Cache-Oblivious Data Structures and Algorithms for Undirected Breadth-First Search and Shortest Paths

Abstract: Frigo, Leiserson, Prokop and Ramachandran in 1999 introduced the ideal-cache model as a formal model of computation for developing algorithms in environments with multiple levels of caching, and coined the terminology of cache-oblivious algorithms. Cache-oblivious algorithms are described as standard RAM algorithms with only one memory level, i.e. without any knowledge about memory hierarchies, but are analyzed in the two-level I/O model of Aggarwal and Vitter for an arbitrary memory and block size and an optimal off-line cache replacement strategy. The result are algorithms that automatically apply to multi-level memory hierarchies. This paper gives an overview of the results achieved on cache-oblivious algorithms and data structures since the seminal paper by Frigo et al.

Abstract: This work treats the problem of designing data-oblivious algorithms for classical and widely used graph problems. A data-oblivious algorithm is defined as having the same sequence of operations regardless of the input data and data-independent memory accesses. Such algorithms are suitable for secure processing in outsourced and similar environments, which serves as the main motivation for this work. We provide data-oblivious algorithms for breadth-first search, single-source single-destination shortest path, minimum spanning tree, and maximum flow, the asymptotic complexities of which are optimal, or close to optimal, for dense graphs.

Abstract: We present static cache-oblivious dictionary structures for strings which provide analogues of tries and suffix trees in the cache-oblivious model. Our construction takes as input either a set of strings to store, a single string for which all suffixes are to be stored, a trie, a compressed trie, or a suffix tree, and creates a cache-oblivious data structure which performs prefix queries in O(logBn + |P|/B) I/Os, where n is the number of leaves in the trie, P is the query string, and B is the block size. This query cost is optimal for unbounded alphabets. The data structure uses linear space.

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.

Abstract: Starting from a continuation-based interpreter for a simple logic programming language, propositional Prolog with cut, we derive the corresponding logic engine in the form of an abstract machine. The derivation originates in previous work (our article at PPDP 2003) where it was applied to the lambda-calculus. The key transformation here is Reynolds’s defunctionalization that transforms a tail-recursive, continuation-passing interpreter into a transition system, i.e., an abstract machine. Similar denotational and operational semantics were studied by de Bruin and de Vink (their article at TAPSOFT 1989), and we compare their study with our derivation. Additionally, we present a direct-style interpreter of propositional Prolog expressed with control operators for delimited continuations.