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Space-Efficient Fault-Tolerant Diameter Oracles [article]

Davide Bilò, Sarel Cohen, Tobias Friedrich, Martin Schirneck
2021 arXiv   pre-print
We design f-edge fault-tolerant diameter oracles (f-FDOs).  ...  We show that for unweighted graphs with polylogarithmic diameter and up to f = o(log n/ loglog n) failures, one can swap approximation for query time and space.  ...  Our fault-tolerant diameter oracle also allows non-edges to be queried, for which we return the original diameter diam(G).  ... 
arXiv:2107.03485v1 fatcat:3a2l7rvbifdyzjiu4q23fhf7uu

Space-Efficient Fault-Tolerant Diameter Oracles

Davide Bilò, Sarel Cohen, Tobias Friedrich, Martin Schirneck, Filippo Bonchi, Simon J. Puglisi
2021
We design f-edge fault-tolerant diameter oracles (f-FDO, or simply FDO if f = 1).  ...  We complement this with a lower bound excluding any finite stretch in o(fn) space. Many real-world networks have polylogarithmic diameter.  ...  18:4 Space-Efficient Fault-Tolerant Diameter Oracles Question 4 -space vs. approximation trade-off for multiple failures.  ... 
doi:10.4230/lipics.mfcs.2021.18 fatcat:ydiydkia6bcbxb675wp2dygwh4

Deterministic Sensitivity Oracles for Diameter, Eccentricities and All Pairs Distances [article]

Davide Bilò, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, Martin Schirneck
2022 arXiv   pre-print
[ITCS 2017] initiated the study of fault-tolerant (sensitivity) oracles for the diameter and vertex eccentricities. We extend this with a special focus on space efficiency.  ...  We further prove lower bounds that show limits to approximation vs. space and diameter vs. space trade-offs for fault-tolerant oracles.  ...  We abbreviate f -edge fault-tolerant diameter oracle as f -FDO and f -edge fault-tolerant eccentricity oracle as f -FEO.  ... 
arXiv:2204.10679v1 fatcat:nm2dizmc7rddbhy6gu4co43wom

Fixed-Parameter Sensitivity Oracles [article]

Davide Bilò, Katrin Casel, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, J.A. Gregor Lagodzinski, Martin Schirneck, Simon Wietheger
2021 arXiv   pre-print
Following our line of research connecting fault-tolerant FPT and shortest paths problems, we also introduce parameterization to the computation of distance preservers.  ...  We study the problem, given a directed unweighted graph with a fixed source s and parameters f and k, to construct a polynomial-sized oracle that efficiently reports, for any target vertex v and set F  ...  Space-Efficient Fault- Tolerant Diameter Oracles.  ... 
arXiv:2112.03059v1 fatcat:ooac3rw4szh63icloztu7jdymm

Can't See the Forest for the Trees

Omri Kahalon, Hung Le, Lazar Milenković, Shay Solomon
2022 Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing  
Beyond its simplicity, the strength of our approach is three-fold: • Applicable: We present a variety of applications of our efficient navigation scheme, including a 2-hop routing scheme in Euclidean spaces  ...  Moreover, one can compute such spanners efficiently in the standard centralized and distributed settings.  ...  A fault-tolerant spanner and navigation scheme.  ... 
doi:10.1145/3519270.3538414 fatcat:oynmomltr5aqbdc56pi7fvfgla

f-Sensitivity Distance Oracles and Routing Schemes [chapter]

Shiri Chechik, Michael Langberg, David Peleg, Liam Roditty
2010 Lecture Notes in Computer Science  
This paper presents an efficiently constructible f -sensitivity distance oracle that given a triplet (s, t, F ), where s and t are vertices and F is a set of forbidden edges such that |F | ≤ f , returns  ...  In contrast, previous papers concern f -sensitive exact distance oracles, which consequently have size Ω(n 2 ). Moreover, those oracles support forbidden sets F of size |F | ≤ 2.  ...  Fault-tolerant label-based distance oracles and routing schemes for graphs of bounded cliquewidth are presented in [19] .  ... 
doi:10.1007/978-3-642-15775-2_8 fatcat:g3sneyv2i5gtnkketjj67q7lmm

f-Sensitivity Distance Oracles and Routing Schemes

Shiri Chechik, Michael Langberg, David Peleg, Liam Roditty
2011 Algorithmica  
This paper presents an efficiently constructible f -sensitivity distance oracle that given a triplet (s, t, F ), where s and t are vertices and F is a set of forbidden edges such that |F | ≤ f , returns  ...  In contrast, previous papers concern f -sensitive exact distance oracles, which consequently have size Ω(n 2 ). Moreover, those oracles support forbidden sets F of size |F | ≤ 2.  ...  Fault-tolerant label-based distance oracles and routing schemes for graphs of bounded cliquewidth are presented in [19] .  ... 
doi:10.1007/s00453-011-9543-0 fatcat:hpy6n45te5fufduswlg45djtuq

