A data structure for dynamic trees

Sleator, Daniel D.; Tarjan, Robert E.

doi:10.1145/800076.802464

Cited by 333 publications

(534 citation statements)

References 13 publications

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“…This decomposition is used, e.g., in the dynamic-tree data structure [4]. Given a rooted tree T , define the weight of each node v of T be the size of the subtree rooted at v. For each nonleaf node v, let heavy(v) denote the child of v having greatest weight (breaking ties arbitrarily).…”

Section: Decomposition Of a Rooted Tree Into Pathsmentioning

confidence: 99%

Computing the Edit-Distance Between Unrooted Ordered Trees

Klein

1998

Algorithms — ESA’ 98

177

175

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Abstract. An ordered tree is a tree in which each node's incident edges are cyclically ordered; think of the tree as being embedded in the plane. Let A and B be two ordered trees. The edit distance between A and B is the minimum cost of a sequence of operations (contract an edge, uncontract an edge, modify the label of an edge) needed to transform A into B. We give an O(n 3 log n) algorithm to compute the edit distance between two ordered trees.

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Section: Decomposition Of a Rooted Tree Into Pathsmentioning

confidence: 99%

Computing the Edit-Distance Between Unrooted Ordered Trees

Klein

1998

Algorithms — ESA’ 98

177

175

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“…The weight of edge (x, y) is equal to the time at which we remove it from G, that is, the time at which x and y become directly disconnected. We store the maximum weight spanning forest F as an ST-tree [21], which allows connectivity queries and updates in O(log n) time.…”

Section: Computing the Reeb Graphmentioning

confidence: 99%

Trajectory Grouping Structure

Buchin

Kreveld³

et al. 2013

Lecture Notes in Computer Science

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Abstract.The collective motion of a set of moving entities like people, birds, or other animals, is characterized by groups arising, merging, splitting, and ending. Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept from topology. The trajectory grouping structure has three natural parameters that allow more global views of the data in group size, group duration, and entity inter-distance. We prove complexity bounds on the maximum number of maximal groups that can be present, and give algorithms to compute the grouping structure efficiently. We also study how the trajectory grouping structure can be made robust, that is, how brief interruptions of groups can be disregarded in the global structure, adding a notion of persistence to the structure. Furthermore, we showcase the results of experiments using data generated by the NetLogo flocking model and from the Starkey project. The Starkey data describe the movement of elk, deer, and cattle. Although there is no ground truth for the grouping structure in this data, the experiments show that the trajectory grouping structure is plausible and has the desired effects when changing the essential parameters. Our research provides the first complete study of trajectory group evolvement, including combinatorial, algorithmic, and experimental results.

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“…We keep a dynamic tree data structure [32] of T (for determining distances between nodes in T ) giving dashed edges length 0 and nondashed edges length 1. 2.…”

Section: Bipartitenessmentioning

confidence: 99%

“…The extended dynamic path data structure extends the dynamic path data structure of [32]. It represents a set of paths such that two paths are either vertex-disjoint or one path is contained in the other one.…”

Section: A Topology Tree T T For T Extended With the Following Labementioning

confidence: 99%

Average-Case Analysis of Dynamic Graph Algorithms

Alberts

Henzinger

1998

Algorithmica

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Abstract. We present a model for edge updates with restricted randomness in dynamic graph algorithms and a general technique for analyzing the expected running time of an update operation. This model is able to capture the average case in many applications, since (1) it allows restrictions on the set of edges which can be used for insertions and (2) the type (insertion or deletion) of each update operation is arbitrary, i.e., not random. We use our technique to analyze existing and new dynamic algorithms for the following problems: maximum cardinality matching, minimum spanning forest, connectivity, 2-edge connectivity, kedge connectivity, k-vertex connectivity, and bipartiteness. Given a random graph G with m 0 edges and n vertices and a sequence of l update operations such that the graph contains m i edges after operation i, the expected time for performing the updates for any l is O(l log n + l i=1 n/ √ m i ) in the case of minimum spanning forests, connectivity, 2-edge connectivity, and bipartiteness. The expected time per update operation is O(n) in the case of maximum matching. We also give improved bounds for k-edge and k-vertex connectivity. Additionally we give an insertions-only algorithm for maximum cardinality matching with worst-case O(n) amortized time per insertion.

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A data structure for dynamic trees

Cited by 333 publications

References 13 publications

Computing the Edit-Distance Between Unrooted Ordered Trees

Computing the Edit-Distance Between Unrooted Ordered Trees

Trajectory Grouping Structure

Average-Case Analysis of Dynamic Graph Algorithms

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