QUBO formulations for the graph isomorphism problem and related problems

We present and compare various methods to construct efficient QUBO formulations for the Graph Isomorphism Problem—one of a very few problems in NP that is neither known to be solvable in polynomial time nor NP-complete—and two related Subgraph Isomorphism Problems that are NP-hard. Experimental resu...

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Bibliographic Details
Published in:	Theoretical computer science Vol. 701; pp. 54 - 69
Main Authors:	Calude, Cristian S., Dinneen, Michael J., Hua, Richard
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 21.11.2017
Subjects:	Adiabatic quantum computing Chimera graph Graph isomorphism problem Quadratic unconstrained binary optimization Subgraph isomorphism problem Graph isomorphism problem Adiabatic quantum computing Quadratic unconstrained binary optimization Chimera graph Subgraph isomorphism problem
ISSN:	0304-3975, 1879-2294
Online Access:	Get full text
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Summary:	We present and compare various methods to construct efficient QUBO formulations for the Graph Isomorphism Problem—one of a very few problems in NP that is neither known to be solvable in polynomial time nor NP-complete—and two related Subgraph Isomorphism Problems that are NP-hard. Experimental results on two QUBO formulations of the Graph Isomorphism Problem suggest that our direct formulation is more practical than the others with respect to running on the D-Wave architecture. •An efficient direct QUBO objective function F for the Graph Isomorphism Problem is proposed.•An efficient QUBO objective function F for the Graph Isomorphism Problem via reduction to the Clique Problem is proposed.•The above constructions have been extended for the (Induced) Subgraph Isomorphism Problem(s).•Experimental results comparing the efficiency of the QUBO formulations is pesented.
ISSN:	0304-3975 1879-2294
DOI:	10.1016/j.tcs.2017.04.016