses the next node to visit by using the weighted distance. It is known that WNN with weight 3 is 16-competitive for planar graphs. In this paper we prove that NN achieves the competitive ratio of 1.5 for cycles. In addition, we show that the analysis for the competitive ratio of NN is tight by providing an instance for which the bound of 1.5 is attained, and NN is the best for cycles among WNN with all possible weights. Furthermore, we prove that no online algorithm to explore cycles is better than 1.25-competitive.