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An efficient upper bound of the rotation distance of binary trees

2000
*
Information Processing Letters
*

A polynomial time algorithm is developed for computing

doi:10.1016/s0020-0190(00)00008-9
fatcat:rnxdteqksbgtblpguwagw5nina
*an**upper**bound*for*the**rotation**distance**of**binary**trees*and equivalently for*the*diagonal-flip*distance**of*convex polygons triangulations. ... In Section 2, we have exhibited*an**upper**bound*δ(T , T )*of**the**rotation**distance*d(T , T ) using ordinal tools. According to*the*above theorem,*an*other*upper**bound*is given by δ(f (T ), f (T )). ... If f (T ) is*the*flexed*tree*corresponding to T , then we have d(f (T ), f (T )) = d(T , T ). We deduce in Section 4*an**efficient*algorithm for computing*an**upper**bound*µ(T , T )*of*d(T , T ). ...##
###
A Linear-Time Approximation Algorithm for Rotation Distance

2010
*
Journal of Graph Algorithms and Applications
*

In this short note, we give

doi:10.7155/jgaa.00212
fatcat:zuttie5y3fh73aqutlw3zer4mm
*an**efficient*, linear-time approximation algorithm, which estimates*the**rotation**distance*, within a provable factor*of*2, between ordered rooted*binary**trees*. ...*Rotation**distance*between rooted*binary**trees*measures*the*number*of*simple operations it takes to transform one*tree*into another. ... By*rotating*to right caterpillar*trees*, Culik and Wood [5] gave*an*immediate*upper**bound**of*2n − 2 for*the**distance*between two*trees*with n interior nodes. ...##
###
A Linear-Time Approximation Algorithm for Rotation Distance
[article]

2009
*
arXiv
*
pre-print

We give

arXiv:0903.0199v2
fatcat:gi6b325dojg7zkfadwp4t6fjhq
*an**efficient*, linear-time approximation algorithm, which estimates*the**rotation**distance*, within a provable factor*of*2, between ordered rooted*binary**trees*. . ...*Rotation**distance*between rooted*binary**trees*measures*the*number*of*simple operations it takes to transform one*tree*into another. ... By*rotating*to right caterpillar*trees*, Culik and Wood [5] gave*an*immediate*upper**bound**of*2n − 2 for*the**distance*between two*trees*with n interior nodes. ...##
###
Expected maximum vertex valence in pairs of polygonal triangulations

2015
*
Involve. A Journal of Mathematics
*

Edge-flip

doi:10.2140/involve.2015.8.763
fatcat:gvld6zuycrbihb5iqiismh3fju
*distance*between triangulations*of*polygons is equivalent to*rotation**distance*between rooted*binary**trees*. Both*distances*measure*the*extent*of*similarity*of*configurations. ...*The*best known exact universal*upper**bounds*on*rotation**distance*arise from measuring*the*maximum total valence*of*a vertex in*the*corresponding triangulation pair obtained by a duality construction. ...*Rotations*in*binary**trees*correspond to edge-flip moves in such triangulations*of*polygons, so*the**rotation**distance*between two rooted ordered*binary**trees*corresponds exactly to*the*edge-flip*distance*...##
###
Bounding restricted rotation distance

2003
*
Information Processing Letters
*

Cleary exhibited a linear

doi:10.1016/j.ipl.2003.08.004
fatcat:rgbl3xhkhfgm3lbohpnkqn5rne
*upper**bound**of*12n for*the*restricted*rotation**distance*between two*trees*with n interior nodes, and a lower*bound**of*(n − 1)/3 if*the*two*trees*satisfy a reduction condition. ... We obtain a significantly improved sharp*upper**bound**of*4n − 8 for restricted*rotation**distance*between two rooted*binary**trees*with n interior nodes, and a significantly improved sharp lower*bound**of*... Using metric estimates in this group, Cleary obtains*an**upper**bound**of*12n on*the*restricted*rotation**distance*between two*binary**trees*with n nodes. ...##
###
The Fermat star of binary trees

2009
*
Information Processing Letters
*

As

doi:10.1016/j.ipl.2009.02.001
fatcat:cqvko3pnove65obqihrlpv5tuu
*an**efficient*procedure for determining*the**rotation**distance**of*two*trees*is unknown, we will study*upper**bounds*on*the*total number δ*of**rotations*needed for transforming*the*given*trees*to a Fermat ...*The*technique*of*[4] was then adopted by Baril and Pallo for evaluating lower and*upper**bounds*on this*distance**efficiently*[1] . ...##
###
Distributions of restricted rotation distances

2021
*
The Art of Discrete and Applied Mathematics
*

There are linear

doi:10.26493/2590-9770.1374.bf0
fatcat:2ocbgugs3fgl5ly5oayy2gc4yy
*upper*and lower*bounds*on restricted*rotation**distance*with respect to*the*sizes*of**the*reduced*tree*pairs. ...*The*associated restricted*rotation*graph has*an**efficient**distance*algorithm. ... We note that*trees*realizing*the*lower*bound**of*restricted*rotation**distance*from [12] would have*an*RRD ratio limiting to 1, and those realizing*the**upper**bound*would have*an*RRD ratio limiting to 4 ...##
###
An Efficient Sampling Algorithm for Difficult Tree Pairs

