Motion planning in cartesian product graphs

• Autorzy: Biswajit Deb , Kalpesh Kapoor
• Języki publikacji: EN

Abstrakty

EN

Let G be an undirected graph with n vertices. Assume that a robot is placed on a vertex and n − 2 obstacles are placed on the other vertices. A vertex on which neither a robot nor an obstacle is placed is said to have a hole. Consider a single player game in which a robot or obstacle can be moved to adjacent vertex if it has a hole. The objective is to take the robot to a fixed destination vertex using minimum number of moves. In general, it is not necessary that the robot will take a shortest path between the source and destination vertices in graph G. In this article we show that the path traced by the robot coincides with a shortest path in case of Cartesian product graphs. We give the minimum number of moves required for the motion planning problem in Cartesian product of two graphs having girth 6 or more. A result that we prove in the context of Cartesian product of Pn with itself has been used earlier to develop an approximation algorithm for (n2 − 1)-puzzle

Słowa kluczowe

EN

robot motion in a graph; Cartesian product of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 2
• Strony: 207-221

Daty

wydano

2014-05-01

online

2014-04-12

Twórcy

autor

Biswajit Deb

• Department of Mathematics Sikkim Manipal Institute of Technology, India

autor

Kalpesh Kapoor

• Department of Mathematics Indian Institute of Technology Guwahati, India

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1726