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Finding and Maintaining Rigid Components
2005
Canadian Conference on Computational Geometry
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To this end, we introduce a new data structure problem called union pairfind, which maintains disjoint edge sets and supports pair-find queries of whether two vertices are spanned by a set. ...
We give the first complete analysis that the complexity of finding and maintaining rigid components of planar bar-and-joint frameworks and arbitrary d-dimensional body-and-bar frameworks, using a family ...
Conclusion We have presented a new data structure problem called union pair-find. ...
dblp:conf/cccg/LeeST05
fatcat:525rnfy7czekphrmumxvz5ggie
Data structures and algorithms for disjoint set union problems
1991
ACM Computing Surveys
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Special attention is devoted to recent extensions of the original set union problem, and an attempt is made to provide a unifying theoretical framework for this growing body of algorithms. ...
This paper surveys algorithmic techniques and data structures that have been proposed tosolve thesetunion problem and its variants, Thediscovery of these data structures required anew set ofalgorithmic ...
Blum [1986] proposed a data structure for the set union problem that supports each union and find in O(log n/log log n) time in the worst case. ...
doi:10.1145/116873.116878
fatcat:vlfyjncu6rhezdk7qvxrlivayu
Worst-case analysis of the set-union problem with extended backtracking
1989
Theoretical Computer Science
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A data structure is presented which maintains a partition of zn n-item set making it possible to perform each Union in O(1g lg n) time, each Find in O(lg n) time and allows backtracking over the Unions ...
Moreover, it is shown that the data structure can be slightly modified as to present an O(k i-in lg n) time complexity on a sequence of k Unions and Backtracks and m Finds. ...
In Section 4 a data structure for the union-@d-backtrack problem is introduced and its worst case time and space complexities are derived. ...
doi:10.1016/0304-3975(89)90119-9
fatcat:ezn6iw2rkrfhnkpzjbeidfzkfu
Union Find
[article]
2021
figshare.com
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In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets. ...
It provides operations for adding new sets, merging sets (replacing them by their union), and finding a representative member of a set. ...
Data structure. • Integer array id[] of size N. 11
network connectivity
quick find
quick union
improvements
applications
Quick-union [lazy approach]Data structure. a truism (roughly) since 1950 ...
doi:10.6084/m9.figshare.13669103.v1
fatcat:3asgmadjsvggrldlfne6crukjm
A partially persistent data structure for the set-union problem
1990
RAIRO - Theoretical Informatics and Applications
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The remainder of this paper is organized as follows: in section 2 we introducé a data structure for the Union-PFind problem, in section 3 we analyse its worst-case time and space complexity. ...
In this paper we consider an extension of the classical Set-Union problem, introducing a new kind of Find, referred as PFind, defined as follows: PFind(x, k)\ given an item xeS, return the name of the ...
doi:10.1051/ita/1990240201891
fatcat:lgjbtvvojvfsveczirvxu5evbe
Union-Find with Constant Time Deletions
[chapter]
2005
Lecture Notes in Computer Science
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A union-find data structure maintains a collection of disjoint sets under makeset, union and find operations. ...
We resolve this open problem by presenting a relatively simple modification of the classical union-find data structure that supports delete, as well as makeset and union, operations in constant time, while ...
) time, as it forms the basis of our new data structure for the union-find-delete problem. ...
doi:10.1007/11523468_7
fatcat:xkel5ldv6bcxlkh7mlxancpony
Union-Find with Constant Time Deletions
2014
ACM Transactions on Algorithms
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A union-find data structure maintains a collection of disjoint sets under makeset, union and find operations. ...
We resolve this open problem by presenting a relatively simple modification of the classical union-find data structure that supports delete, as well as makeset and union, operations in constant time, while ...
) time, as it forms the basis of our new data structure for the union-find-delete problem. ...
doi:10.1145/2636922
fatcat:2wvjhpdm75cjda775ikz2twryu
A persistent union-find data structure
2007
Proceedings of the 2007 workshop on Workshop on ML - ML '07
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The problem of disjoint sets, also known as union-find, consists in maintaining a partition of a finite set within a data structure. ...
This paper details the implementation of a persistent union-find data structure as efficient as its imperative counterpart. ...
