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
Navigating in Unfamiliar Geometric Terrain
SIAM Journal on Computing
How to learn an unknown environment. I: the rectilinear case
Journal of the ACM (JACM)
The power of a pebble: exploring and mapping directed graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Exploring unknown undirected graphs
Journal of Algorithms
Exploring Unknown Environments
SIAM Journal on Computing
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
Tree exploration with little memory
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Graph Theory
Oracle size: a new measure of difficulty for communication tasks
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Map construction of unknown graphs by multiple agents
Theoretical Computer Science
Trade-offs between the size of advice and broadcasting time in trees
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Remembering without Memory: Tree Exploration by Asynchronous Oblivious Robots
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
On the Power of Local Orientations
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Deterministic Models of Communication Faults
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Information and Computation
Memory Efficient Anonymous Graph Exploration
Graph-Theoretic Concepts in Computer Science
Exploration of Periodically Varying Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Remembering without memory: Tree exploration by asynchronous oblivious robots
Theoretical Computer Science
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Communication algorithms with advice
Journal of Computer and System Sciences
DISC'10 Proceedings of the 24th international conference on Distributed computing
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
Improved distributed exploration of anonymous networks
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
Journal of Parallel and Distributed Computing
Tree exploration with an oracle
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
On the power of waiting when exploring public transportation systems
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
Deterministic network exploration by a single agent with Byzantine tokens
Information Processing Letters
Online multi-robot exploration of grid graphs with rectangular obstacles
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Collaborative search on the plane without communication
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Deterministic network exploration by anonymous silent agents with local traffic reports
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Online graph exploration: New results on old and new algorithms
Theoretical Computer Science
On the exploration of time-varying networks
Theoretical Computer Science
Hi-index | 5.23 |
A robot has to visit all nodes and traverse all edges of an unknown undirected connected graph, using as few edge traversals as possible. The quality of an exploration algorithm A is measured by comparing its cost (number of edge traversals) to that of the optimal algorithm having full knowledge of the graph. The ratio between these costs, maximized over all starting nodes in the graph and over all graphs in a given class U, is called the overhead of algorithm A for the class U of graphs. We consider three scenarios, providing the robot with varying amount of information. The robot may either know nothing about the explored graph, or have an unlabeled isomorphic copy of it (an unanchored map), or have such a copy with a marked starting node (an anchored map).For all of the above scenarios, we construct natural exploration algorithms that have smallest, or--in one case--close to smallest, overhead. While for the class of all graphs, depth-first search turns out to be an optimal algorithm for all scenarios, the situation for trees is much different. We show that, under the scenario without any knowledge, DFS is still optimal for trees but this is not the case if a map is available. Under the scenario with an unanchored map, we show that optimal overhead is at least √3 but strictly below 2 (and thus DFS is not optimal). Under the scenario with an anchored map, we construct an optimal algorithm for trees and show that its overhead is 3/2. We also consider exploration of the class of lines (simple paths). In this case, depth-first search remains optimal for the scenario without any knowledge, with overhead 2. Under the scenario with an unanchored map, we construct an optimal algorithm and show that its overhead is √3. Finally, under the scenario with an anchored map, we construct an optimal algorithm and show that its overhead is 7/5. An important contribution of this paper is establishing lower bounds that prove optimality of these exploration algorithms.