Showing papers by "Ulrich Meyer published in 2004"
08 Jul 2004
TL;DR: In this paper, the authors present improved cache-oblivious data structures and algorithms for breadth-first search and the single-source shortest path problem on undirected graphs with non-negative edge weights.
Abstract: We present improved cache-oblivious data structures and algorithms for breadth-first search and the single-source shortest path problem on undirected graphs with non-negative edge weights. Our results removes the performance gap between the currently best cache-aware algorithms for these problems and their cache-oblivious counterparts. Our shortest-path algorithm relies on a new data structure, called bucket heap, which is the first cache-oblivious priority queue to efficiently support a weak DecreaseKey operation.
48 citations
01 Jan 2004
TL;DR: This work presents improved cache-oblivious data structures and algorithms for breadth-first search and the single-source shortest path problem on undirected graphs with non-negative edge weights and removes the performance gap between the currently best cache-aware algorithms for these problems.
38 citations
TL;DR: The cache-oblivious SSSP-algorithm takes nearly full advantage of block transfers for dense graphs, and the number of I/Os for sparse graphs is reduced by a factor of nearly sqrt{B}, where B is the cache-block size.
Abstract: We present improved cache-oblivious data structures and algorithms for breadth-first search (BFS) on undirected graphs and the single-source shortest path (SSSP) problem on undirected graphs with non-negative edge weights. For the SSSP problem, our result closes the performance gap between the currently best cache-aware algorithm and the cache-oblivious counterpart. Our cache-oblivious SSSP-algorithm takes nearly full advantage of block transfers for dense graphs. The algorithm relies on a new data structure, called bucket heap , which is the first cache-oblivious priority queue to efficiently support a weak D ECREASE K EY operation. For the BFS problem, we reduce the number of I/Os for sparse graphs by a factor of nearly sqrt{B}, where B is the cache-block size, nearly closing the performance gap between the currently best cache-aware and cache-oblivious algorithms.
24 citations
12 Jul 2004
TL;DR: In this paper, the first I/O-efficient algorithm for APSP was proposed for general undirected graphs with nonnegative edge weights and E/V = o(B/ log V) I/Os.
Abstract: We develop I/O-efficient algorithms for diameter and all-pairs shortest-paths (APSP). For general undirected graphs G(V,E) with non-negative edge weights and E/V = o(B/ log V) our approaches are the first to achieve o(V 2) I/Os. We also show that for unweighted undirected graphs, APSP can be solved with just \(O(V \cdot \textrm{sort}(E))\) I/Os. Both our weighted and unweighted approaches require O(V 2) space. For diameter computations we provide I/O-space tradeoffs. Finally, we provide improved results for both diameter and APSP computation on directed planar graphs.
23 citations
01 Jan 2004
TL;DR: I/O-efficient algorithms for diameter and all-pairs shortest-paths (APSP) and it is shown that for unweighted undirected graphs, APSP can be solved with just \(O(V \cdot \textrm{sort}(E))\) I/Os.
Abstract: We develop I/O-efficient algorithms for diameter and all-pairs shortest-paths (APSP). For general undirected graphs G(V,E) with non-negative edge weights and E/V = o(B/ log V) our approaches are the first to achieve o(V 2) I/Os. We also show that for unweighted undirected graphs, APSP can be solved with just \(O(V \cdot \textrm{sort}(E))\) I/Os. Both our weighted and unweighted approaches require O(V 2) space. For diameter computations we provide I/O-space tradeoffs. Finally, we provide improved results for both diameter and APSP computation on directed planar graphs.
1 citations