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On polynomial time isomorphisms of some new complete sets

1978
*
Journal of computer and system sciences (Print)
*

*ISOMORPHISMS*OF NP

*COMPLETE*SETS We recall that NP, PTAPE,

*and*EXTAPE denote, respectively,

*the*families of languages acceptable in nondeterministic

*polynomial*

*time*, in

*polynomial*tape,

*and*exponential ...

*problems*arising in number theory are p-

*isomorphic*to

*the*classical NP

*complete*

*problems*

*and*to point out that

*the*other

*complete*

*problems*are easily seen to be p-

*isomorphic*to

*the*previously known

*complete*...

##
###
Towards an Isomorphism Dichotomy for Hereditary Graph Classes

2017
*
Theory of Computing Systems
*

First, we develop a methodology to show

doi:10.1007/s00224-017-9775-8
fatcat:7afqdktaubhtll2kklqcdzvbeq
*isomorphism**completeness*of*the**isomorphism**problem**on*graph classes by providing a general framework unifying various reduction techniques. ... We show that*isomorphism*of graphs of bounded generalized color valence can be solved in*polynomial**time*. ... Acknowledgments I thank Matasha Mazis for inspiring comments*and*suggestions. P. Schweitzer ...##
###
On the Complexity of Polytope Isomorphism Problems
[article]

2002
*
arXiv
*
pre-print

*The*main difference between

*the*current

*and*

*the*former version is a new

*polynomial*

*time*algorithm for polytope

*isomorphism*in bounded dimension that does not rely

*on*Luks

*polynomial*

*time*algorithm for ...

*On*

*the*other hand, we give a

*polynomial*

*time*algorithm for

*the*combinatorial polytope

*isomorphism*

*problem*in bounded dimensions. ... Ziegler for careful reading an earlier version of

*the*paper

*and*for stimulating discussions, in particular, for bringing Bayer's work [3] to our attention. ...

##
###
Testing homotopy equivalence is isomorphism complete

1986
*
Discrete Applied Mathematics
*

It is shown that homotopy equivalence of finite topological spaces is

doi:10.1016/0166-218x(86)90074-0
fatcat:6d6wh7dx4jcwxa3pkizer2bppm
*polynomially*equivalent to testing graph*isomorphism*. ... Introduction A*problem*that is*polynomial**time*equivalent to graph*isomorphism*is known as*isomorphism**complete*([l] , [2] , [3] , [51, [6] ). ... So q~ restricted to X is an*isomorphism*of X*and*Y. Thus*the*transformation X~)( is a*polynomial**time*reduction of poser*isomorphism*to*isomorphism*of cores. ...##
###
Page 662 of Mathematical Reviews Vol. , Issue 95b
[page]

1995
*
Mathematical Reviews
*

*The*authors derive from

*the*interactive proof theory 05 COMBINATORICS 662

*the*fact that if

*the*graph

*isomorphism*

*problem*is NP-

*complete*, then

*the*

*polynomial*-

*time*hierarchy collapses. ... Chapter 2 introduces

*the*

*polynomial*-

*time*hierarchy (of complexity classes between NP

*and*PSPACE),

*and*

*the*class IP of

*problems*that admit interactive proof systems. ...

##
###
Graph isomorphism is in the low hierarchy

1988
*
Journal of computer and system sciences (Print)
*

This implies that this

doi:10.1016/0022-0000(88)90010-4
fatcat:4l6j2onzijbslnow4v6g34m3mu
*problem*is not NP-*complete*(even under weaker forms of*polynomial*reducibilities, like y-reducibility) unless*the**polynomial*-*time*hierarchy collapses to some finite level. ... It is shown that*the*graph*isomorphism**problem*is located in level L$ of*the*low hierarchy in NP. ... ACKNOWLEDGMENTS*The*author thanks Oded Goldreich, Ker-I Ko, Kurt Mehlhorn, Silvio Micah, Osamu Watanabe, Klaus Wagner,*and**the*anonymous referee for their constructive criticism*on**the*earlier versions ...##
###
On the GI-Completeness of a Sorting Networks Isomorphism
[article]

2016
*
arXiv
*
pre-print

*isomorphism*

*problem*can be efficiently solved in

*polynomial*

*time*. ...

*The*main consequence of our work is that currently no

*polynomial*-

*time*algorithm exists for solving

*the*BZ sorting network subitemset

*isomorphism*

*problem*; however

*the*CM (Choi

*and*Moon) sorting network ... Moreover, we show that

*the*Itemset

*Isomorphism*

*problem*is GI-

*Complete*; that is

*polynomial*-

*time*equivalent to

*the*Graph

*Isomorphism*(GI)

*problem*. ...

##
###
Page 3129 of Mathematical Reviews Vol. , Issue 82g
[page]

1982
*
Mathematical Reviews
*

*The*resulting ‘intermediate’ complexity status of

*the*

*problem*has incited

*the*investigation into

*isomorphism*

*complete*

*problems*,

*problems*which are

*polynomial*

*time*equivalent to

*the*graph

*isomorphism*

*problem*... From

*the*text: “

*The*purpose of this paper is to collect together some new

*and*old results

*on*

*isomorphism*

*complete*matrix

*problems*. ...

