TY - JOUR
A2 - Kang, Liying
AU - Schellewald, Christian
PY - 2012
DA - 2012/02/07
TI - A Convex Relaxation Bound for Subgraph Isomorphism
SP - 908356
VL - 2012
AB - In this work a convex relaxation of a subgraph isomorphism problem is proposed, which leads to a new lower bound that can provide a proof that a subgraph isomorphismbetween two graphs can not be found. The bound is based on a semidefinite programming relaxation of a combinatorial optimisation formulation for subgraph isomorphism and is explained in detail. We consider subgraph isomorphism problem instances of simple graphs which means that only the structural information of the two graphs is exploited and other information that might be available (e.g., node positions) is ignored. The bound is based on the fact that a subgraph isomorphism always leads to zero as lowest possible optimal objective value in the combinatorial problem formulation. Therefore, for problem instances with a lower bound that is larger than zero this represents a proof that a subgraph isomorphism can not exist. But note that conversely, a negative lower bound does not imply that a subgraph isomorphism must be present and only indicates that a subgraph isomorphism can not be excluded. In addition, the relation of our approach and the reformulation of the largest common subgraph problem into a maximum clique problem is discussed.
SN - 1687-9163
UR - https://doi.org/10.1155/2012/908356
DO - 10.1155/2012/908356
JF - International Journal of Combinatorics
PB - Hindawi Publishing Corporation
KW -
ER -