Questions tagged [isomorphism-testing]

Algorithmic questions concerning isomorphism testing. A prime example is the graph isomorphism problem, which is to decide if two input graphs are isomorphic. This tag may also be used for isomorphism testing between other objects (such as groups).

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9 votes
2 answers
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A "subtle" isomorphism testing problem: $\mathbb{Z}\ltimes_{A} \mathbb{Z}^5\cong \mathbb{Z}\ltimes_{B}\mathbb{Z}^5$ or not?

EDIT: I've made a mistake with the matrices. Now it is corrected. A couple of days ago I asked this question. There, answerers gave me excellent hints to solve that case and others too. But I've found ...
Alejandro Tolcachier's user avatar
12 votes
2 answers
286 views

Permutation search problems with no known $o(n!)$ algorithms

I am looking for problems for whose solution no known subfactorial algorithms are known. I am particularly interested in questions of isomorphism; that is, is there a permutation that converts one ...
Bryce Sandlund's user avatar
11 votes
3 answers
482 views

Finite objects for which isomorphism is NP-hard or harder?

Are there finite objects for which deciding isomorphism is NP-hard or harder? Graphs and groups are not solutions. Searching the web didn't return answer for me. Partial result based on Chow's ...
joro's user avatar
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5 votes
2 answers
495 views

Diffie Hellman cryptography based on graph isomorphism?

We got a cryptographic algorithm and computer implementation based on graph isomorphism. An isomorphism between two graphs is a bijection between their vertices that pre serves the edges. For a graph $...
joro's user avatar
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4 votes
0 answers
237 views

Can we make cryptography signature algorithm based on hardness of isomorphism?

In public key cryptography, Alice knows functions $f$ and its inverse $f^{-1}$. $f$ is public and $f^{-1}$ is secret. To sign a message $m$, she gives $(m,a=f^{-1}(m))$. To verify a signature, the ...
joro's user avatar
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3 votes
2 answers
313 views

Relation graph isomorphism to discrete logarithm

$\DeclareMathOperator\ora{ora}$Let $A_0$ be the adjacency matrix of graph $G$ and $P_0$ permutation matrix of multiplicative order $\rho$. Let $X$ be positive integer and $B_0=P_0^X A_0 P_0^{-X}$. Q1 ...
joro's user avatar
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2 votes
0 answers
129 views

Permutation similarity of matrices with many distinct entries

This is related to graph isomorphism. Here matrices are square $n \times n$ with non-negative integer entries. Two matrices $A,B$ are permutation similar if there exist permutation matrix $P$ such ...
joro's user avatar
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1 vote
0 answers
106 views

Hard instances for this graph isomorphism algorithm based on powers of weighted adjacency matrices?

In short, I found an algorithm for GI and the only hard instances I found so far are non-isomorphic strongly regular graphs with large automorphism groups. Q1 What are hard instances for the ...
joro's user avatar
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1 vote
0 answers
163 views

Reduction graph isomorphism to maximum independent set in very dense graph

We got a reduction graph isomorphism to MIS in a very dense graph, or alternatively negative monotone 2-CNF to MAX-ONEs with a formula with many clauses. Let $G,H$ be graphs of order $n$ and adjacency ...
joro's user avatar
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