A hundred impossibility proofs for distributed computing
Proceedings of the eighth annual ACM Symposium on Principles of distributed computing
Theoretical Computer Science
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Piecemeal Learning of an Unknown Environment
Machine Learning - Special issue on COLT '93
Piecemeal graph exploration by a mobile robot (extended abstract)
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases
IEEE Transactions on Parallel and Distributed Systems
Navigating in Unfamiliar Geometric Terrain
SIAM Journal on Computing
How to learn an unknown environment. I: the rectilinear case
Journal of the ACM (JACM)
Randomized robot navigation algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Exploring unknown undirected graphs
Journal of Algorithms
Exploring Unknown Environments
SIAM Journal on Computing
Selective families, superimposed codes, and broadcasting on unknown radio networks
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Optimal constrained graph exploration
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Broadcasting Algorithms in Radio Networks with Unknown Topology
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Hundreds of impossibility results for distributed computing
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Tree exploration with little memory
Journal of Algorithms
Optimal graph exploration without good maps
Theoretical Computer Science
Faster communication in known topology radio networks
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Oracle size: a new measure of difficulty for communication tasks
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Journal of Graph Theory
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
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Local MST computation with short advice
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Trade-offs between the size of advice and broadcasting time in trees
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Fast Radio Broadcasting with Advice
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
r3: Resilient Random Regular Graphs
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Theoretical Computer Science
Online Computation with Advice
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Online computation with advice
Theoretical Computer Science
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We study the amount of knowledge about the network that is required in order to efficiently solve a task concerning this network. The impact of available information on the efficiency of solving network problems, such as communication or exploration, has been investigated before but assumptions concerned availability of particular items of information about the network, such as the size, the diameter, or a map of the network. In contrast, our approach is quantitative: we investigate the minimum number of bits of information (minimum oracle size) that has to be given to an algorithm in order to perform a task with given efficiency. We illustrate this quantitative approach to available knowledge by the task of tree exploration. A mobile entity (robot) has to traverse all edges of an unknown tree, using as few edge traversals as possible. The quality of an exploration algorithm ${\cal A}$ is measured by its competitive ratio, i.e., by comparing its cost (number of edge traversals) to the length of the shortest path containing all edges of the tree. Depth-First-Search has competitive ratio 2 and, in the absence of any information about the tree, no algorithm can beat this value. We determine the minimum number of bits of information that has to be given to an exploration algorithm in order to achieve competitive ratio strictly smaller than 2. Our main result establishes an exact threshold oracle size that turns out to be roughly loglogD, where D is the diameter of the tree. More precisely, for any constant c, we construct an exploration algorithm with competitive ratio smaller than 2, using an oracle of size at most loglogD –c, and we show that every algorithm using an oracle of size loglogD –g(D), for any function g unbounded from above, has competitive ratio at least 2.