We also thank the members of the Proval project for many discussions related to the persistent union-find problem. In particular, we are grateful to Claude Marché for mentioning T.-R. ...
doi:10.1145/1292535.1292541
dblp:conf/ml/ConchonF07
fatcat:f2dqeya3t5ag5e4mnay5oxzzva
A lower bound for the complexity of the Union-Split-Find problem
[chapter]
1987
Lecture Notes in Computer Science
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We prove a 8{loglogn) (i.e. matching upper and lower) bound on the complexity of the Union-Split-Find problem, a variant of the Union-Find problem . ...
We complement this with a 9(logn) bound for the Split-Find problem under the separation assumption. This shows that the separation assumption can imply an exponential loss in efficiency. ...
This is true for t he worst-case complexity and for the amortized complexity
Concl usions and Open Problems In this paper we proved several new lower hounds for the Union-Split-Find problem . ...
doi:10.1007/3-540-18088-5_41
fatcat:i5zsjvppkzcepnnvvjtnpru4ou
Semi-dynamic Connectivity in the Plane
[chapter]
2015
Lecture Notes in Computer Science
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Motivated by a path planning problem we consider the following procedure. Assume that we have two points s and t in the plane and take K = ∅. ...
We show how to add one set to K in O(1 + kα(n)) amortized time plus the time needed to find all sets of K intersecting the newly added set, where n is the cardinality of K, k is the number of sets in K ...
Acknowledgments We thank Chee Yap for posing to us the problem about connectivity under subdivisions. ...
doi:10.1007/978-3-319-21840-3_10
fatcat:i73ungmkwzhhzat6pdgn7t22de
Page 133 of Administrative Science Quarterly Vol. 4, Issue 1
[page]
1959
Administrative Science Quarterly
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Disregarding acknowledged weaknesses in the data, we find here a rather stimulating and promising discussion of the nature and consequences of different organizational control structures Among other problems ...
While the reader may not necessarily find in the authors’ new tech- ...
Semi-dynamic connectivity in the plane
[article]
2015
arXiv
pre-print
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Motivated by a path planning problem we consider the following procedure. Assume that we have two points s and t in the plane and take K=∅. ...
We show how to add one set to K in O(1+kα(n)) amortized time plus the time needed to find all sets of K intersecting the newly added set, where n is the cardinality of K, k is the number of sets in K intersecting ...
Acknowledgments We thank Chee Yap for posing to us the problem about connectivity under subdivisions. ...
arXiv:1502.03690v1
fatcat:6vm7a36oevd2pde3blrhydysu4
Don't rush into a union
2011
Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11
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For t U = Ω(t q ), the problem is equivalent to the well-understood union-find problem: INSERTEDGE(s, t) can be implemented by UNION(FIND(s), FIND(t)). ...
We present a new threshold phenomenon in data structure lower bounds where slightly reduced update times lead to exploding query times. ...
Concerning finds in the union-find data structure, we get one for each original find on a non-free node. ...
doi:10.1145/1993636.1993711
dblp:conf/stoc/PatrascuT11a
fatcat:fd6g22oi6rd3tnmp6h3w22z6wm
Don't Rush into a Union: Take Time to Find Your Roots
[article]
2011
arXiv
pre-print
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For t_u = Omega(t_q), the problem is equivalent to the well-understood union-find problem: InsertEdge(s,t) can be implemented by Union(Find(s), Find(t)). ...
We present a new threshold phenomenon in data structure lower bounds where slightly reduced update times lead to exploding query times. ...
Concerning finds in the union-find data structure, we get one for each original find on a non-free node. ...
arXiv:1102.1783v2
fatcat:n34xpbua45a3po2sx6tnskkjo4
Efficient union-find for planar graphs and other sparse graph classes
1998
Theoretical Computer Science
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We solve the Union-Find Problem (UF) efficiently for the case the input is restricted to several graph classes, namely partial k-trees for any fixed k, d-dimensional grids for any fixed dimension d and ...
By efficiency we do not only mean linear time in a theoretical setting but also a practical reorganization of memory such that a dynamic data structures for UF is allocated consecutively. ...
The real world bottleneck for Union-Find is the use of a dynamic data structure. ...
doi:10.1016/s0304-3975(97)00291-0
fatcat:zc2ae36f7zgqpjfh7a5ic3j5wm
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