Results 1  10
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1,671
Depth first search and linear graph algorithms
 SIAM JOURNAL ON COMPUTING
, 1972
"... The value of depthfirst search or "backtracking" as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components of an undirect ..."
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Cited by 1406 (19 self)
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of an undirect graph are presented. The space and time requirements of both algorithms are bounded by k 1V + k2E d k for some constants kl, k2, and k a, where Vis the number of vertices and E is the number of edges of the graph being examined.
Probabilistic Roadmaps for Path Planning in HighDimensional Configuration Spaces
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edg ..."
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Cited by 1277 (120 self)
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edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two
A distributed algorithm for minimumweight spanning trees
, 1983
"... A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange ..."
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Cited by 435 (3 self)
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A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm
Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
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Cited by 401 (2 self)
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We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest
Edgeconnectivity augmentations of graphs and hypergraphs
"... A. Frank (Augmenting graphs to meet edgeconnectivity requirements, ..."
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Cited by 3 (2 self)
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A. Frank (Augmenting graphs to meet edgeconnectivity requirements,
Edgeconnectivity augmentation with partition constraints
 SIAM J. Discrete Mathematics
, 1999
"... When k is even the minmax formula for the partitionconstrained problem is a natural generalization of [3]. However this generalization fails when k is odd. We show that at most one more edge is needed when k is odd and we characterize the graphs that require such an extra edge. ..."
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Cited by 17 (10 self)
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When k is even the minmax formula for the partitionconstrained problem is a natural generalization of [3]. However this generalization fails when k is odd. We show that at most one more edge is needed when k is odd and we characterize the graphs that require such an extra edge.
EdgeConnectivity Augmentation Preserving Simplicity
, 1997
"... Given a simple graph G = (V; E), the goal is to find a smallest set F of new edges such that G = (V; E [ F ) is kedgeconnected and simple. Very recently this problem was shown to be NPcomplete. In this paper we prove that if OPT k P is high enough  depending on k only  then OPT k S = OPT ..."
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Cited by 15 (8 self)
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Given a simple graph G = (V; E), the goal is to find a smallest set F of new edges such that G = (V; E [ F ) is kedgeconnected and simple. Very recently this problem was shown to be NPcomplete. In this paper we prove that if OPT k P is high enough  depending on k only  then OPT k S = OPT
When trees collide: An approximation algorithm for the generalized Steiner problem on networks
, 1994
"... We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with linkcosts and, for each pair fi; jg of nodes, an edgeconnectivity requirement r ij . The goal is to find a minimumcost network using the a ..."
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Cited by 249 (38 self)
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We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with linkcosts and, for each pair fi; jg of nodes, an edgeconnectivity requirement r ij . The goal is to find a minimumcost network using
Detachments Preserving Local EdgeConnectivity of Graphs
, 1999
"... Let G = (V + s, E) be a graph and let = (d 1 , ..., d p ) be a set of positive integers with splits s into a set of p independent vertices s 1 , ..., s p with d(s j ) = d j , 1 p. Given a requirement function r(u, v) on pairs of vertices of V , an is called radmissible if the detac ..."
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Cited by 11 (4 self)
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admissible if the detached graph G # satisfies #G # (x, y) for every pair x, y V . Here #H (u, v) denotes the local edgeconnectivity between u and v in graph H .
Geometric Compression through Topological Surgery
 ACM TRANSACTIONS ON GRAPHICS
, 1998
"... ... this article introduces a new compressed representation for complex triangulated models and simple, yet efficient, compression and decompression algorithms. In this scheme, vertex positions are quantized within the desired accuracy, a vertex spanning tree is used to predict the position of each ..."
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Cited by 283 (28 self)
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the geometric coherence of several ancestors in the vertex spanning tree, preserving the connectivity with no loss of information, avoiding vertex repetitions, and using about three times fewer bits for the connectivity. However, since decompression requires random access to all vertices, this method must
Results 1  10
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