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The Union-Find Problem Is Linear

by Hantao Zhang
"... This paper has an error and has been retracted. It should simply be deleted from Citeseer. Baring that, I am submitting this "correction". The union-find 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This paper has an error and has been retracted.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 union-find problem, also known as the disjoint set union problem, involves two operations, union and find, on a collection of disjoint sets

Union-Find with Constant Time Deletions

by Stephen Alstrup, Inge Li Gørtz, Theis Rauhe, Mikkel Thorup, Uri Zwick
"... A union-find 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 ..."
Abstract - Cited by 6 (1 self) - Add to MetaCart
A union-find 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

Union-Find With Deletions

by Haim Kaplan, Nira Shafrir, Robert E. Tarjan , 2002
"... In the classical union-find 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 ..."
Abstract - Cited by 8 (2 self) - Add to MetaCart
In the classical union-find 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 Union-Find Problem

by J.A. La Poutré - UTRECHT UNIVERSITY , 1989
"... A well-known 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 ..."
Abstract - Cited by 8 (0 self) - Add to MetaCart
for the individual instructions. The new lgorithm is important in all set-manipulation 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 UNION-FIND problem

Wait-free Parallel Algorithms for the Union-Find Problem

by Richard J. Anderson, Heather Woll - 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 Union-Find 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 ..."
Abstract - Cited by 51 (0 self) - Add to MetaCart
We are interested in designing efficient data structures for a shared memory multiprocessor. In this paper we focus on the Union-Find 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

by Alon Itai , 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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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 Union-Find Data Structure

by Sylvain Conchon
"... Abstract The problem of disjoint sets, also known as union-find, 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 union-find, consistsin maintaining a partition of a finite set within a data structure.

I/O-Efficient Batched Union-Find and Its . . .

by Pankaj K. Agarwal, et al.
"... Despite extensive study over the last four decades and numerous applications, no I/O-efficient al-gorithm is known for the union-find problem. In this paper we present an I/O-efficient algorithm for the batched (off-line) version of the union-find 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/O-efficient al-gorithm is known for the union-find problem. In this paper we present an I/O-efficient algorithm for the batched (off-line) version of the union-find problem. Given any sequence of N mixed union

Union-Find and Congruence Closure Algorithms that Produce Proofs

by Robert Nieuwenhuis, Albert Oliveras - 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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of view, the problem of extracting such small proofs.

Meldable Heaps and Boolean Union-Find (Extended Abstract)

by Haim Kaplan, Nira Shafrir, Robert E Tarjan , 2002
"... In the classical meldable heap data type we maintain an item-disjoint collection of heaps under the operations find-min, insert, delete, decrease-key, and meld. In the usual definition decrease-key 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 item-disjoint collection of heaps under the operations find-min, insert, delete, decrease-key, and meld. In the usual definition decrease-key and delete get the item and the heap containing it as parameters. We consider the modified problem
Results 1 - 10 of 38