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Path-Fault-Tolerant Approximate Shortest-Path Trees
[article]
2015
arXiv
pre-print
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In this paper we show how to enrich a single-source shortest-path tree (SPT) of G with a sparse set of auxiliary edges selected from E, in order to create a structure which tolerates effectively a path ...
This consists of a simultaneous fault of a set F of at most f adjacent edges along a shortest path emanating from the source, and it is recognized as one of the most frequent disruption in an SPT. ...
We say that a spanning subgraph H of G is a Path-Fault-Tolerant α-Approximate SPT (in short, α-PASPT), with α ≥ 1, if, for each vertex z ∈ V (G), the following inequality holds: d H−F (z) ≤ α · d G−F ( ...
arXiv:1507.01695v1
fatcat:u754yg7ynrhsjnssk27rl72gee
Fault-Tolerant Approximate Shortest-Path Trees
[article]
2016
arXiv
pre-print
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., sparse and fast) fault-tolerant approximate shortest-path trees, for both the edge and vertex single-failure case. ...
Moreover, we also focus on the unweighted case, and we prove that an ordinary (α,β)-spanner can be slightly augmented in order to build efficient fault-tolerant approximate breadth-first-search trees. ...
to pay for having fault-tolerant shortest paths! ...
arXiv:1407.0637v2
fatcat:nkpgrjyjsfhilbftisz5rycvqm
Multiple-Edge-Fault-Tolerant Approximate Shortest-Path Trees
[article]
2016
arXiv
pre-print
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For any given integer f > 1, we study the problem of designing a sparse f-edge-fault-tolerant (f-EFT) σ -approximate single-source shortest-path tree (σ-ASPT), namely a subgraph of G having as few edges ...
distance from the source to any node, and a corresponding approximate path in the same amount of time plus the path's size. ...
Related Work In the recent past, several single and multiple edge/vertex-fault-tolerant approximate SPT (ASPT) structures have been devised. ...
arXiv:1601.04169v2
fatcat:l6ytznxbifaaxlneu6r4tpqpfy
Sparse Fault-Tolerant BFS Trees
[chapter]
2013
Lecture Notes in Computer Science
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For a source node s, a target node t and an edge e ∈ G, the shortest s − t path P s,t,e that does not go through e is known as a replacement path. ...
This paper considers breadth-first search (BFS) spanning trees, and addresses the problem of designing a sparse fault-tolerant BFS tree, or FT-BFS tree for short, namely, a sparse subgraph T of the given ...
Most previous work on sparse / compact fault-tolerant structures and services concerned structures that are distance-preserving (i.e., dealing with distances, shortest paths or shortest routes), global ...
doi:10.1007/978-3-642-40450-4_66
fatcat:kh6kjrc6hjffrapwlrubk22tua
Sparse Fault-Tolerant BFS Trees
[article]
2013
arXiv
pre-print
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We then consider fault-tolerant multi-source BFS trees, or FT-MBFS trees for short, aiming to provide (following a failure) a BFS tree rooted at each source s∈ S for some subset of sources S⊆ V. ...
This paper addresses the problem of designing a sparse fault-tolerant BFS tree, or FT-BFS tree for short, namely, a sparse subgraph T of the given network G such that subsequent to the failure of a single ...
Most previous work on sparse / compact fault-tolerant structures and services concerned structures that are distance-preserving (i.e., dealing with distances, shortest paths or shortest routes), global ...
arXiv:1302.5401v1
fatcat:a24ze5t5nzai3fj3brlvv3i6am
Fault-Tolerant Edge-Disjoint Paths – Beyond Uniform Faults
[article]
2020
arXiv
pre-print
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This work studies the Fault-Tolerant Path (FTP) problem, the counterpart of the Shortest Path problem in this fault model and the Fault-Tolerant Flow problem (FTF), the counterpart of the ℓ-disjoint Shortest ...
The overwhelming majority of survivable (fault-tolerant) network design models assume a uniform fault model. ...
Fault-Tolerant Paths
Directed Versus Undirected Graphs The classical shortest path problem is set on directed graphs. ...
arXiv:2009.05382v1
fatcat:tgjf4qtcofcovl3gsst4pn335m
Fast failover of multicast sessions in software-defined networks
[article]
2017
arXiv
pre-print
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Tree implementations To showcase and evaluate our algorithm, we will implement the join function for two different trees: the Shortest Paths Tree (SPT) and an approximation tree for the Dynamic Steiner ...
Tree (DST) problem [32] . 1) Shortest Paths Tree: Given a network G. ...
arXiv:1701.08182v1
fatcat:c4g6hmxyefe2zetgeaslttabjy
Generic Single Edge Fault Tolerant Exact Distance Oracle
2018
International Colloquium on Automata, Languages and Programming
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In a related problem of finding fault tolerant subgraph, Parter and Peleg (ESA 2013) showed that if detours of replacement paths ending at a vertex t are disjoint, then the number of such paths is O( √ ...
Given an undirected unweighted graph G and a source set S of |S| = σ sources, we want to build a data structure which can process the following query Q(s, t, e) : find the shortest distance from s to t ...
