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The UnionFind Problem Is Linear
"... This paper has an error and has been retracted. It should simply be deleted from Citeseer. Baring that, I am submitting this "correction".
The unionfind problem, also known as the disjoint set union problem, involves two operations, union and find, on a collection of disjoint sets. Th ..."
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This paper has an error and has been retracted. It should simply be deleted from Citeseer. Baring that, I am submitting this "correction".
The unionfind problem, also known as the disjoint set union problem, involves two operations, union and find, on a collection of disjoint sets
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
UnionFind With Deletions
, 2002
"... In the classical unionfind problem we maintain a partition of a universe of n elements into disjoint sets subject to the operations union and find. The operation union(A; B;C) replaces sets A and B in the partition by their union, given the name C. The operation find(x) returns the name of the set ..."
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Cited by 8 (2 self)
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In the classical unionfind problem we maintain a partition of a universe of n elements into disjoint sets subject to the operations union and find. The operation union(A; B;C) replaces sets A and B in the partition by their union, given the name C. The operation find(x) returns the name of the set
New Techniques for the UnionFind Problem
 UTRECHT UNIVERSITY
, 1989
"... A wellknown result of Tarjan (cf. [10]) states that a program of up to n UNION and m FIND instructions can be executed in O(n + m.c(m, n)) time on a collection of n elements, where a(m, n) denotes the functional inverse of Ackermann's function. In this paper we develop a new approach to the ..."
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Cited by 8 (0 self)
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for the individual instructions. The new lgorithm is important in all setmanipulation problems that require frequent FIND's. Because a(m, n) is O(1) in all practical cases, the new lgorithms guarantees that FIND's are essentially O(1) worst case, within the optimal bound for the UNIONFIND problem
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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Cited by 51 (0 self)
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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
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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Cited by 4 (0 self)
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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
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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Cited by 8 (0 self)
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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.
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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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
UnionFind and Congruence Closure Algorithms that Produce Proofs
 2nd International Workshop on Pragmatics of Decision Procedures in Automated Reasoning
, 2004
"... Congruence closure algorithms are nowadays central in many modern applications in automated deduction and verification, where it is frequently required to recover the set of merge operations that caused the equivalence of a given pair of terms. For this purpose we study, from the algorithmic point o ..."
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Cited by 3 (0 self)
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of view, the problem of extracting such small proofs.
Meldable Heaps and Boolean UnionFind (Extended Abstract)
, 2002
"... In the classical meldable heap data type we maintain an itemdisjoint collection of heaps under the operations findmin, insert, delete, decreasekey, and meld. In the usual definition decreasekey and delete get the item and the heap containing it as parameters. We consider the modified problem whe ..."
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In the classical meldable heap data type we maintain an itemdisjoint collection of heaps under the operations findmin, insert, delete, decreasekey, and meld. In the usual definition decreasekey and delete get the item and the heap containing it as parameters. We consider the modified problem
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