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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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 ...
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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 ...
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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 ...
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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 $...
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votes
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answers
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...