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EXPLORING UNKNOWN ENVIRONMENTS SUSANNE ALBERSy AND MONIKA R. HENZINGERz
 

Summary: EXPLORING UNKNOWN ENVIRONMENTS
SUSANNE ALBERSy AND MONIKA R. HENZINGERz
Abstract. We consider exploration problems where a robot has to construct a complete map
of an unknown environment. We assume that the environment is modeled by a directed, strongly
connected graph. The robot's task is to visit all nodes and edges of the graph using the minimum
number R of edge traversals. Koutsoupias 16] gave a lower bound for R of (d2m), and Deng and
Papadimitriou 12] showed an upper bound of dO(d)m, where m is the number of edges in the graph
and d is the minimum number of edges that have to be added to make the graph Eulerian. We give
the rst sub-exponential algorithm for this exploration problem, which achieves an upper bound of
dO(logd)m. We also show a matching lower bound of d (log d)m for our algorithm. Additionally, we
give lower bounds of 2 (d)m, resp. d (log d)m for various other natural exploration algorithms.
Key words. directed graph, exploration algorithm
AMS subject classi cations. 05C20, 68Q20, 68Q25, 68R10
1. Introduction. Suppose that a robot has to construct a complete map of an
unknown environment using a path that is as short as possible. In many situations
it is convenient to model the environment in which the robot operates by a graph.
This allows to neglect geometric features of the environment and to concentrate on
combinatorial aspects of the exploration problem. Deng and Papadimitriou 12] for-
mulated thus the following exploration problem. A robot has to explore all nodes and
edges of an unknown, strongly connected directed graph. The robot visits an edge

  

Source: Albers, Susanne - Institut für Informatik, Humboldt-Universität zu Berlin

 

Collections: Computer Technologies and Information Sciences