A Functional Approach to External Graph Algorithms

Abello, James; Buchsbaum, Adam L.; Westbrook, Jeffery

doi:10.1007/s00453-001-0088-5

Cited by 102 publications

(125 citation statements)

References 24 publications

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“…For instance, the sequence a = (1,4,4,3,5,7,8,8,6,4,1) has the typical sequence τ (a) = (1, 8, 1). To obtain τ (a), first remove the second 4 and the second 8 (duplicate removal); then delete entries 4, 3, 5, 7 between the first 1 and the 8 and entries 6, 4 between the 8 and the last 1 (typical operations).…”

Section: Typical Sequences and Typical Listsmentioning

confidence: 99%

“…The best known deterministic algorithm for computing a maximal matching I/O-efficiently [1] takes O(sort(|E|) log 2 (|V |/B)) I/Os. No deterministic algorithm for finding a maximal independent set I/O-efficiently is known.…”

Section: Previous Workmentioning

confidence: 99%

“…No deterministic algorithm for finding a maximal independent set I/O-efficiently is known. In [1], randomized algorithms for these two problems are proposed; their I/O-complexity is O(sort(|E|)) with high probability.…”

Section: Previous Workmentioning

confidence: 99%

“…Note that the function γ can be conveniently represented by storing colors γ ((v, w)) and γ ((w, v)) with edge {v, w} ∈ U(G). Given a pair c = (c 1 , c 2 ) of colors, we define c (1) = c 1 and c (2) = c 2 . This defines two functions γ (1) and γ (2) , where γ (1) (e) = c 1 and γ (2) (e) = c 2 , for any edge e with γ (e) = (c 1 , c 2 ).…”

Section: Flippable Dagsmentioning

confidence: 99%

“…Given a pair c = (c 1 , c 2 ) of colors, we define c (1) = c 1 and c (2) = c 2 . This defines two functions γ (1) and γ (2) , where γ (1) (e) = c 1 and γ (2) (e) = c 2 , for any edge e with γ (e) = (c 1 , c 2 ). For a color c ∈ {blue, red}, we definec to be its opposite color; that is, if c = blue, thenc = red, and vice versa.…”

Section: Flippable Dagsmentioning

confidence: 99%

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I/O-Efficient Algorithms for Graphs of Bounded Treewidth

Maheshwari

Zeh

2007

Algorithmica

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We present an algorithm that takes O(sort(N )) I/Os (sort(N ) = ((N/ (DB)) log M/B (N/B)) is the number of I/Os it takes to sort N data items) to compute a tree decomposition of width at most k, for any graph G of treewidth at most k and size N , where k is a constant. Given such a tree decomposition, we use a dynamic programming framework to solve a wide variety of problems on G in O(N/(DB)) I/Os, including the single-source shortest path problem and a number of problems that are NP-hard on general graphs. The tree decomposition can also be used to obtain an optimal separator decomposition of G. We use such a decomposition to perform depth-first search in G in O(N/(DB)) I/Os.As important tools that are used in the tree decomposition algorithm, we introduce flippable DAGs and present an algorithm that computes a perfect elimination ordering of a k-tree in O(sort(N )) I/Os.The second contribution of our paper, which is of independent interest, is a general and simple framework for obtaining I/O-efficient algorithms for a number of graph problems that can be solved using greedy algorithms in internal memory. We apply this framework in order to obtain an improved algorithm for finding a maximal matching and the first deterministic I/O-efficient algorithm for finding a maximal inAn abstract of this paper was presented at

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Section: Typical Sequences and Typical Listsmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

Section: Flippable Dagsmentioning

confidence: 99%

Section: Flippable Dagsmentioning

confidence: 99%

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I/O-Efficient Algorithms for Graphs of Bounded Treewidth

Maheshwari

Zeh

2007

Algorithmica

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Algorithms for Data Streams

Demetrescu

Finocchi

2007

Handbook of Applied Algorithms

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Data stream processing has gained increasing popularity in the last few years as an effective paradigm for processing massive data sets. A wide range of applications in computational sciences generate huge and rapidly changing data streams that need to be continuously monitored in order to support exploratory analyses and to detect correlations, rare events, fraud, intrusion, unusual or anomalous activities. Relevant examples include monitoring network traffic, online auctions, transaction logs, telephone call records, automated bank machine operations, atmospheric and astronomical events. Due to the high sequential access rates of modern disks, streaming algorithms can also be effectively deployed for processing massive files on secondary storage, providing new insights into the solution of several computational problems in external memory.Streaming models constrain algorithms to access the input data in one or few sequential passes, using only a small amount of working memory and processing each input item quickly. Solving computational problems under these restrictions poses several algorithmic challenges. This chapter is intended as an overview and survey of the main models and techniques for processing data streams and their applications.

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Real‐time monitoring of undirected networks: Articulation points, bridges, and connected and biconnected components

2012

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In this article, we present the first algorithm in the streaming model to characterize completely the biconnectivity properties of undirected networks: articulation points, bridges, and connected and biconnected components. The motivation of our work was the development of a real-time algorithm to monitor the connectivity of the autonomous systems (AS) network, but the solution provided is general enough to be applied to any network. The network structure is represented by a graph, and the algorithm is analyzed in the datastream framework. Here, as in the on-line model, the input graph is revealed one item (i.e., graph edge) after the other, in an on-line fashion; but, if compared to traditional on-line computation, there are stricter requirements for both memory occupation and per item processing time. Our algorithm works by properly updating a forest over the graph nodes. All the graph (bi)connectivity properties are stored in this forest. We prove the correctness of the algorithm, together with its space (O(nlog n), with n being the number of nodes in the graph) and time bounds. We also present the results of a brief experimental evaluation against real-world graphs, including many samples of the AS network, ranging from medium to massive size. These preliminary experimental results confirm the effectiveness of our approach. © 2012 Wiley Periodicals, Inc. NETWORKS, Vol. 2012 Copyright © 2012 Wiley Periodicals, Inc

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A Functional Approach to External Graph Algorithms

Cited by 102 publications

References 24 publications

I/O-Efficient Algorithms for Graphs of Bounded Treewidth

I/O-Efficient Algorithms for Graphs of Bounded Treewidth

Algorithms for Data Streams

Real‐time monitoring of undirected networks: Articulation points, bridges, and connected and biconnected components

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