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A Persistent UnionFind Data Structure
"... Abstract The problem of disjoint sets, also known as unionfind, consistsin maintaining a partition of a finite set within a data structure. ..."
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Abstract The problem of disjoint sets, also known as unionfind, consistsin maintaining a partition of a finite set within a data structure.
A PotentialBased Amortized Analysis of th e UnionFind Data Structur e
, 2000
"... Abstract. We present a simple, new potentialbased amortized analysis for the standar d unionfind data structure. Key words. Amortized analysis, potential functions, disjoint sets, Tarjan's multiple partitioning, Ackermann's function AMS(MOS) subject classifications. 68P05, 68Q25, 68R9 9 ..."
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Abstract. We present a simple, new potentialbased amortized analysis for the standar d unionfind data structure. Key words. Amortized analysis, potential functions, disjoint sets, Tarjan's multiple partitioning, Ackermann's function AMS(MOS) subject classifications. 68P05, 68Q25, 68R9 9
Unionfind volume segmentation
 In 7th International Workshop on Combinatorial Image Analysis (IWCIA'00), pp 181197
, 2000
"... We present an efficient method to segment large 3d images that takes the whole 3dimensional structure into account. We use a UnionFind data structure to record and maintain the necessary informations during the segmentation process. This structure leads to a volume labelling and facilitates intera ..."
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We present an efficient method to segment large 3d images that takes the whole 3dimensional structure into account. We use a UnionFind data structure to record and maintain the necessary informations during the segmentation process. This structure leads to a volume labelling and facilitates
UnionFind with Constant Time Deletions
"... A unionfind data structure maintains a collection of disjoint sets under makeset, union and find operations. Kaplan, Shafrir and Tarjan [SODA 2002] designed data structures for an extension of the unionfind problem in which elements of the sets maintained may be deleted. The cost of a delete opera ..."
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Cited by 6 (1 self)
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A unionfind data structure maintains a collection of disjoint sets under makeset, union and find operations. Kaplan, Shafrir and Tarjan [SODA 2002] designed data structures for an extension of the unionfind problem in which elements of the sets maintained may be deleted. The cost of a delete
Waitfree Parallel Algorithms for the UnionFind Problem
 In Proc. 23rd ACM Symposium on Theory of Computing
, 1994
"... We are interested in designing efficient data structures for a shared memory multiprocessor. In this paper we focus on the UnionFind data structure. We consider a fully asynchronous model of computation where arbitrary delays are possible. Thus we require our solutions to the data structure problem ..."
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We are interested in designing efficient data structures for a shared memory multiprocessor. In this paper we focus on the UnionFind data structure. We consider a fully asynchronous model of computation where arbitrary delays are possible. Thus we require our solutions to the data structure
I/OEfficient Batched UnionFind and Its . . .
"... Despite extensive study over the last four decades and numerous applications, no I/Oefficient algorithm is known for the unionfind problem. In this paper we present an I/Oefficient algorithm for the batched (offline) version of the unionfind problem. Given any sequence of N mixed union andfin ..."
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arises from problems in terrain analysis. A terrain can be abstracted as a height function defined over R2, and many problems that deal with suchfunctions require a unionfind data structure. With the emergence of modern mapping technologies, huge amount of data is being generated that is too large
Linear Time Restricted Union/Find
, 2006
"... We consider the following restricted Union/find problem: The universe is [0..n−1] and the unions are restricted to sets of consecutive integers. Initially all the sets are singletons. To maintain the above condition, a union between sets A and B, Union(A, B), is permitted only if max{A} = min{B} − ..."
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universes, such that the kth microuniverse consists of [(k − 1)b.. kb − 1]. The data structure consists of two tiers. The upper one is a regular Union/find data structure whose universe consists of the first and last element of each microuniverse (a total of 2n/b elements). The operations on this set are macrofind
I/Oefficient batched unionfind and its applications to terrain analysis
 IN PROC. 22ND ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY
, 2006
"... Despite extensive study over the last four decades and numerous applications, no I/Oefficient algorithm is known for the unionfind problem. In this paper we present an I/Oefficient algorithm for the batched (offline) version of the unionfind problem. Given any sequence of N union and find opera ..."
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Cited by 23 (9 self)
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because of its applications in terrain analysis. A terrain can be abstracted as a height function defined over R2, and many problems that deal with such functions require a unionfind data structure. With the emergence of modern mapping technologies, huge amount of elevation data is being generated
Reference Counting in Library Design – Optionally and with UnionFind Optimization
"... Reference counting has been used and described in abundance. We present novel ideas aimed at class implementations in library design: (1) In library design, generic classes can have variable size, such that an optimal decision for or against reference counting is not possible. We postpone this decis ..."
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based on an unionfind data structure. (3) Reference counting and polymorphic class hierarchies can be combined reusing the pointer in the handle class for the polymorphism. A policybased generic C++ solution realizes all ideas. Standard allocators manage all dynamic memory.
Reference Counting in Library Design – Optionally and with UnionFind Optimization
"... Reference counting has been used and described in abundance. We present novel ideas aimed at class implementations in library design: (1) In library design, generic classes can have variable size, such that an optimal decision for or against reference counting is not possible. We postpone this decis ..."
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based on an unionfind data structure. (3) Reference counting and polymorphic class hierarchies can be combined reusing the pointer in the handle class for the polymorphism. A policybased generic C++ solution realizes all ideas. Standard allocators manage all dynamic memory.
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