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Path-Fault-Tolerant Approximate Shortest-Path Trees [article]

Annalisa D'Andrea, Mattia D'Emidio, Daniele Frigioni, Stefano Leucci, Guido Proietti
2015 arXiv   pre-print
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]

Davide Bilò and Luciano Gualà and Stefano Leucci and Guido Proietti
2016 arXiv   pre-print
., 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]

Davide Bilò, Luciano Gualà, Stefano Leucci, Guido Proietti
2016 arXiv   pre-print
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]

Merav Parter, David Peleg
2013 Lecture Notes in Computer Science  
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]

Merav Parter, David Peleg
2013 arXiv   pre-print
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]

David Adjiashvili, Felix Hommelsheim, Moritz Mühlenthaler, Oliver Schaudt
2020 arXiv   pre-print
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]

Jorik Oostenbrink, Niels L. M. van Adrichem, Fernando A. Kuipers
2017 arXiv   pre-print
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

Manoj Gupta, Aditi Singh, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
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

Frank Olaf Sem-Jacobsen, Olav Lysne
2012 2012 12th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (ccgrid 2012)  
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

Varun Rajan, Marc Herbstritt
2012 Foundations of Software Technology and Theoretical Computer Science  
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

Hong Shen, F. Chin, Yi Pan
1999 IEEE Transactions on Parallel and Distributed Systems  
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]

Manoj Gupta, Aditi Singh
2018 arXiv   pre-print
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]

François Queyroi
2018 arXiv   pre-print
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]

Daniel Zappala, Aaron Fabbri
2001 Lecture Notes in Computer Science  
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]

Surender Baswana, Keerti Choudhary, Liam Roditty
2015 Lecture Notes in Computer Science  
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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