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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Vydáno v:Theoretical computer science Ročník 701; s. 54 - 69
Hlavní autoři: Calude, Cristian S., Dinneen, Michael J., Hua, Richard
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 21.11.2017
Témata:
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
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Popis
Shrnutí: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