TY - GEN

T1 - Efficient ising model mapping for induced subgraph isomorphism problems using ising machines

AU - Yoshimura, Natsuhito

AU - Tawada, Masashi

AU - Tanaka, Shu

AU - Arai, Junya

AU - Yagi, Satoshi

AU - Uchiyama, Hiroyuki

AU - Togawa, Nozomu

N1 - Publisher Copyright:
© 2019 IEEE.

PY - 2019/9

Y1 - 2019/9

N2 - 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. By using the penalty functions correspond 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 using the Isingmodel based simulated annealing.

AB - 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. By using the penalty functions correspond 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 using the Isingmodel based simulated annealing.

KW - Annealing machine

KW - Induced subgraph

KW - Ising machines

KW - Ising model

KW - Isomorphism problem

UR - http://www.scopus.com/inward/record.url?scp=85078897605&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85078897605&partnerID=8YFLogxK

U2 - 10.1109/ICCE-Berlin47944.2019.8966218

DO - 10.1109/ICCE-Berlin47944.2019.8966218

M3 - Conference contribution

AN - SCOPUS:85078897605

T3 - IEEE International Conference on Consumer Electronics - Berlin, ICCE-Berlin

SP - 227

EP - 232

BT - Proceedings - 2019 IEEE 9th International Conference on Consumer Electronics, ICCE-Berlin 2019

A2 - Velikic, Gordan

A2 - Gross, Christian

PB - IEEE Computer Society

T2 - 9th IEEE International Conference on Consumer Electronics, ICCE-Berlin 2019

Y2 - 8 September 2019 through 11 September 2019

ER -