Graph isomorphism is in SPP

Arvind, Vikraman; Kurur, Piyush P.

doi:10.1109/sfcs.2002.1181999

Cited by 34 publications

(30 citation statements)

References 38 publications

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“…In the case of graphs, studying automorphism problem has been fruitful.(e.g. see [Luk80,BGM82,AK02].) In this section we turn our attention to Matroid automorphism problem.…”

Section: Thus Inmentioning

confidence: 99%

On the Complexity of Matroid Isomorphism Problem

Rao

Sarma

2010

Theory Comput Syst

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We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in Σ p 2 . In the case of linear matroids, which are represented over polynomially growing fields, we note that the problem is unlikely to be Σ p 2 -complete and is coNP-hard. We show that when the rank of the matroid is bounded by a constant, linear matroid isomorphism, and matroid isomorphism are both polynomial time many-one equivalent to graph isomorphism.We give a polynomial time Turing reduction from graphic matroid isomorphism problem to the graph isomorphism problem. Using this, we are able to show that graphic matroid isomorphism testing for planar graphs can be done in deterministic polynomial time. We then give a polynomial time many-one reduction from bounded rank matroid isomorphism problem to graphic matroid isomorphism, thus showing that all the above problems are polynomial time equivalent.Further, for linear and graphic matroids, we prove that the automorphism problem is polynomial time equivalent to the corresponding isomorphism problems. In addition, we give a polynomial time membership test algorithm for the automorphism group of a graphic matroid.

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“…In the case of graphs, studying automorphism problem has been fruitful.(e.g. see [Luk80,BGM82,AK02].) In this section we turn our attention to Matroid automorphism problem.…”

Section: Thus Inmentioning

confidence: 99%

On the Complexity of Matroid Isomorphism Problem

Rao

Sarma

2010

Theory Comput Syst

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“…The main lemma of [AK02] creates an oracle reduction to a grouptheoretically defined language L such that every query w to L has a unique witnessing answer. Arvind and Kurur remark that the queries are "UP-like."…”

Section: Corollary 1 Uap Is Closed Under All Boolean Operationsmentioning

confidence: 99%

A Protocol for Serializing Unique Strategies

Crasmaru

Glaßer

Regan

et al. 2004

Lecture Notes in Computer Science

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Abstract. We devise an efficient protocol by which a series of twoperson games Gi with unique winning strategies can be combined into a single game G with unique winning strategy, even when the result of G is a non-monotone function of the results of the Gi that is unknown to the players. In computational complexity terms, we show that the class UAP of Niedermeier and Rossmanith [NR98] of languages accepted by unambiguous polynomial-time alternating TMs is self-low, i.e., UAP UAP = UAP. It follows that UAP contains the Graph Isomorphism problem, nominally improving the problem's classification into SPP by Arvind and Kurur [AK02] since UAP is a subclass of SPP [NR98]. We give some other applications, oracle separations, and results on problems related to unique-alternation formulas.

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“…Although no containment is known between BQP and SPP, it is interesting to compare these classes in terms of natural problems they contain. Important problems known to be in SPP are Graph Isomorphism and the hidden subgroup problem for permutation groups [1]. These problems have resisted efficient deterministic or randomized algorithms, but are considered potential candidates for quantum algorithms.…”

Section: Spp and Other Counting Complexity Classesmentioning

confidence: 99%

On the Complexity of Computing Units in a Number Field

Arvind

Kurur

2004

Lecture Notes in Computer Science

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Given an algebraic number field K, such that [K : Q] is constant, we show that the problem of computing the units group O * K is in the complexity class SPP. As a consequence, we show that principal ideal testing for an ideal in OK is in SPP. Furthermore, assuming the GRH, the class number of K, and a presentation for the class group of K can also be computed in SPP. A corollary of our result is that solving PELL S EQUATION, recently shown by Hallgren [12] to have a quantum polynomial-time algorithm, is also in SPP.

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Graph isomorphism is in SPP

Cited by 34 publications

References 38 publications

On the Complexity of Matroid Isomorphism Problem

On the Complexity of Matroid Isomorphism Problem

A Protocol for Serializing Unique Strategies

On the Complexity of Computing Units in a Number Field

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