Embedding Graphs into the Extended Grid

Let G = (V;E) be an arbitrary undirected source graph to be embedded in a target graph EM , the extended grid with vertices on integer grid points and edges to nearest and next-nearest neighbours. We present an algorithm showing how to embed G into EM in both time and space O(jV j) using the new notions of islands and bridges. An island is a connected subgraph in the target graph which is mapped from exactly one vertex in the source graph while a bridge is an edge between two islands which is mapped from exactly one edge in the source graph. This work is motivated by real industrial applications in the eld of quantum computing and a need to e ciently embed source graphs in the extended grid.