Exploring unknown undirected graphs
Petrişor Panaite,Andrzej Pelc +1 more
- pp 316-322
TLDR
In this paper, the authors give an exploration algorithm whose penalty is O(|V(G)|) for every graph, and also show that some natural exploration algorithms cannot achieve this efficiency.Abstract:
A robot has to construct a complete map of an unknown environment modeled as an undirected connected graph. The task is to explore all nodes and edges of the graph using the minimum number of edge traversals. The penalty of an exploration algorithm running on a graph G = (V(G), E(G)) is the worst-case number of traversals in excess of the lower bound |E(G)| that it must perform in order to explore the entire graph. We give an exploration algorithm whose penalty is O(|V(G)|) for every graph. We also show that some natural exploration algorithms cannot achieve this efficiency.read more
Citations
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Proceedings ArticleDOI
The power of a pebble: exploring and mapping directed graphs
TL;DR: A model that makes very limited assumptions about the environment is considered that can solve the mapping problem in this general setting and shows that if the robot knows an upper bound on the number of vertices then it can learn the graph efficiently with only one pebble.
Journal ArticleDOI
The Power of a Pebble
TL;DR: A model that makes very limited assumptions about the environment is considered, and it is shown that if the robot knows an upper bound on the number of vertices then it can learn the graph efficiently with only one pebble, and if it does not, then pebbles are both necessary and sufficient.
Journal ArticleDOI
Graph exploration by a finite automaton
TL;DR: It is shown that, for any K-state robot and any d ≥ 3, there exists a planar graph of maximum degree d with at most K + 1 nodes that the robot cannot explore, which improves all previous bounds in the literature.
Journal ArticleDOI
Exploring unknown undirected graphs
Petrişor Panaite,Andrzej Pelc +1 more
TL;DR: An exploration algorithm whose penalty is O(|V(G)|) for every graph is given and it is shown that some natural exploration algorithms cannot achieve this efficiency.
Journal ArticleDOI
Exploring an unknown graph
TL;DR: The main result is an algorithm that achieves a bounded ratio when the deficiency of the graph is unbounded, and two is achievable by a simple algorithm.
References
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Exploring an unknown graph
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Proceedings ArticleDOI
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