A Linear Algorithm for Exact Pattern Matching in Planar Subdivisions

Graph sub-isomorphism is a very common approach to solving pattern search problems, but this is a NP-complete problem. This way, it is necessary to invest in research of approximate solutions, or in special cases of the problem. Planar subdivisions can be considered as a special case of graphs, because, in addition to nodes and edges, there is a more rigid topology in relation to the order of the edges, arising to the concept of face. This work presents a linear algorithm for pattern search in planar subdivisions. The presented algorithm is based on a hybrid approach between the dual and the region adjacency graph (RAG) to represent the patterns, saving any additional storage cost. Thus, the patterns are looked over the search subdivision, using a region growing algorithm.