I/O-Efficient Planar Separators and Applications
نویسنده
چکیده
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(ph) each. The size of S is O(N=ph). Computing S takes O(sort(N)) I/Os and linear space, provided that M 56h log2 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.
منابع مشابه
Listing all the minimal separators of a planar graph
I present an efficient algorithm which lists the minimal separators of a planar graph in O(n) per separator.
متن کاملI/O-Efficient Algorithms for Planar Graphs I: Separators∗
We present I/O-efficient algorithms for computing optimal separator partitions of planar graphs. Our main result shows that, given a planar graph G with N vertices and an integer r > 0, a vertex separator of size O (N/√r) that partitions G into O(N/r) subgraphs of size at most r and boundary size O (√r) can be computed in O(sort(N)) I/Os, provided that M ≥ 56r log B. Together with the planar em...
متن کاملMultiway Simple Cycle Separators and I/O-Efficient Algorithms for Planar Graphs
We revisit I/O-efficient solutions to a number of fundamental problems on planar graphs: single-source shortest paths, topological sorting, and computing strongly connected components. Existing I/O-efficient solutions to these problems pay for I/O efficiency using excessive computation time in internal memory, thereby completely negating the performance gain achieved by minimizing the number of...
متن کاملAn External Memory Data Structure for Shortest Path Queries ( Extended Abstract ) ⋆
We present results related to satisfying shortest path queries on a planar graph stored in external memory. In particular, we show how to store rooted trees in external memory so that bottom-up paths can be traversed I/O-efficiently, and we present I/O-efficient algorithms for triangulating planar graphs and computing small separators of such graphs. Using these techniques, we can construct a d...
متن کاملI/O-Efficient Planar Separators
We present I/O-efficient algorithms for computing optimal separator partitions of planar graphs. Our main result shows that, given a planar graph G with N vertices and an integer r > 0, a vertex separator of size O(N/ √ r) that partitions G into O(N/r) subgraphs of size at most r and boundary size O( √ r) can be computed in O(sort(N)) I/Os. This bound holds provided that M ≥ 56r log B. Together...
متن کامل