An ‘All pairs shortest paths’ distributed algorithm using 2n 2 messages

Haldar, S.

doi:10.1007/3-540-57899-4_65

Cited by 13 publications

(14 citation statements)

References 6 publications

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“…While computing shortest paths is among the earliest studied problems in distributed computing, many classic works on this problem concern other objectives, such as the message complexity and convergence. When faced with the bandwidth constraint, the time complexities of these algorithms become higher than the trivial O(m)-time algorithm; e.g., BellmanFord algorithm and algorithms in [AR82,Hal97,AR93] require Ω(n 2 ) time.…”

Section: Related Workmentioning

confidence: 99%

Distributed approximation algorithms for weighted shortest paths

Nanongkai

2014

Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing

139

257

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A distributed network is modeled by a graph having n nodes (processors) and diameter D. We study the time complexity of approximating weighted (undirected) shortest paths on distributed networks with a O(log n) bandwidth restriction on edges (the standard synchronous CONGEST model). The question whether approximation algorithms help speed up the shortest paths (more precisely distance computation) was raised , which holds even when D = Θ(log n), up to a poly log n factor.As a by-product of our technique, we obtain a simpleÕ(n)-time (1 + o(1))-approximation algorithm for APSP, improving the previousÕ(n)-time O(1)-approximation algorithm following from the results of Lenzen and Patt-Shamir. We also prove a matching lower bound. Our techniques also yield anÕ(n 1/2 ) time algorithm on fully-connected networks, which guarantees an exact solution for SSSP and a (2 + o(1))-approximate solution for APSP. All our algorithms rely on two new simple tools: light-weight algorithm for bounded-hop SSSP and shortest-path diameter reduction via shortcuts. These tools might be of an independent interest and useful in designing other distributed algorithms.

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Section: Related Workmentioning

confidence: 99%

Distributed approximation algorithms for weighted shortest paths

Nanongkai

2014

Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing

139

257

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“…The exact all-pairs shortest path (APSP) problem has been studied extensively in the sequential setting, and was also given several solutions in the distributed setting [2,13,23,29,51]. The algorithm by Kanchi and Vineyard [29] is fast (runs in O(n) time) but involves using large messages, hence does not apply in the CONGEST model.…”

Section: Distributed Algorithms For Exact All-pairs Shortest-pathsmentioning

confidence: 99%

“…The algorithm of Antonio et al [2] uses short (i.e., O(log n) bits) messages, hence it can be executed in the CONGEST model, but it requires O(n log n) time, and moreover, it applies only to the special family of BHC graphs, which are graphs structured as a balanced hierarchy of clusters. Most of the distributed algorithms for the APSP problem aim at minimizing the message complexity, rather than the time; for instance, the algorithm of Haldar [23] requires O(n 2 ) time. For unweighted networks, a trivial lower bound of Ω(n) applies for exact APSP in the CONGEST model, as Ω(n) node identifiers may have to be communicated through a bottleneck edge.…”

Section: Distributed Algorithms For Exact All-pairs Shortest-pathsmentioning

confidence: 99%

Distributed distance computation and routing with small messages

2018

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We consider shortest paths computation and related tasks from the viewpoint of network algorithms, where the n-node input graph is also the computational system: nodes represent processors and edges represent communication links, which can in each time step carry an O(log n)-bit message. We identify several basic distributed distance computation tasks that are highly useful in the design of more sophisticated algorithms and provide efficient solutions. We showcase the utility of these tools by means of several applications.

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“…The all-pairs shortest path (APSP) problem has been studied extensively in the sequential setting, and was also given several solutions in the distributed setting [3,8,14,16,23]. The algorithm of [16] is fast (O(n) time) but involves using large messages, hence does not apply in the CONGEST model.…”

Section: Related Workmentioning

confidence: 99%

“…Most of the distributed algorithms for the APSP problem aim at minimizing the message complexity, rather than the time. The algorithm of [14] requires time O(n 2 ). In the CONGEST model, a trivial lower bound of Ω(n) applies, which has independently been asymptotically matched by two algorithms [15,20].…”

Section: Related Workmentioning

confidence: 99%

Efficient distributed source detection with limited bandwidth

Lenzen

Peleg

2013

Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing

140

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Given a simple graph G = (V, E) and a set of sources S ⊆ V , denote for each node v ∈ V by L (∞) v the lexicographically ordered list of distance/source pairs (d(s, v), s), where s ∈ S. For integers d, k ∈ N∪{∞}, we consider the source detection,Solutions to this problem provide natural generalizations of concurrent breadth-first search (BFS) tree constructions. For example, the special case of k = ∞ requires each source s ∈ S to build a complete BFS tree rooted at s, whereas the special case of d = ∞ and S = V requires constructing a partial BFS tree comprising at least k nodes from every node in V .In this work, we give a simple, near-optimal solution for the source detection task in the CONGEST model, where messages contain at most O(log n) bits, running in d + k rounds. We demonstrate its utility for various routing problems, exact and approximate diameter computation, and spanner construction. For those problems, we obtain algorithms in the CONGEST model that are faster and in some cases much simpler than previous solutions.

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An ‘All pairs shortest paths’ distributed algorithm using 2n 2 messages

Cited by 13 publications

References 6 publications

Distributed approximation algorithms for weighted shortest paths

Distributed approximation algorithms for weighted shortest paths

Distributed distance computation and routing with small messages

Efficient distributed source detection with limited bandwidth

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