##
###
The comparison of tree-sibling time consistent phylogenetic networks is graph isomorphism-complete
[article]

2009
*
arXiv
*
pre-print

More precisely, we proof that

arXiv:0902.4640v1
fatcat:wpuuzvcxbfdgjeazr6ywz7t2vy
*the**isomorphism**problem*for generic tree-sibling*time*consistent phylogenetic networks is*polynomially*equivalent to*the*graph*isomorphism**problem*. ... In a previous work, we gave a metric*on**the*class of semibinary tree-sibling*time*consistent phylogenetic networks that is computable in*polynomial**time*; in particular,*the**problem*of deciding if two networks ... Acknowledgements*The*authors would like to thank Antoni Lozano for his comments*on*an early version of this manuscript. ...##
###
Subcomplete generalizations of graph isomorphism

1982
*
Journal of computer and system sciences (Print)
*

We give technical evidence that none of

doi:10.1016/0022-0000(82)90015-0
fatcat:s3f46hjm5ncyhoyu37c5dm7qea
*the**problems*is NP-*complete*,*and*give*polynomial**time*reductions among*the**problems*. ... , situated properly between*the*class of NP-*complete**problems**and**the*class P of*problems*decidable in deterministic*polynomial**time*. ... Much recent research*on*graph*isomorphism*has concentrated*on*finding*problems**polynomial**time*equivalent to graph*isomorphism*. ...##
###
LD: A Polynomial Time Algorithm for Tree Isomorphism

2011
*
Procedia Engineering
*

show that

doi:10.1016/j.proeng.2011.08.376
fatcat:ynnfueu4yzcxhkmbzvoc5p634e
*the*algorithm can determine*the*class in*polynomial**time*tree*isomorphism**problem*. ... In this paper, class tree is proposed based*on**the*node to delete*the*exact graph*isomorphism**problem*, you can quickly determine*the*graph*isomorphism**problem*,*and*theoretical analysis*and*experiments ... Acknowledgements This work was supported in part by*the*Chinese National Science Foundation under grants No.60873014, No.61003082, No.60921062*and*No.60903059. ...##
###
Page 467 of Mathematical Reviews Vol. , Issue 96a
[page]

1996
*
Mathematical Reviews
*

*The*paper provides detailed proof

*and*ex- amples to prove that these average-case NP-

*complete*

*problems*are

*polynomially*

*isomorphic*under many-

*one*reductions. ... Because in 1977 all known NP-

*complete*

*problems*were polyno- mially

*isomorphic*, Berman

*and*Hartmanis conjectured that all NP-

*complete*

*problems*are

*polynomially*

*isomorphic*. ...

##
###
One-way functions and the isomorphism conjecture

1994
*
Theoretical Computer Science
*

.,

doi:10.1016/0304-3975(94)90031-0
fatcat:fsck4buhybhdxnukblpse4geue
*One*-way functions*and**the**isomorphism*conjecture, Theoretical Computer Science 129 (1994) 3099321.*The**isomorphism*conjecture is investigated for exponential-*time**and*other complexity classes. ... If*one*-way functions exist, we also show that there are k-*completely*creative sets in NP with*one*-way productive functions but which are p-*isomorphic*to standard*complete*sets. ... Acknowledgment I would like to thank Steve Homer for his contribution to Theorem 3.9*and*for his helpful ideas*and*comments. I would also like to thank James Royer for his help*on*Lemma 3.8. ...##
###
Page 3613 of Mathematical Reviews Vol. , Issue 2000e
[page]

2000
*
Mathematical Reviews
*

*The*existence of

*one*-way functions casts doubt

*on*

*the*va- lidity of

*the*

*isomorphism*conjecture, for if f is

*one*-way, how does

*one*construct a

*polynomial*-

*time*

*isomorphism*between SAT

*and*f (SAT)? ... It states that

*the*NP-

*complete*sets, which are, of course, all

*polynomial*-

*time*reducible to each other, are in fact

*polynomial*-

*time*

*isomorphic*. ...

##
###
Towards an Isomorphism Dichotomy for Hereditary Graph Classes
[article]

2014
*
arXiv
*
pre-print

First, we develop a methodology to show

arXiv:1411.1977v1
fatcat:4s5nlu54pnfwrdpht47ztm4dri
*isomorphism**completeness*of*the**isomorphism**problem**on*graph classes by providing a general framework unifying various reduction techniques. ... We show that*isomorphism*of graphs of bounded generalized color valence can be solved in*polynomial**time*. ...*On*all but finitely many classes of*the*form (H 1 , H 2 )-free*the*graph*isomorphism**problem*is*polynomial**time*solvable or*isomorphism*-*complete*. Contribution. ...
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