An external memory data structure for shortest path queries

Hutchinson, D. A. W.; Maheshwari, Anil; Zeh, Norbert

doi:10.1016/s0166-218x(02)00217-2

Cited by 40 publications

(69 citation statements)

References 20 publications

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“…In Section 3, we show how a tree T can be blocked in a succinct fashion such that a bottom-up traversal requires O(K/B) I/Os using only 2N + ǫN log B N + o(N) bits to store T , where K is the path length and 0 < ǫ < 1. This technique is based on [7], and achieves an improvement on the space bound by a factor of lg N. 2. In Section 4, we show that a binary tree, with keys of size q = O(lg N) bits, can be stored using (3 + q)N + o(N) bits so that a root-to-node path of length K can be reported…”

Section: Our Resultsmentioning

confidence: 99%

“…In the example in Figure 2, the duplicate path of the second block consists of nodes 7, 4, 2, 1. A duplicate path has at most τ B nodes and satisfies the following property (this is analogous to Property 3 in Hutchinson et al [7]): Property 1. Given a tree block (or superblock) Y , for any node x in Y there exists a path from x to either the top of its layer consisting entirely of nodes in Y , or to a node in the duplicate path of Y consisting entirely of nodes in Y plus one node in the duplicate path.…”

Section: Blocking Strategymentioning

confidence: 97%

“…Hutchinson et al [7] examined the case of bottom-up traversal, where the path begins with some node in the tree and proceeds to the root. They gave a blocking that supports bottom-up traversal in O(K/B) I/Os when the tree is stored in O(N/B) blocks (see Lemma 2).…”

Section: Previous Workmentioning

confidence: 99%

“…Hutchinson et al [7] presented a blocking technique for rooted trees in the I/O model that supports bottom-up traversal. Their result is summarized in the following lemma:…”

Section: I/o Efficient Tree Traversalmentioning

confidence: 99%

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Succinct and I/O Efficient Data Structures for Traversal in Trees

Dillabaugh

Maheshwari

2008

Algorithms and Computation

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Abstract. We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to the root. For a bottom-up path of length K, we design data structures that permit traversal of this path in O(K/B) I/Os (B denotes the size of a disk block) using only 2N + ǫN log B N + o(N ) bits, for an arbitrarily selected constant, ǫ, where 0 < ǫ < 1. Our second result is for top-down traversal in binary trees. We store the tree in (3 + q)N + o(N ) bits, where q is the number of bits required to store a key, while top-down traversal can still be performed in an asymptotically optimal number of I/Os.

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Section: Our Resultsmentioning

confidence: 99%

Section: Blocking Strategymentioning

confidence: 97%

Section: Previous Workmentioning

confidence: 99%

“…Hutchinson et al [7] presented a blocking technique for rooted trees in the I/O model that supports bottom-up traversal. Their result is summarized in the following lemma:…”

Section: I/o Efficient Tree Traversalmentioning

confidence: 99%

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Succinct and I/O Efficient Data Structures for Traversal in Trees

Dillabaugh

Maheshwari

2008

Algorithms and Computation

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“…Lemma 2 ( [7]). A rooted tree T on N nodes can be stored in O(N/B) blocks on disk such that a bottom-up path of length K in T can be traversed in O(K/τ B) I/Os, where 0 < τ < 1 is a constant.…”

Section: I/o Efficient Tree Traversalmentioning

confidence: 99%

Succinct and I/O Efficient Data Structures for Traversal in Trees

Dillabaugh

Maheshwari

2011

Algorithmica

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I/O-Efficient Algorithms on Near-Planar Graphs

Haverkort

Toma

2006

LATIN 2006: Theoretical Informatics

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Obtaining I/O-efficient algorithms for basic graph problems on sparse directed graphs has been a long-standing open problem. The best known algorithms for most basic problems on such graphs still require Ω(V ) I/Os in the worst case, where V is the number of vertices in the graph. Nevertheless optimal O(sort(V )) I/O algorithms are known for special classes of sparse graphs, like planar graphs and grid graphs. It is hard to accept that a problem becomes difficult as soon as the graph contains a few deviations from planarity. In this paper we extend the class of graphs on which basic graph problems can be solved I/O-efficiently. We discuss several ways to transform graphs that are almost planar into planar graphs (given a suitable drawing), and based on those transformations we obtain the first I/O-efficient algorithms for directed graphs that are almost planar.Let G be a directed graph that is given as a planar subgraph (V, E) and a set of additional edges EC . Our main result is a single-source-shortestpaths algorithm that runs in O(EC + sort(V + EC )) I/Os. When EC is small our algorithm is a significant improvement over the best previously known algorithms, which required Ω(V ) I/Os. Alternatively, when G is given with a drawing with T crossings, we can compute single-source shortest paths in O(sort(V + T )) I/Os. We obtain similar bounds for computing (strongly) connected components, breadth-first and depth-first traversals and topological ordering.

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An external memory data structure for shortest path queries

Cited by 40 publications

References 20 publications

Succinct and I/O Efficient Data Structures for Traversal in Trees

Succinct and I/O Efficient Data Structures for Traversal in Trees

Succinct and I/O Efficient Data Structures for Traversal in Trees

I/O-Efficient Algorithms on Near-Planar Graphs

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