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On polynomial time isomorphisms of some new complete sets

J. Hartmanis, L. Berman
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  ... 
doi:10.1016/0022-0000(78)90027-2 fatcat:q775w4wqyradhphkiyneqi2rtu

Towards an Isomorphism Dichotomy for Hereditary Graph Classes

Pascal Schweitzer
2017 Theory of Computing Systems  
First, we develop a methodology to show 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  ... 
doi:10.1007/s00224-017-9775-8 fatcat:7afqdktaubhtll2kklqcdzvbeq

On the Complexity of Polytope Isomorphism Problems [article]

Volker Kaibel, Alexander Schwartz
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.  ... 
arXiv:math/0106093v2 fatcat:bfjohaaltvhpdo3ezuhs45gw6a

Testing homotopy equivalence is isomorphism complete

Yechezkel Zalcstein, Stanley P. Franklin
1986 Discrete Applied Mathematics  
It is shown that homotopy equivalence of finite topological spaces is 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.  ... 
doi:10.1016/0166-218x(86)90074-0 fatcat:6d6wh7dx4jcwxa3pkizer2bppm

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

Uwe Schöning
1988 Journal of computer and system sciences (Print)  
This implies that this 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  ... 
doi:10.1016/0022-0000(88)90010-4 fatcat:4l6j2onzijbslnow4v6g34m3mu

On the GI-Completeness of a Sorting Networks Isomorphism [article]

Martin Marinov, David Gregg
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.  ... 
arXiv:1507.05841v3 fatcat:74cacpau45b5jgkbyi23ivdfh4

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]

Gabriel Cardona, Merce Llabres, Francesc Rossello, Gabriel Valiente
2009 arXiv   pre-print
More precisely, we proof that 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.  ... 
arXiv:0902.4640v1 fatcat:wpuuzvcxbfdgjeazr6ywz7t2vy

Subcomplete generalizations of graph isomorphism

Christoph M. Hoffmann
1982 Journal of computer and system sciences (Print)  
We give technical evidence that none of 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.  ... 
doi:10.1016/0022-0000(82)90015-0 fatcat:s3f46hjm5ncyhoyu37c5dm7qea

LD: A Polynomial Time Algorithm for Tree Isomorphism

Baida Zhang, Yuhua Tang, Junjie Wu, Shuai Xu
2011 Procedia Engineering  
show that 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.  ... 
doi:10.1016/j.proeng.2011.08.376 fatcat:ynnfueu4yzcxhkmbzvoc5p634e

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

K. Ganesan
1994 Theoretical Computer Science  
., 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.  ... 
doi:10.1016/0304-3975(94)90031-0 fatcat:fsck4buhybhdxnukblpse4geue

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]

Pascal Schweitzer
2014 arXiv   pre-print
First, we develop a methodology to show 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.  ... 
arXiv:1411.1977v1 fatcat:4s5nlu54pnfwrdpht47ztm4dri
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