Constructing competitive tours from local information
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Online computation and competitive analysis
Online computation and competitive analysis
Sense of direction in distributed computing
Theoretical Computer Science - Special issue: Distributed computing
Impact of memory size on graph exploration capability
Discrete Applied Mathematics
Weighted nearest neighbor algorithms for the graph exploration problem on cycles
Information Processing Letters
On the Advice Complexity of Online Problems
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Fast radio broadcasting with advice
Theoretical Computer Science
Communication algorithms with advice
Journal of Computer and System Sciences
Local MST Computation with Short Advice
Theory of Computing Systems - Special Title: Parallelism on Algorithms and Architectures (SPAA); Guest Editors: Cyril Gavoille, Boaz Patt-Shamir and Christian Scheideler
Information complexity of online problems
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Online computation with advice
Theoretical Computer Science
On the advice complexity of the k-server problem
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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
Journal of Parallel and Distributed Computing
Editorial: The traveling salesman problem
Discrete Optimization
On the nearest neighbor rule for the traveling salesman problem
Operations Research Letters
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 graph with non-negative edge weights. Starting at a distinguished initial vertex s, an agent must visit every vertex of the graph and return to s. Upon visiting a node, the agent learns all incident edges, their weights and endpoints. The goal is to find a tour with minimal cost of traversed edges. This variant of the exploration problem has been introduced by Kalyanasundaram and Pruhs in [18] and is known as a fixed graph scenario. There have been recent advances by Megow, Mehlhorn, and Schweitzer ([19]), however the main question whether there exists a deterministic algorithm with constant competitive ratio (w.r.t. to offline algorithm knowing the graph) working on all graphs and with arbitrary edge weights remains open. In this paper we study this problem in the context of advice complexity, investigating the tradeoff between the amount of advice available to the deterministic agent, and the quality of the solution. We show that Ω(n logn) bits of advice are necessary to achieve a competitive ratio of 1 (w.r.t. an optimal algorithm knowing the graph topology). Furthermore, we give a deterministic algorithm which uses O(n) bits of advice and achieves a constant competitive ratio on any graph with arbitrary weights. Finally, going back to the original problem, we prove a lower bound of 5/2−ε for deterministic algorithms working with no advice, improving the best previous lower bound of 2−ε of Miyazaki, Morimoto, and Okabe from [20]. In this case, significantly more elaborate technique was needed to achieve the result.