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Finding and Maintaining Rigid Components

2005
*
Canadian Conference on Computational Geometry
*

To this end, we introduce

dblp:conf/cccg/LeeST05
fatcat:525rnfy7czekphrmumxvz5ggie
*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*. ...##
###
Data structures and algorithms for disjoint set union problems

1991
*
ACM Computing Surveys
*

Special attention is devoted to recent extensions of

doi:10.1145/116873.116878
fatcat:vlfyjncu6rhezdk7qvxrlivayu
*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. ...##
###
Worst-case analysis of the set-union problem with extended backtracking

1989
*
Theoretical Computer Science
*

*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. ...

##
###
Union Find
[article]

2021
*
figshare.com
*

In computer science,

doi:10.6084/m9.figshare.13669103.v1
fatcat:3asgmadjsvggrldlfne6crukjm
*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 ...##
###
A partially persistent data structure for the set-union problem

1990
*
RAIRO - Theoretical Informatics and Applications
*

*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*...

##
###
Union-Find with Constant Time Deletions
[chapter]

2005
*
Lecture Notes in Computer Science
*

*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*. ...

##
###
Union-Find with Constant Time Deletions

2014
*
ACM Transactions on Algorithms
*

*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*. ...

##
###
A persistent union-find data structure

2007
*
Proceedings of the 2007 workshop on Workshop on ML - ML '07
*

*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. ...

##
###
A lower bound for the complexity of the Union-Split-Find problem
[chapter]

1987
*
Lecture Notes in Computer Science
*

We prove

doi:10.1007/3-540-18088-5_41
fatcat:i5zsjvppkzcepnnvvjtnpru4ou
*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*. ...##
###
Semi-dynamic Connectivity in the Plane
[chapter]

2015
*
Lecture Notes in Computer Science
*

Motivated by

doi:10.1007/978-3-319-21840-3_10
fatcat:i73ungmkwzhhzat6pdgn7t22de
*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. ...##
###
Page 133 of Administrative Science Quarterly Vol. 4, Issue 1
[page]

1959
*
Administrative Science Quarterly
*

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

Motivated by

arXiv:1502.03690v1
fatcat:6vm7a36oevd2pde3blrhydysu4
*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. ...##
###
Don't rush into a union

2011
*
Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11
*

*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. ...

##
###
Don't Rush into a Union: Take Time to Find Your Roots
[article]

2011
*
arXiv
*
pre-print

*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. ...

##
###
Efficient union-find for planar graphs and other sparse graph classes

1998
*
Theoretical Computer Science
*

We solve

doi:10.1016/s0304-3975(97)00291-0
fatcat:zc2ae36f7zgqpjfh7a5ic3j5wm
*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*. ...
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