7200990
Geodesic Convexity in Discrete Spaces
Abstract A pebbled graph is called “(geodesically) convex” if at least one shortest path between any two unpebbled nodes has no pebbles on any of its nodes. There exist conditions on the node neighborhoods in a pebbled graph that imply convexity, but no such conditions can be necessary for convexity. The convex pebblings can be characterized for various special types of graphs, such as cycles, trees, and cliques. For a graph L whose nodes are the lattice points in the plane under the relation of row or column adjacency, we show that a pebbling of L is convex iff the set of unpebbled nodes is connected and orthoconvex.
11867822
Landmarks in Graphs
Navigation 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 new results are that the metric dimension of a graph with n nodes can be approximated in polynomial time within a factor of O(log n), and some properties of graphs with metric dimension two.
11015048
Centers of sets of pixels
Abstract The center of a connected graph G is the set of nodes of G for which the maximum distance to any other node of G is as small as possible. If G is a simply connected set of lattice points (“pixels”) with graph structure defined by 4-neighbor adjacency, we show that the center of G is either a 2×2 square block, a diagonal staircase, or a (dotted) diagonal line with no gaps.
1024289
Strong arcs in fuzzy graphs
An arc of a fuzzy graph is called strong if its weight is at least as great as the strength of connectedness of its end nodes when it is deleted. An arc is strong iff its weight is equal to the strength of connectedness of its end nodes. A bridge is strong, but a strong arc need not be a bridge. An arc of maximum weight is strong, but a strong arc need not have maximum weight. In a connected graph, there is a strong path (a path consisting of strong arcs) between any two nodes. A fuzzy graph is a fuzzy tree iff there is a unique strong path between any two of its nodes. In a fuzzy tree, an arc is strong iff it is a bridge, and a strong path between two nodes is a path of maximum strength between them.
1884675
Fuzzy end nodes in fuzzy graphs
We define a fuzzy end node in a fuzzy graph, and show that no node can be both a cut node and a fuzzy end node. In a fuzzy tree, every node is either a cut node or a fuzzy end node, but the converse is not true. We also show that any nontrivial fuzzy tree has at least two fuzzy end nodes, and we characterize fuzzy cycles that have no cut nodes or no fuzzy end nodes.
121993192
Recognition by Functional Parts
Abstract We present an approach to function-based object recognition that reasons about the functionality of an object's intuitive parts. We extend the popular "recognition by parts" shape recognition framework to support "recognition by functional parts," by combining a set of functional primitives and their relations with a set of abstract volumetric shape primitives and their relations. Previous approaches have relied on more global object features, often ignoring the problem of object segmentation and thereby restricting themselves to range images of unoccluded scenes. We show how these shape primitives and relations can be easily recovered from superquadric ellipsoids which, in turn, can be recovered from either range or intensity images of occluded scenes, Furthermore, the proposed framework supports both unexpected (bottom-up) object recognition and expected (top-down) object recognition, We demonstrate the approach on a simple domain by recognizing a restricted class of hand-tools from 2-D images.
203665251
Understanding Object Motion of Tools and Vehicles.
206614039
Array Grammars
This tutorial briefly introduces array grammars, in which rewriting rules involve replacement of subarrays by subarrays. Strings can be regarded as one-dimensional arrays; but as we shall see, in higher dimensions special problems arise. In this tutorial we consider only the twodimensional case, but the extension to arbitrary dimensions is straightforward. A more detailed review of array grammars of various types, as well as the corresponding types of array acceptors, can be found in [1]. Array grammars (like string grammars) can be regarded as a class of graph grammars, but it seems more natural to regard them as rewriting systems of a special type.
11359905
The function of documents
Abstract The purpose of a document is to facilitate the transfer of information from its author to its readers. It is the author's job to design the document so that the information it contains can be interpreted accurately and efficiently. To do this, the author can make use of a set of stylistic tools. In this paper, we introduce the concept of document functionality, which attempts to describe the roles of documents and their components in the process of transferring information. A functional description of a document provides insight into the type of the document, into its intended uses, and into strategies for automatic document interpretation and retrieval. To demonstrate these ideas, we define a taxonomy of functional document components and show how functional descriptions can be used to reverse-engineer the intentions of the author, to navigate in document space, and to provide important contextual information to aid in interpretation.
29950481
Graphbots: Mobility in Discrete Spaces
Most previous theoretical work on motion planning has addressed the problem of path planning for geometrically simple robots in geometrically simple regions of Euclidean space (e.g., a planar region containing polygonal obstacles). In this paper we define a natural version of the motion planning problem in a graph theoretic setting. We establish conditions under which a “robot” or team of robots having a particular graph structure can move from any start location to any goal destination in a graph-structured space.