I/O-Optimal Algorithms for Outerplanar Graphs [chapter]

Anil Maheshwari, Norbert Zeh
2006 Graph Algorithms and Applications 5  
We present linear-I/O algorithms for fundamental graph problems on embedded outerplanar graphs. We show that breadth-first search, depth-first search, single-source shortest paths, triangulation, and computing anseparator of size O(1/ ) take O(scan(N )) I/Os on embedded outerplanar graphs. We also show that it takes O(sort(N )) I/Os to test whether a given graph is outerplanar and to compute an outerplanar embedding of an outerplanar graph, thereby providing O(sort(N ))-I/O algorithms for the
more » ... ove problems if no embedding of the graph is given. As all these problems have linear-time algorithms in internal memory, a simple simulation technique can be used to improve the I/O-complexity of our algorithms from O(sort(N )) to O(perm(N )). We prove matching lower bounds for embedding, breadth-first search, depth-first search, and singlesource shortest paths if no embedding is given. Our algorithms for the above problems use a simple linear-I/O time-forward processing algorithm for rooted trees whose vertices are stored in preorder.
doi:10.1142/9789812773289_0005 fatcat:umf5ff7saba3dejo7sf4qcrvoq