Buckets, Heaps, Lists, and Monotone Priority Queues

Cherkassky, Boris V.; Goldberg, Andrew V.; Silverstein, Craig

doi:10.1137/s0097539796313490

Cited by 67 publications

(44 citation statements)

References 12 publications

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“…Consider a relaxation of an edge (u, v) ∈ E and let x, y, and z be as in condition (4) in the definition of a component tree. Then either priority(y) < priority(z), in which case the simulated time of P u never lags behind that of P v , or c(u, v) ≥ 2 i−1 , where i = level (x).…”

Section: Shortest Paths In Directed Networkmentioning

confidence: 99%

“…A different algorithm by Thorup [20] achieves O(n + m(log log n) 2 ) time using linear space, O(n + m). Algorithms that are faster for denser networks were indicated by Ahuja et al [2], Cherkassky et al [4], and Raman [14,15,16]; their running times are of the forms O(m + n(log n) Θ (1) ) and O(m + nw Θ (1) ). Some of these algorithms employ randomization, multiplication, and/or superlinear space.…”

Section: Introductionmentioning

confidence: 99%

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Improved Shortest Paths on the Word RAM

Hagerup

2000

Automata, Languages and Programming

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Abstract. Thorup recently showed that single-source shortest-paths problems in undirected networks with n vertices, m edges, and edge weights drawn from {0, . . . , 2 w − 1} can be solved in O(n + m) time and space on a unit-cost random-access machine with a word length of w bits. His algorithm works by traversing a so-called component tree. Two new related results are provided here. First, and most importantly, Thorup's approach is generalized from undirected to directed networks. The resulting time bound, O(n + m log w), is the best deterministic linearspace bound known for sparse networks unless w is superpolynomial in log n. As an application, all-pairs shortest-paths problems in directed networks with n vertices, m edges, and edge weights in {−2 w , . . . , 2 w } can be solved in O(nm + n 2 log log n) time and O(n + m) space (not counting the output space). Second, it is shown that the component tree for an undirected network can be constructed in deterministic linear time and space with a simple algorithm, to be contrasted with a complicated and impractical solution suggested by Thorup. Another contribution of the present paper is a greatly simplified view of the principles underlying algorithms based on component trees.

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Section: Shortest Paths In Directed Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Improved Shortest Paths on the Word RAM

Hagerup

2000

Automata, Languages and Programming

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“…We used the DBLP co-authorship graphs 7 , IMDB co-starring graphs 8 and Ontario road network graphs 9 . The nodes for the DBLP co-authorship graphs are authors and the edges denote the collaborations.…”

Section: Datasetsmentioning

confidence: 99%

“…We used the fast implementation mentioned in [9] to generate this golden set. As mentioned earlier, this is the alternative (but brute-force method) for determine the precise node pairs with the maximum distance changes.…”

Section: Datasetsmentioning

confidence: 99%

Finding Top-k Shortest Path Distance Changes in an Evolutionary Network

Gupta

Aggarwal²

2011

Advances in Spatial and Temporal Databases

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Abstract. Networks can be represented as evolutionary graphs in a variety of spatio-temporal applications. Changes in the nodes and edges over time may also result in corresponding changes in structural garph properties such as shortest path distances. In this paper, we study the problem of detecting the top-k most significant shortest-path distance changes between two snapshots of an evolving graph. While the problem is solvable with two applications of the all-pairs shortest path algorithm, such a solution would be extremely slow and impractical for very large graphs. This is because when a graph may contain millions of nodes, even the storage of distances between all node pairs can become inefficient in practice. Therefore, it is desirable to design algorithms which can directly determine the significant changes in shortest path distances, without materializing the distances in individual snapshots. We present algorithms that are up to two orders of magnitude faster than such a solution, while retaining comparable accuracy.

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“…Ever since, many variations of shortest path algorithms have been proposed in the literature [8], [2], mainly based on different proposals for a priority queue [3]. Nearly all proposed shortest path algorithms are designed to Þnd a shortest paths tree rooted at the source to all other nodes.…”

Section: Introductionmentioning

confidence: 99%

Bi-directional Search in QoS Routing

Kuipers

Mieghem

2003

Quality for All

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Abstract. The "bi-directional search method" used for unicast routing is brießy reviewed. The extension of this method unicast QoS routing is discussed and an exact hybrid QoS algorithm HAMCRA that is partly based on bi-directional search is proposed. HAMCRA uses the speed of a heuristic when the constraints are loose and efficiently maintains exactness where heuristics fail. The performance of HAMCRA is simulated.

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Buckets, Heaps, Lists, and Monotone Priority Queues

Cited by 67 publications

References 12 publications

Improved Shortest Paths on the Word RAM

Improved Shortest Paths on the Word RAM

Finding Top-k Shortest Path Distance Changes in an Evolutionary Network

Bi-directional Search in QoS Routing

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