I/O-Efficient Planar Separators

We present a new algorithm to compute a subset S of vertices of a planar graph G whose removal partitions G into O(N/h) subgraphs of size O(h) and with boundary size O( h) each. The size of S is O(N/ h). Computing S takes O(sort(N)) I/Os and linear space, provided that M 56hlog2 B. Together with recent reducibility results, this leads to O(sort(N)) I/O algorithms for breadth-first search (BFS), depth-first search (DFS), and single source shortest paths (SSSP) on undirected embedded planar graphs. Our separator algorithm does not need a BFS tree or an embedding of G to be given as part of the input. Instead we argue that "local embeddings" of subgraphs of G are enough.

• Type: Journal
• Year: 2008
• Where: SIAMCOMP
• Authors: Anil Maheshwari, Norbert Zeh
• Keywords: Algorithm, Planar Graphs, Removal Partitions, SIAMCOMP 2008