However, in the fault tolerant model, we expect the failure to be repaired readily and restore our original graph. In this paper, we study the shortest path problem in the fault tolerant model. ...
doi:10.4230/lipics.icalp.2018.72
dblp:conf/icalp/GuptaS18
fatcat:zp4ji73twncszcxp3dtofgxiym
Topology Agnostic Dynamic Quick Reconfiguration for Large-Scale Interconnection Networks
2012
2012 12th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (ccgrid 2012)
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We demonstrate that the method is workable for meshes, tori and fat-trees, and that it is able to guarantee one-fault tolerance for all of these topologies. ...
Toleration of faults in the interconnection networks is of vital importance in todays huge computer installations. Still, the existing solutions are short of being satisfactory. ...
Figure 4 . 4 Mesh fault tolerance capability.
Figure 5 . 5 Torus fault-tolerant capability.
Figure 6 . 6 Fat tree fault tolerance comparison. ...
doi:10.1109/ccgrid.2012.62
dblp:conf/ccgrid/Sem-JacobsenL12
fatcat:uzicuw4rfzcone7636hbmv52gq
Space Efficient Edge-Fault Tolerant Routing
2012
Foundations of Software Technology and Theoretical Computer Science
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Moreover, the stretch of the routing scheme, i.e., the maximum ratio of the cost of the path along which the packet is routed to the cost of the actual shortest path that avoids the fault, is only O(k ...
As an intermediate result, we show that computing this in a distributed model that stores at each vertex the shortest path tree rooted at that node requires Θ(mn) message passings in the worst case. ...
T u : the shortest path tree rooted at u. T u (v) : the subtree of T u , rooted at v. P(u, v) : the original shortest path between u, v. δ(u, v) : the length of the path P(u, v). ...
doi:10.4230/lipics.fsttcs.2012.350
dblp:conf/fsttcs/Rajan12
fatcat:jre5vgaspvfczmw5y2v3gbz4pu
Efficient fault-tolerant routing in multihop optical WDM networks
1999
IEEE Transactions on Parallel and Distributed Systems
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Our strategy is to first enhance the physical paths constructed by the algorithms for reliable networks to ensure success of fault-tolerant routing, and then to route among the enhanced paths to establish ...
a set of fault-free physical routes to complete the corresponding routing request for each of the communication patterns. ...
The basic idea to achieve fault-tolerant multicast is to enhance every edge in multicast tree w with multiple alternative paths such that w is always connected via at least one of these paths in the case ...
doi:10.1109/71.808141
fatcat:scuhul5gdbbjjf2azkddfithga
Generic Single Edge Fault Tolerant Exact Distance Oracle
[article]
2018
arXiv
pre-print
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In a related problem of finding fault tolerant subgraph, Parter and Peleg (ESA 2013) showed that if detours of the replacement paths ending at a vertex t are disjoint, then the number of such paths is ...
Given an undirected unweighted graph G and a source set S of |S| = σ sources, we want to build a data structure which can process the following query Q(s,t,e): find the shortest distance from s to t avoiding ...
However, in the fault tolerant model, we expect the failure to be repaired readily and restore our original graph. In this paper, we study the shortest path problem in the fault tolerant model. ...
arXiv:1805.00190v1
fatcat:5pq33yiegfbr5dbu5oa6nwmcoi
Biological and Shortest-Path Routing Procedures for Transportation Network Design
[article]
2018
arXiv
pre-print
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We use it to compare biological and a shortest-path routing approaches. ...
We adopt the approximation algorithm described in [12] . It starts with a suboptimal solution where the flows are routed on a low-stretch spanning tree (distance preserving tree). ...
In practice it involves computing as many shortest-path tree as the size of the minimal vertex cover of transfers higher than 0 (which is at most n). ...
arXiv:1803.03528v1
fatcat:ldbrbc4rcjapdlgks3cicdho5i
An Evaluation of Shared Multicast Trees with Multiple Active Cores
[chapter]
2001
Lecture Notes in Computer Science
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Core-based multicast trees use less routing state compared to shortest-path trees, but generally have higher end-to-end delay and poor fault tolerance. ...
, and fault tolerance. ...
Acknowledgments The authors would like to thank Krishnan Sivaramakrishna Iyer for help developing the dominating set approximation algorithm and Ragini Singh for help verifying the simulator. ...
doi:10.1007/3-540-47728-4_61
fatcat:ipyhp6dftrabzg6l42dut4iihe
Fault Tolerant Reachability for Directed Graphs
[chapter]
2015
Lecture Notes in Computer Science
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reachability tree T . ...
For the restricted case when the reachability tree T is a Depth-First-Search (DFS) tree it is straightforward to bound the size of the optimal set E by n − 1 using semidominators with respect to DFS trees ...
[8] established a lower bound of Ω(m) for single source fault tolerant shortest paths structure. ...
doi:10.1007/978-3-662-48653-5_35
fatcat:w2rrfc3e7fbi3ckjeswkfkwoxq
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