I/O-Efficient Algorithms for Graphs of Bounded Treewidth

2007 Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX)

Osipov

2007

Breadth first search (BFS) traversal on massive graphs in external memory was considered non-viable until recently, because of the large number of I/Os it incurs. Ajwani et al. [3] showed that the randomized variant of the o(n) I/O algorithm of Mehlhorn and Meyer [24] (MM BFS) can compute the BFS level decomposition for large graphs (around a billion edges) in a few hours for small diameter graphs and a few days for large diameter graphs. We improve upon their implementation of this algorithm by reducing the overhead associated with each BFS level, thereby improving the results for large diameter graphs which are more difficult for BFS traversal in external memory. Also, we present the implementation of the deterministic variant of MM BFS and show that in most cases, it outperforms the randomized variant. The running time for BFS traversal is further improved with a heuristic that preserves the worst case guarantees of MM BFS. Together, they reduce the time for BFS on large diameter graphs from days shown in [3] to hours. In particular, on line graphs with random layout on disks, our implementation of the deterministic variant of MM BFS with the proposed heuristic is more than 75 times faster than the previous best result for the randomized variant of MM BFS in [3].

Section: Computation Modelsmentioning

confidence: 99%

Improved external memory BFS implementations

Ajwani

2007 Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX)

Osipov

2007

“…I/O-efficient graph algorithms have been considered by a number of authors [1,2,4,5,6,10,12,14,16,19,20,21,22,23,24,26,30]. We review the previous results most relevant to our work (see Table 1).…”

Section: I/o-model and Previous Resultsmentioning

confidence: 99%

On External-Memory Planar Depth-First Search

Arge¹,

Graph Algorithms and Applications 4

Toma³

et al. 2006

Self Cite

Even though a large number of I/O-efficient graph algorithms have been developed, a number of fundamental problems still remain open. For example, no space-and I/O-efficient algorithms are known for depth-first search or breath-first search in sparse graphs. In this paper, we present two new results on I/O-efficient depth-first search in an important class of sparse graphs, namely undirected embedded planar graphs. We develop a new depth-first search algorithm that uses O(sort(N ) log(N/M )) I/Os, and show how planar depth-first search can be reduced to planar breadthfirst search in O(sort(N )) I/Os. As part of the first result, we develop the first I/O-efficient algorithm for finding a simple cycle separator of an embedded biconnected planar graph. This algorithm uses O(sort(N )) I/Os.

“…For special graph classes, such as planar graphs and graphs of bounded tree-width, optimal SSSP algorithms with I/O complexity O(sort(n)) are known [Maheshwari and Zeh 2001;Arge et al 2004a]. Haverkort and Toma [2006] showed how to extend the results for planar graphs to graphs that are nearly planar for different measures of nonplanarity.…”

Section: Previous Workmentioning

confidence: 99%

I/O-efficient shortest path algorithms for undirected graphs with random or bounded edge lengths

Zeh

2012

ACM Trans. Algorithms

Self Cite

We present I/O-efficient single-source shortest path algorithms for undirected graphs. Our main result is an algorithm with I/O complexity O (nmlog L)/B + MST(n, m) on graphs with n vertices, m edges, and arbitrary edge lengths between 1 and L; MST(n, m) denotes the I/O complexity of computing a minimum spanning tree; B denotes the disk block size. If the edge lengths are drawn uniformly at random from (0, 1], the expected I/O complexity of the algorithm is O nm/B + (m/B) log B + MST(n, m) . A simpler algorithm has expected I/O complexity O (nmlog B)/B + MST(n, m) for uniformly random edge lengths.