Mapping Induced Subgraph Isomorphism Problems to Ising Models and Its Evaluations by an Ising Machine

Natsuhito YOSHIMURA  Masashi TAWADA  Shu TANAKA  Junya ARAI  Satoshi YAGI  Hiroyuki UCHIYAMA  Nozomu TOGAWA  

IEICE TRANSACTIONS on Information and Systems   Vol.E104-D    No.4    pp.481-489
Publication Date: 2021/04/01
Publicized: 2021/01/07
Online ISSN: 1745-1361
DOI: 10.1587/transinf.2020EDP7026
Type of Manuscript: PAPER
Category: Fundamentals of Information Systems
induced subgraph,  isomorphism problem,  Ising machines,  Ising model,  annealing machine,  quadratic unconstraint binary optimization,  

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Ising machines have attracted attention as they are expected to solve combinatorial optimization problems at high speed with Ising models corresponding to those problems. An induced subgraph isomorphism problem is one of the decision problems, which determines whether a specific graph structure is included in a whole graph or not. The problem can be represented by equality constraints in the words of combinatorial optimization problem. By using the penalty functions corresponding to the equality constraints, we can utilize an Ising machine to the induced subgraph isomorphism problem. The induced subgraph isomorphism problem can be seen in many practical problems, for example, finding out a particular malicious circuit in a device or particular network structure of chemical bonds in a compound. However, due to the limitation of the number of spin variables in the current Ising machines, reducing the number of spin variables is a major concern. Here, we propose an efficient Ising model mapping method to solve the induced subgraph isomorphism problem by Ising machines. Our proposed method theoretically solves the induced subgraph isomorphism problem. Furthermore, the number of spin variables in the Ising model generated by our proposed method is theoretically smaller than that of the conventional method. Experimental results demonstrate that our proposed method can successfully solve the induced subgraph isomorphism problem by using the Ising-model based simulated annealing and a real Ising machine.