The graph realization problem is that of computing the relative locations of a set of vertices placed in Euclidean space, relying only upon some set of inter-vertex distance measurements. This paper is concerned with the closely related problem of determining whether or not a graph has a unique realization. Both these problems are NP-hard, but the proofs rely upon special combinations of edge lengths. If one assumes the vertex locations are unrelated, then the uniqueness question can be approached from a purely graph theoretic angle that ignores edge lengths. This paper identifies three necessary graph theoretic conditions for a graph to have a unique realization in any dimension. Efficient sequential and NC algorithms are presented for each condition, although these algorithms have very different flavors in different dimensions.

Conditions for unique graph realizations

This paper shows that the weighted matching problem on general graphs can be solved in time O(n(m + n log n)), f or n and m the number of vertices and edges, respectively. This was previously known only for bipartite graphs. It also shows that a sequence of m nca and link operations on n nodes can be processed on-line in time O(ma(m, n)+n). This was previously known only for a restricted type of link operation.

Data structures for weighted matching and nearest common ancestors with linking

An Algorithm for Two-Dimensional Rigidity Percolation

Wireless localization techniques are an area that has attracted interest from both industry and academia, with self-localization capability providing a highly desirable characteristic of wireless sensor networks. Localization Algorithms and Strategies for Wireless Sensor Networks encompasses the significant and fast growing area of wireless localization techniques. This book provides comprehensive and up-to-date coverage of topics and fundamental theories underpinning measurement techniques and localization algorithms. A useful compilation for academicians, researchers, and practitioners, this Premier Reference Source contains relevant references and the latest studies emerging out of the wireless sensor network field.

Localization Algorithms and Strategies for Wireless Sensor Networks: Monitoring and Surveillance Techniques for Target Tracking

Display screen with animated graphical user interface

This paper presents improved algorithms for matroid-partitioning problems, such as finding a maximum cardinality set of edges of a graph that can be partitioned intok forests, and finding as many disjoint spanning trees as possible. The notion of a clump in a matroid sum is introduced, and efficient algorithms for clumps are presented. Applications of these algorithms are given to problems arising in the study of the structural rigidity of graphs, the Shannon switching game, and others.

Forests, frames, and games: Algorithms for matroid sums and applications

This paper presents improved algorithms for matroid partitioning problems, such as finding a maximum cardinality set of edges of a graph that can be partitioned into k forests. The notion of a clamp in a matroid sum is introduced. Efficient algorithms for problems involving clumps are presented. Applications of these algorithms to problems arising in the study of structural rigidity of graphs, the Shannon switching game and others are given.

Forests, frames, and games: algorithms for matroid sums and applications

Forests, Frames and Games: Algorithms for Matroid Sums and Applications ; CU-CS-446-89

A method and apparatus for laying out a plurality of instances of graphical objects within a view displayed on a graphical display device. The view contains one or more regions into which the instances may be placed. The placement is done by associating an attribute, parameter or variable with the definition of each of the instances of graphic objects. The attribute defines into which of the regions of the view the instance should be placed. Layout routines are provided to extract the value of the attribute from the definition of the instance of the graphic object and to use it to associate the instance with the region in which it is to be displayed. The layout routines then calculate an optimum display for all of the instances within the region. In addition, a method for moving the instances of the graphic objects from one region to another region This involves changing the value of the attribute and reordering the instances within the regions.

Region layout in a view on a graphical display screen

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Forests, frames, and games: Algorithms for matroid sums and applications

Forests, frames, and games: algorithms for matroid sums and applications

Forests, Frames and Games: Algorithms for Matroid Sums and Applications ; CU-CS-446-89

Region layout in a view on a graphical display screen