2022
*
Acta Cybernetica
*

between

doi:10.14232/actacyb.285522
fatcat:evbcamhn4zdubneyzcex4tsucm
*an*arbitrary pair*of**trees*, (S, T), can be*efficiently*reduced to*the*problem*of*computing*the**rotation**distance*between a difficult pair*of**trees*(S', T'), where there is no known first step ... It is*an*open question whether there exists a polynomial-time algorithm for computing*the**rotation**distances*between pairs*of*extended ordered*binary*trees.The problem*of*computing*the**rotation**distance*... In many*of*these very specific cases, analysis to that family*of*instances can give coincident*upper*and lower*bounds*on*rotation**distance*, giving*an*exact calculation. ...##
###
An efficient sampling algorithm for difficult tree pairs
[article]

2020
*
arXiv
*
pre-print

*The*problem

*of*computing

*the*

*rotation*

*distance*between

*an*arbitrary pair

*of*

*trees*, (S, T), can be

*efficiently*reduced to

*the*problem

*of*computing

*the*

*rotation*

*distance*between a difficult pair

*of*

*trees*... It is

*an*open question whether there exists a polynomial-time algorithm for computing

*the*

*rotation*

*distances*between pairs

*of*extended ordered

*binary*

*trees*. ... One widely-considered

*tree*

*distance*metric on

*trees*with a natural left-to-right order on leaves is that

*of*

*the*

*rotation*

*distance*between a pair

*of*extended ordered

*binary*

*trees*. ...

##
###
Distributions of restricted rotation distances
[article]

2020
*
arXiv
*
pre-print

There are linear

arXiv:2005.00518v2
fatcat:guknzztbk5ctjln7zikcwjf3xu
*upper*and lower*bounds*on restricted*rotation**distance*with respect to*the*sizes*of**the*reduced*tree*pairs. ...*The*associated restricted*rotation*graph has*an**efficient**distance*algorithm. ... We note that*trees*realizing*the**the*lower*bound**of*restricted*rotation**distance*from [11] would have*an*RRD ratio limiting to 1, and those realizing*the**the**upper**bound*would have*an*RRD ratio limiting ...##
###
Efficient lower and upper bounds of the diagonal-flip distance between triangulations

2006
*
Information Processing Letters
*

We present

doi:10.1016/j.ipl.2006.07.001
fatcat:qfvdl4lglvfrfo2iiavvf6busi
*an**efficient*algorithm for computing lower and*upper**bounds**of*this*distance*between a pair*of*triangulations. ... There remains today*an*open problem whether*the**rotation**distance*between*binary**trees*or equivalently*the*diagonal-flip*distance*between triangulations can be computed in polynomial time. ... Acknowledgements We are grateful to*an*anonymous referee for*the*improvement*of**the*proofs*of*Theorems 4 and 5. ...##
###
Restricted rotation distance between binary trees

2002
*
Information Processing Letters
*

We obtain linear

doi:10.1016/s0020-0190(02)00315-0
fatcat:vy6ncgqlezgklkyu5sl5lwuc6y
*upper*and lower*bounds*for restricted*rotation**distance*in terms*of**the*number*of*interior nodes in*the**trees*. ... Restricted*rotation**distance*between pairs*of*rooted*binary**trees*measures differences in*tree*shape and is related to*rotation**distance*. ... With this minimal sufficient set*of*allowed*rotations*, we find*an**upper**bound**of*12n for*the*restricted*rotation**distance*between any two rooted*trees*with n nodes, and a lower*bound**of*(n − 1)/3 for*the*...##
###
BOUNDING RIGHT-ARM ROTATION DISTANCES

2007
*
International journal of algebra and computation
*

We describe several types

doi:10.1142/s0218196707003664
fatcat:zkedag5c6bh53amsynqperog4e
*of**rotation**distance*, and provide*upper**bounds*on*distances*between*trees*with a fixed number*of*nodes with respect to each type. ...*Rotation**distance*quantifies*the*difference in shape between two rooted*binary**trees**of**the*same size by counting*the*minimum number*of*elementary changes needed to transform one*tree*to*the*other. ... This produces*an**upper**bound**of*4n − 8 < 4n − 8 on*the*restricted right-arm*rotation**distance*between*the*two*trees*. ...##
###
Page 6641 of Mathematical Reviews Vol. , Issue 90K
[page]

1990
*
Mathematical Reviews
*

(I-SLRN)
On

*the**upper**bound*on*the**rotation**distance**of**binary**trees*. Inform. Process. Lett. 31 (1989), no. 2, 57-60. ... Summary: “*The**rotation**distance*d(7\,7>) between two*binary*search*trees*7; and 7> on nm nodes is*the*minimum number*of**rotations*needed to transform 7; into 7>. ...##
###
Rotation Distance is Fixed-Parameter Tractable
[article]

2009
*
arXiv
*
pre-print

*The*proof relies on

*the*kernalization

*of*

*the*initial

*trees*to

*trees*with size

*bounded*by 7k. ... In

*the*case

*of*ordered rooted

*trees*, we show that

*the*

*rotation*

*distance*between two ordered

*trees*is fixed-parameter tractable, in

*the*parameter, k,

*the*

*rotation*

*distance*. ... Conclusion We have shown that

*rotation*

*distance*

*of*ordered

*trees*is fixed-parameter tractable in parameter, k,

*the*

*distance*. ...

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