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28
Programming Parallel Algorithms
, 1996
"... In the past 20 years there has been treftlendous progress in developing and analyzing parallel algorithftls. Researchers have developed efficient parallel algorithms to solve most problems for which efficient sequential solutions are known. Although some ofthese algorithms are efficient only in a th ..."
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Cited by 238 (10 self)
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In the past 20 years there has been treftlendous progress in developing and analyzing parallel algorithftls. Researchers have developed efficient parallel algorithms to solve most problems for which efficient sequential solutions are known. Although some ofthese algorithms are efficient only in a theoretical framework, many are quite efficient in practice or have key ideas that have been used in efficient implementations. This research on parallel algorithms has not only improved our general understanding ofparallelism but in several cases has led to improvements in sequential algorithms. Unf:ortunately there has been less success in developing good languages f:or prograftlftling parallel algorithftls, particularly languages that are well suited for teaching and prototyping algorithms. There has been a large gap between languages
A Theory of Network Localization
, 2004
"... In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigid ..."
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Cited by 122 (12 self)
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In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.
Rigidity, Computation, and Randomization in Network Localization
 In Proceedings of IEEE INFOCOM ’04, Hong Kong
, 2004
"... In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigid ..."
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Cited by 112 (16 self)
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In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.
Planarity Testing in Parallel
, 1994
"... We present a parallel algorithm based on open ear decomposition to construct an embedding of a graph onto the plane or report that the graph is nonplanar. Our parallel algorithm runs on a CRCW PRAM in logarithmic time with a number of processors bounded by that needed for finding connected component ..."
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Cited by 33 (6 self)
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We present a parallel algorithm based on open ear decomposition to construct an embedding of a graph onto the plane or report that the graph is nonplanar. Our parallel algorithm runs on a CRCW PRAM in logarithmic time with a number of processors bounded by that needed for finding connected components in a graph and for performing bucket sort.
Parallel Open Ear Decomposition with Applications to Graph Biconnectivity and Triconnectivity
 Synthesis of Parallel Algorithms
, 1992
"... This report deals with a parallel algorithmic technique that has proved to be very useful in the design of efficient parallel algorithms for several problems on undirected graphs. We describe this method for searching undirected graphs, called "open ear decomposition", and we relate thi ..."
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Cited by 26 (9 self)
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This report deals with a parallel algorithmic technique that has proved to be very useful in the design of efficient parallel algorithms for several problems on undirected graphs. We describe this method for searching undirected graphs, called "open ear decomposition", and we relate this decomposition to graph biconnectivity. We present an efficient parallel algorithm for finding this decomposition and we relate it to a sequential algorithm based on depthfirst search. We then apply open ear decomposition to obtain an efficient parallel algorithm for testing graph triconnectivity and for finding the triconnnected components of a graph.
Improved algorithms for graph fourconnectivity
 J. Comp. System Sci
, 1991
"... We present a new algorithm based on open ear decomposition for testing vertex fourconnectivity and for finding all separating triplets in a triconnected graph. A sequential implementation of our algorithm runs in O(n 2) time and a parallel implementation runs in O(log 2 n) time using O(n 2) process ..."
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Cited by 22 (5 self)
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We present a new algorithm based on open ear decomposition for testing vertex fourconnectivity and for finding all separating triplets in a triconnected graph. A sequential implementation of our algorithm runs in O(n 2) time and a parallel implementation runs in O(log 2 n) time using O(n 2) processors on an ARBITRARY CRCW PRAM, where n is the number of vertices in the graph. This improves previous bounds for the problem for both the sequential and parallel cases. The sequential time bound is the best possible, to within a constant factor, if the input is specified in adjacency matrix form, or if the input graph is dense. 1.
Operations on rigid formations of autonomous agents
 COMMUNICATIONS IN INFORMATION AND SYSTEMS
, 2004
"... This paper is concerned with the maintenance of rigid formations of mobile autonomous agents. A key element in all future multiagent systems will be the role of sensor and communication networks as an integral part of coordination. Network topologies are critically important for autonomous systems ..."
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Cited by 21 (10 self)
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This paper is concerned with the maintenance of rigid formations of mobile autonomous agents. A key element in all future multiagent systems will be the role of sensor and communication networks as an integral part of coordination. Network topologies are critically important for autonomous systems involving mobile underwater, ground and air vehicles and for sensor networks. This paper focuses on developing techniques and strategies for the analysis and design of sensor and network topologies required to achieve a rigid formation for cooperative tasks. Energy efficiency and communication bandwidth are critically important in formations of mobile autonomous agents, and hence strategies that make efficient use of power and energy are beneficial. Therefore, we develop topologies for providing sensing and communications with the minimum number of links, and propose methods requiring the minimum number of changes in the set of links in dynamic missions and maneuvers, including agent departure from a rigid formation, splitting a rigid formation and merging rigid subformations. To do this in a systematic manner, it is necessary to develop a framework for modeling agent formations that characterizes the sensing and communication links needed to maintain the formations. The challenge is that a comprehensive theory of such topologies of formations with sensing and communication limitations is in the earliest stage of development. Central to the development of these techniques and strategies will be the use of tools from rigidity theory, and graph theory.
Towards overcoming the transitiveclosure bottleneck: efficient parallel algorithms for planar digraphs
 J. Comput. System Sci
, 1993
"... Abstract. Currently, there is a significant gap between the best sequential and parallel complexities of many fundamental problems related to digraph reachability. This complexity bottleneck essentially reflects a seemingly unavoidable reliance on transitive closure techniques in parallel algorithms ..."
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Cited by 11 (1 self)
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Abstract. Currently, there is a significant gap between the best sequential and parallel complexities of many fundamental problems related to digraph reachability. This complexity bottleneck essentially reflects a seemingly unavoidable reliance on transitive closure techniques in parallel algorithms for digraph reachability. To pinpoint the nature of the bottleneck, we de* velop a collection of polylogtime reductions among reachability problems. These reductions use only linear processors and work for general graphs. Furthermore, for planar digraphs, we give polylogtime algorithms for the following problems: (1) directed ear decomposition, (2) topological ordering, (3) digraph reachability, (4) descendent counting, and (5) depthfirst search. These algorithms use only linear processors and therefore reduce the complexity to within a polylog factor of optimal.
Limit Points for Average Genus (I): 3Connected and 2Connected Simplicial Graphs
 J. Combinatorial Theory B
, 1992
"... It is demonstrated that a given value of average genus is shared by at most finitely many 2connected simplicial graphs and by at most finitely many 3connected graphs. Moreover, the distribution of values of average genus is sparse, in the following sense: within any finite real interval, there are ..."
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Cited by 10 (5 self)
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It is demonstrated that a given value of average genus is shared by at most finitely many 2connected simplicial graphs and by at most finitely many 3connected graphs. Moreover, the distribution of values of average genus is sparse, in the following sense: within any finite real interval, there are at most finitely many different numbers that are values of average genus for 2connected simplicial graphs or for 3connected graphs. Thus, there are no limit points for the values of average genus of graphs in these classes. The potential applicability of these results to graph isomorphism testing is considered. April 27, 1992 1 Supported by Engineering Excellence Award from Texas A&M University. 2 Supported by ONR Contract N00014850768. CUCS02092 1 Introduction In this paper, one of a series, a topological invariant of recent interest, the average genus of graphs, is investigated. By the average genus of a graph G, we mean the average value of the genus of the imbedding surfa...