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 <em>cache-aware</em> algorithm and the <em>cache-oblivious</em> counterpart. Our cache-oblivious SSSP-algorithm takes nearly full advantage of block transfers for <em>dense</em> graphs. The algorithm relies on a new data structure, called <em>bucket heap</em>, which is the first cache-oblivious priority queue to efficiently support a weak D<small>ECREASE</small>K<small>EY</small> operation. For the BFS problem, we reduce the number of I/Os for <em>sparse</em> graphs by a factor of nearly sqrt{B}, where B is the cache-block size, nearly closing the performance gap between the currently best <em>cache-aware</em> and <em>cache-oblivious</em> algorithms.
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