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Localization in Graphs

dc.contributor.authorKhuller, Samiren_US
dc.contributor.authorRaghavachari, Balajien_US
dc.contributor.authorRosenfeld, Azrielen_US
dc.description.abstractNavigation can be studied in a graph-structured framework in which the navigating agent (which we shall assume to be a point robot) moves from node to node of a ``graph space''. The robot can locate itself by the presence of distinctively labeled ``landmark'' nodes in the graph space. For a robot navigating in Euclidean space, visual detection of a distinctive landmark provides information about the direction to the landmark, and allows the robot to determine its position by triangulation. On a graph, however, there is neither the concept of direction nor that of visibility. Instead, we shall assume that a robot navigating on a graph can sense the distances to a set of landmarks. Evidently, if the robot knows its distances to a sufficiently large set of landmarks, its position on the graph is uniquely determined. This suggests the following problem: given a graph, what are the fewest number of landmarks needed, and where should they be located, so that the distances to the landmarks uniquely determine the robot's position on the graph? This is actually a classical problem about metric spaces. A minimum set of landmarks which uniquely determine the robot's position is called a ``metric basis'', and the minimum number of landmarks is called the ``metric dimension'' of the graph. In this paper we present some results about this problem. Our main {\em new\/} result is that the metric dimension can be approximated in polynomial time within a factor of $O(\log n)$; we also establish some properties of graphs with metric dimension 2. (Also cross-referenced as UMIACS-TR-94-92)en_US
dc.format.extent145401 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3326en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-94-92en_US
dc.titleLocalization in Graphsen_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US

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