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Topologically Sweeping Visibility Complexes via Pseudotriangulations
, 1996
"... This paper describes a new algorithm for constructing the set of free bitangents of a collection of n disjoint convex obstacles of constant complexity. The algorithm runs in time O(n log n + k), where k is the output size, and uses O(n) space. While earlier algorithms achieve the same optimal run ..."
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Cited by 85 (9 self)
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This paper describes a new algorithm for constructing the set of free bitangents of a collection of n disjoint convex obstacles of constant complexity. The algorithm runs in time O(n log n + k), where k is the output size, and uses O(n) space. While earlier algorithms achieve the same optimal running time, this is the first optimal algorithm that uses only linear space. The visibility graph or the visibility complex can be computed in the same time and space. The only complicated data structure used by the algorithm is a splittable queue, which can be implemented easily using redblack trees. The algorithm is conceptually very simple, and should therefore be easy to implement and quite fast in practice. The algorithm relies on greedy pseudotriangulations, which are subgraphs of the visibility graph with many nice combinatorial properties. These properties, and thus the correctness of the algorithm, are partially derived from properties of a certain partial order on the faces of th...
Mobileassisted localization in wireless sensor networks
 In Proceedings of IEEE INFOCOM ’05
, 2005
"... Abstract — The localization problem is to determine an assignment of coordinates to nodes in a wireless adhoc or sensor network that is consistent with measured pairwise node distances. Most previously proposed solutions to this problem assume that the nodes can obtain pairwise distances to other n ..."
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Cited by 46 (2 self)
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Abstract — The localization problem is to determine an assignment of coordinates to nodes in a wireless adhoc or sensor network that is consistent with measured pairwise node distances. Most previously proposed solutions to this problem assume that the nodes can obtain pairwise distances to other nearby nodes using some ranging technology. However, for a variety of reasons that include obstructions and lack of reliable omnidirectional ranging, this distance information is hard to obtain in practice. Even when pairwise distances between nearby nodes are known, there may not be enough information to solve the problem uniquely. This paper describes MAL, a mobileassisted localization method which employs a mobile user to assist in measuring distances between node pairs until these distance constraints form a “globally rigid ” structure that guarantees a unique localization. We derive the required constraints on the mobile’s movement and the minimum number of measurements it must collect; these constraints depend on the number of nodes visible to the mobile in a given region. We show how to guide the mobile’s movement to gather a sufficient number of distance samples for node localization. We use simulations and measurements from an indoor deployment using the Cricket location system to investigate the performance of MAL, finding in realworld experiments that MAL’s median pairwise distance error is less than 1.5 % of the true node distance. I.
The cricket indoor location system
, 2005
"... Indoor environments present opportunities for a rich set of locationaware applications such as navigation tools for humans and robots, interactive virtual games, resource discovery, asset tracking, locationaware sensor networking etc. Typical indoor applications require better accuracy than what c ..."
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Cited by 35 (0 self)
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Indoor environments present opportunities for a rich set of locationaware applications such as navigation tools for humans and robots, interactive virtual games, resource discovery, asset tracking, locationaware sensor networking etc. Typical indoor applications require better accuracy than what current outdoor location systems provide. Outdoor location technologies such as GPS have poor indoor performance because of the harsh nature of indoor environments. Further, typical indoor applications require different types of location information such as physical space, position and orientation. This dissertation describes the design and implementation of the Cricket indoor location system that provides accurate location in the form of user space, position and orientation to mobile and sensor network applications. Cricket consists of location beacons that are attached to the ceiling of a building, and receivers, called listeners, attached to devices that need location. Each beacon periodically transmits its location information in an RF message. At the same time,
Computing the Visibility Graph via Pseudotriangulations
 In Proc. 11th Annu. ACM Sympos. Comput. Geom
, 1995
"... We show that the k free bitangents of a collection of n pairwise disjoint convex plane sets can be computed in time O(k+n log n) and O(n) working space. The algorithm uses only one advanced data structure, namely a splittable queue. We introduce (weakly) greedy pseudotriangulations, whose combinat ..."
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Cited by 31 (2 self)
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We show that the k free bitangents of a collection of n pairwise disjoint convex plane sets can be computed in time O(k+n log n) and O(n) working space. The algorithm uses only one advanced data structure, namely a splittable queue. We introduce (weakly) greedy pseudotriangulations, whose combinatorial properties are crucial for our method. 1 Introduction Consider a collection O of pairwise disjoint convex objects in the plane. We are interested in problems in which these objects arise as obstacles, either in connection with visibility problems where they can block the view from an other geometric object, or in motion planning, where these objects may prevent a moving object from moving along a straight line path. The visibility graph is a central object in such contexts. For polygonal obstacles the vertices of these polygons are the nodes of the visibility graph, and two nodes are connected by an arc if the corresponding vertices can see each other. [9] describes the first nontriv...
Lowdimensional embedding with extra information
 IN PROCEEDINGS OF THE 20TH ANNUAL ACM SYMPOSIUM ON COMPUTATIONAL GEOMETRY
, 2004
"... A frequently arising problem in computational geometry is whena physical structure, such as an adhoc wireless sensor network or ..."
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Cited by 22 (4 self)
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A frequently arising problem in computational geometry is whena physical structure, such as an adhoc wireless sensor network or
Visibility Graphs and Oriented Matroids
, 2002
"... We describe a set of necessary conditions for a given graph to be the visibility graph of a simple polygon. For every graph satisfying these conditions we show that a uniform rank 3 oriented matroid can be constructed in polynomial time, which if affinely coordinatizable yields a simple polygon whos ..."
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Cited by 11 (2 self)
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We describe a set of necessary conditions for a given graph to be the visibility graph of a simple polygon. For every graph satisfying these conditions we show that a uniform rank 3 oriented matroid can be constructed in polynomial time, which if affinely coordinatizable yields a simple polygon whose visibility graph is isomorphic to the given graph.
Planar embeddings of graphs with specified edge lengths
, 2007
"... We consider the problem of finding a planar straightline embedding of a graph with a prescribed Euclidean length on every edge. There has been substantial previous work on the problem without the planarity restrictions, which has close connections to rigidity theory, and where it is easy to see tha ..."
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Cited by 5 (1 self)
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We consider the problem of finding a planar straightline embedding of a graph with a prescribed Euclidean length on every edge. There has been substantial previous work on the problem without the planarity restrictions, which has close connections to rigidity theory, and where it is easy to see that the problem is NPhard. In contrast, we show that the problem is tractable—indeed, solvable in linear time on a real RAM—for straightline embeddings of planar 3connected triangulations, even if the outer face is not a triangle. This result is essentially tight: the problem becomes NPhard if we consider instead straightline embeddings of planar 3connected infinitesimally rigid graphs with unit edge lengths, a natural relaxation of triangulations in this context.