Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs

King, Valerie

doi:10.1109/sffcs.1999.814580

Cited by 169 publications

(220 citation statements)

References 10 publications

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“…In the running time, the parameter q then counts the number of node insertions or node deletions, respectively. We note that, while there is no previous literature on this problem, one can parallelize the algorithm of Even and Shiloach [ES81] (see also [Kin99,RZ11]) to obtain an amortized update time of O(nD q + 1) over q changes in both the incremental and the decremental setting. This bound is sublinear in D when q = ω(n).…”

Section: Introductionmentioning

confidence: 99%

Sublinear-Time Maintenance of Breadth-First Spanning Tree in Partially Dynamic Networks

Henzinger

Krinninger

Nanongkai

2013

Automata, Languages, and Programming

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We study the problem of maintaining a breadth-rst spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic (1 + ε)-approximation algorithms whose amortized time (over some number of link changes) is sublinear in D, the maximum diameter of the network.Our technique also leads to a deterministic (1 + ε)-approximate incremental algorithm for single-source shortest paths (SSSP) in the sequential (usual RAM) model. Prior to our work, the state of the art was the classic exact algorithm of Even and Shiloach [ES81] that is optimal under some assumptions [RZ11, Hen + 15]. Our result is the rst to show that, in the incremental setting, this bound can be beaten in certain cases if some approximation is allowed.

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Section: Introductionmentioning

confidence: 99%

Sublinear-Time Maintenance of Breadth-First Spanning Tree in Partially Dynamic Networks

Henzinger

Krinninger

Nanongkai

2013

Automata, Languages, and Programming

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“…The first dynamic algorithm for handling all pairs shortest paths in a graph was presented by King [45], with the constraint that all costs are positive integers and bounded by a value b. Initially, they proved that any shortest paths tree, where the length of each path is at most δ, can be maintained in time O(mδ), where m is the cardinality of the arcs set, during a sequence of arbitrary number of arc deletions.…”

Section: The Algorithm Is Able To Process Only a Batch Of Arc Deletiomentioning

confidence: 99%

Shortest Paths on Dynamic Graphs: A Survey

Ferone¹,

Festa²,

Napoletano³

et al. 2017

Pesqui. Oper.

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ABSTRACT. This paper provides an overview of the state-of-the art and the current research trends concerning shortest paths problem on dynamic graphs. The discussion is divided in two main topics: reoptimization and time-dependent shortest paths. Reoptimization consists in the solution of a sequence of shortest path problems in which each instance slightly differs from the previous one. The reoptimization tackles this problem wisely using information stored in an optimal solution previously computed. On the other hand, shortest path problems on time-dependent graphs are characterized by a weight function which not only depends upon the arcs but changes in time according to a certain time horizon.

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“…Network modules that need shortest path computations typically rely on Dijkstra's algorithm, or a variation thereof [6,8,12,5], to compute shortest path, shortest-widesth path etc. These algorithms pre-compute shortest paths such that queries can be answered in O(1) time.…”

Section: Background On Shortest Path Algorithmsmentioning

confidence: 99%

Dynamic graph query primitives for SDN-based cloudnetwork management

Raghavendra

Lobo

Lee

2012

Proceedings of the First Workshop on Hot Topics in Software Defined Networks

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The need to provide customers with the ability to configure the network in current cloud computing environments has motivated the Networking-as-a-Service (NaaS) systems designed for the cloud. Such systems can provide cloud customers access to virtual network functions, such as network-aware VM placement, real time network monitoring, diagnostics and management, all while supporting multiple device management protocols. These network management functionalities depend on a set of underlying graph primitives. In this paper, we present the design and implementation of the software architecture including a shared graph library that can support network management operations. Using the illustrative case of all pair shortest path algorithm, we demonstrate how scalable lightweight dynamic graph query mechanisms can be implemented to enable practical computation times, in presence of network dynamism.

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Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs

Cited by 169 publications

References 10 publications

Sublinear-Time Maintenance of Breadth-First Spanning Tree in Partially Dynamic Networks

Sublinear-Time Maintenance of Breadth-First Spanning Tree in Partially Dynamic Networks

Shortest Paths on Dynamic Graphs: A Survey

Dynamic graph query primitives for SDN-based cloudnetwork management

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