Theoretical Computer Science
Information and Computation
Constructing competitive tours from local information
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Piecemeal Learning of an Unknown Environment
Machine Learning - Special issue on COLT '93
Online computation and competitive analysis
Online computation and competitive analysis
Piecemeal graph exploration by a mobile robot
Information and Computation
Exploring unknown undirected graphs
Journal of Algorithms
Exploring Unknown Environments
SIAM Journal on Computing
On a Simple Depth-First Search Strategy for Exploring Unknown Graphs
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
On-line Searching and Navigation
Developments from a June 1996 seminar on Online algorithms: the state of the art
Optimal graph exploration without good maps
Theoretical Computer Science
Networks
Optimal constrained graph exploration
ACM Transactions on Algorithms (TALG)
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
The power of team exploration: two robots can learn unlabeled directed graphs
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Impact of memory size on graph exploration capability
Discrete Applied Mathematics
Memory Efficient Anonymous Graph Exploration
Graph-Theoretic Concepts in Computer Science
Weighted nearest neighbor algorithms for the graph exploration problem on cycles
Information Processing Letters
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Smart robot teams exploring sparse trees
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
On the nearest neighbor rule for the traveling salesman problem
Operations Research Letters
Online exploration of all vertices in a simple polygon
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
The power of recourse for online MST and TSP
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Online graph exploration with advice
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Collecting information by power-aware mobile agents
DISC'12 Proceedings of the 26th international conference on Distributed Computing
A brief history of web crawlers
CASCON '13 Proceedings of the 2013 Conference of the Center for Advanced Studies on Collaborative Research
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We study the problem of exploring an unknown undirected connected graph. Beginning in some start vertex, a searcher must visit each node of the graph by traversing edges. Upon visiting a vertex for the first time, the searcher learns all incident edges and their respective traversal costs. The goal is to find a tour of minimum total cost. Kalyanasundaram and Pruhs [23] proposed a sophisticated generalization of a Depth First Search that is 16-competitive on planar graphs. While the algorithm is feasible on arbitrary graphs, the question whether it has constant competitive ratio in general has remained open. Our main result is an involved lower bound construction that answers this question negatively. On the positive side, we prove that the algorithm has constant competitive ratio on any class of graphs with bounded genus. Furthermore, we provide a constant competitive algorithm for general graphs with a bounded number of distinct weights.