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23
Quantum query complexity of some graph problems
 Proceedings of the 31st International Colloquium on Automata, Lanaguages, and Programming
, 2004
"... Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency listlike array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity, Strong Connectivity, Minimum Spanning Tree, and Single Sourc ..."
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Cited by 40 (3 self)
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Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency listlike array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity, Strong Connectivity, Minimum Spanning Tree, and Single Source Shortest Paths. For example we show that the query complexity of Minimum Spanning Tree is in Θ(n 3/2) in the matrix model and in Θ ( √ nm) in the array model, while the complexity of Connectivity is also in Θ(n 3/2) in the matrix model, but in Θ(n) in the array model. The upper bounds utilize search procedures for finding minima of functions under various conditions.
LinearTime PointerMachine Algorithms for Least Common Ancestors, MST Verification, and Dominators
 IN PROCEEDINGS OF THE THIRTIETH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1998
"... We present two new data structure toolsdisjoint set union with bottomup linking, and pointerbased radix sortand combine them with bottomlevel microtrees to devise the first lineartime pointermachine algorithms for offline least common ancestors, minimum spanning tree (MST) verification, ..."
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Cited by 27 (4 self)
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We present two new data structure toolsdisjoint set union with bottomup linking, and pointerbased radix sortand combine them with bottomlevel microtrees to devise the first lineartime pointermachine algorithms for offline least common ancestors, minimum spanning tree (MST) verification, randomized MST construction, and computing dominators in a flowgraph.
Practical Parallel Algorithms for Minimum Spanning Trees
 In Workshop on Advances in Parallel and Distributed Systems
, 1998
"... We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m=n p, where p is the number of processors. For this case, we show that simple algorithms with dataindependent communication patterns ..."
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Cited by 16 (0 self)
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We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m=n p, where p is the number of processors. For this case, we show that simple algorithms with dataindependent communication patterns are efficient, both in theory and in practice. The algorithms are evaluated theoretically using Valiant's BSP model of parallel computation and empirically through implementation results.
Segmentation Graph Hierarchies
 In: Proceedings of Joint Workshops on Structural, Syntactic, and Statistical Pattern Recognition S+SSPR. Volume 3138 of Lecture Notes in Computer Science
, 2004
"... The region's internal properties (color, texture, ...) help to identify them and their external relations (adjacency, inclusion, ...) are used to build groups of regions having a particular consistent meaning in a more abstract context. Lowlevel cue image segmentation in a bottomup way, cannot ..."
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Cited by 12 (5 self)
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The region's internal properties (color, texture, ...) help to identify them and their external relations (adjacency, inclusion, ...) are used to build groups of regions having a particular consistent meaning in a more abstract context. Lowlevel cue image segmentation in a bottomup way, cannot and should not produce a complete final "good" segmentation. We present a hierarchical partitioning of images using a pairwise similarity function on a graphbased representation of an image.
What is a matroid?
, 2007
"... Matroids were introduced by Whitney in 1935 to try to capture abstractly the essence of dependence. Whitney’s definition embraces a surprising diversity of combinatorial structures. Moreover, matroids arise naturally in combinatorial optimization since they are precisely the structures for which th ..."
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Cited by 10 (0 self)
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Matroids were introduced by Whitney in 1935 to try to capture abstractly the essence of dependence. Whitney’s definition embraces a surprising diversity of combinatorial structures. Moreover, matroids arise naturally in combinatorial optimization since they are precisely the structures for which the greedy algorithm works. This survey paper introduces matroid theory, presents some of the main theorems in the subject, and identifies some of the major problems of current research interest.
Grouping and Segmentation in a Hierarchy of Graphs
 Proceeding of the 16th IS&T/SPIE Annual Symposium
, 2004
"... We review multilevel hierarchies under the special aspect of their potential for segmentation and grouping. The onetoone correspondence between salient image features and salient model features are a limiting assumption that makes prototypical or generic object recognition impossible. The region’s ..."
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Cited by 5 (0 self)
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We review multilevel hierarchies under the special aspect of their potential for segmentation and grouping. The onetoone correspondence between salient image features and salient model features are a limiting assumption that makes prototypical or generic object recognition impossible. The region’s internal properties (color, texture, shape,...) help to identify them and their external relations (adjacency, inclusion, similarity of properties) are used to build groups of regions having a particular consistent meaning in a more abstract context. Lowlevel cue image segmentation in a bottomup way, cannot and should not produce a complete final “good” segmentation. We present a hierarchical partitioning of images using a pairwise similarity function on a graphbased representation of an image. This function measures the difference along the boundary of two components relative to a measure of differences of the components ’ internal differences. Two components are merged if there is a lowcost connection between them. We use this idea to find region borders quickly and effortlessly in a bottomup way, based on local differences in a specific feature. The aim of this paper is to build a minimum weight spanning tree (MST) in order to find region borders quickly in a bottomup ’stimulusdriven ’ way based on local differences in a specific feature.
Hierarchical image partitioning using combinatorial maps
 Technical University Vienna
, 2005
"... We present a hierarchical partitioning of images using a pairwise similarity function on a combinatorial map based representation. We used the idea of minimal spanning tree to find region borders quickly and effortlessly in a bottomup way, based on local differences in a color space. The result is ..."
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Cited by 4 (0 self)
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We present a hierarchical partitioning of images using a pairwise similarity function on a combinatorial map based representation. We used the idea of minimal spanning tree to find region borders quickly and effortlessly in a bottomup way, based on local differences in a color space. The result is a hierarchy of partitions with multiple resolutions suitable for further goal driven analysis. The algorithm can handle large variation and gradient intensity in images. Dual graph pyramid representations lack the explicit encoding of edge orientation around vertices i.e they lack an explicit encoding of the orientation of planes, existing in combinatorial maps. Moreover with combinatorial maps, the dual must not be explicitly represented because one map is enough to fully characterize the partition. 1
Quantum Clustering Algorithms
"... de Montréal, Département d’informatique et de recherche opérationnelle ..."
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Cited by 3 (0 self)
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de Montréal, Département d’informatique et de recherche opérationnelle
The Diameter of the Minimum Spanning Tree of a Complete Graph
"... } be independent identically distributed weights for the edges of Kn. If Xi � = Xj for i � = j, then ..."
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Cited by 3 (1 self)
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} be independent identically distributed weights for the edges of Kn. If Xi � = Xj for i � = j, then
Minimal Congestion Trees
, 2004
"... Abstract. Let G be a graph and let T be a tree with the same vertex set. Let e be an edge of T and Ae and Be be the vertex sets of the components of T obtained after removal of e. Let EG(Ae, Be) be the set of edges of G with one endvertex in Ae and one endvertex in Be. Let The paper is devoted to mi ..."
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Cited by 3 (1 self)
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Abstract. Let G be a graph and let T be a tree with the same vertex set. Let e be an edge of T and Ae and Be be the vertex sets of the components of T obtained after removal of e. Let EG(Ae, Be) be the set of edges of G with one endvertex in Ae and one endvertex in Be. Let The paper is devoted to minimization of ec(G: T) • Over all trees with the same vertex set as G. • Over all spanning trees of G. ec(G: T): = max EG(Ae, Be). e These problems can be regarded as “congestion ” problems.