Implementation of Quantum Search Algorithm using Classical Fourier Optics

N. Bhattacharya, H. B. van Linden van den Heuvell, R. J. C. Spreeuw
2002 Physical Review Letters  
We report on an experiment on Grover's quantum search algorithm showing that classical waves can search a N-item database as efficiently as quantum mechanics can.  ...  Although the lack of quantum entanglement limits the size of our database, our results show that entanglement is neither necessary for the algorithm itself, nor for its efficiency.  ...  Theoretical studies have investigated fault tolerance [21, 22] and noise [23] in Grover's algorithm, predicting damping of the cycles of finding and "unfinding," as we also see in the experiment.  ... 
doi:10.1103/physrevlett.88.137901 pmid:11955125 fatcat:bs27iyemyrcupgob7j2fdqggse

Network(graph) data research in the coordinate system

Liu Hui, Lin Zhi, Waqas Ahmad
2018 Mathematical Foundations of Computing  
analysis of network(graph) data correlated with Internet, social networks, communication networks, knowledge graph etc, but few of them have been applied in the coordinate system which is thought to be an efficient  ...  Coordinates embedding and transforming even make parallel routing (faulttolerant routing) and wide diameter (fault-tolerant diameter) calculating of DLN become easily, once wide diameter calculating thought  ...  In particular, it has been studied with respect to network properties such as diameter [10] , fault tolerance [6] [2] , and message routing [8] [27] .Currently, though DLN is no longer a hot spot  ... 
doi:10.3934/mfc.2018001 fatcat:j5ikmkma4vg2bbwriude3k5dse

X-BOT: A Protocol for Resilient Optimization of Unstructured Overlays

João Carlos Antunes Leitao, João Pedro da Silva Ferreira Moura Marques, José Orlando Roque Nascimento Pereira, Luís Eduardo Teixeira Rodrigues
2009 2009 28th IEEE International Symposium on Reliable Distributed Systems  
In many cases, it is interesting to bias the random overlay in order to optimize some efficiency criteria, for instance, to reduce the stretch of the overlay routing.  ...  Experimental results show that X-BOT can generate more efficient overlays than previous approaches. * This work was partially supported by project "Redico" (PTDC/EIA/71752/2006).  ...  This partial view is used for fault tolerance, as it works like a backup list of nodes that are used to ensure a constant out-degree for nodes.  ... 
doi:10.1109/srds.2009.20 dblp:conf/srds/LeitaoMPR09 fatcat:s456xquwnvfwjdi57qadqhrnhe

Can't See The Forest for the Trees: Navigating Metric Spaces by Bounded Hop-Diameter Spanners [article]

Omri Kahalon, Hung Le, Lazar Milenkovic, Shay Solomon
2022 arXiv   pre-print
To control the hop-length of paths, one can try to upper bound the spanner's hop-diameter, but naturally bounded hop-diameter spanners are more complex than spanners with unbounded hop-diameter, which  ...  an efficient algorithm finding it?  ...  Fault-tolerant routing Fault-tolerant routing in trees. We describe a fault-tolerant routing scheme for trees of the robust tree cover presented in Section 4.  ... 
arXiv:2107.14221v2 fatcat:dwdkmbygvzggvm5zz372xbalhm

Optimal Vertex Fault Tolerant Spanners (for fixed stretch) [chapter]

Greg Bodwin, Michael Dinitz, Merav Parter, Virginia Vassilevska Williams
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
We also consider the edge fault tolerant (EFT) model, defined analogously with edge failures rather than vertex failures. We show that the same spanner upper bound applies in this setting.  ...  Spanners were introduced by Peleg and Ullman [46] and Peleg and Schäffer [45], and have a wide range of applications in routing [47], synchronizers [6], broadcasting [5, 43], distance oracles [49], graph  ...  Fault-tolerant approximate shortest-path trees. 19] T-H Hubert Chan, Mingfei Li, and Li Ning. Sparse fault-tolerant spanners for doubling metrics with bounded hop-diameter or degree.  ... 
doi:10.1137/1.9781611975031.123 dblp:conf/soda/BodwinDPW18 fatcat:t5sr4ib7freujfdjufj4sidzqe

Conditional Hardness for Sensitivity Problems

Monika Henzinger, Andrea Lincoln, Stefan Neumann, Virginia Vassilevska Williams, Marc Herbstritt
2017 Innovations in Theoretical Computer Science  
Many of our lower bounds also hold for static oracle data structures where no sensitivity is required.  ...  We extend our reduction from BMM to Diameter to give a reduction from All Pairs Shortest Paths to Diameter under one deletion in weighted graphs.  ...  An optimal dual fault tolerant reachability oracle. In ICALP, pages 130:1-130:13, 2016. 21 Søren Dahlgaard. On the hardness of partially dynamic graph problems and connections to diameter.  ... 
doi:10.4230/lipics.itcs.2017.26 dblp:conf/innovations/HenzingerL0W17 fatcat:6mw52rwkafcothehbz4nua27wq

Conditional Hardness for Sensitivity Problems [article]

Monika Henzinger, Andrea Lincoln, Stefan Neumann, Virginia Vassilevska Williams
2017 arXiv   pre-print
Many of our lower bounds also hold for static oracle data structures where no sensitivity is required.  ...  This result is surprising since in the static setting it is not clear whether a reduction from BMM to diameter is possible.  ...  An optimal dual fault tolerant reachability oracle. In ICALP, pages 130:1-130:13, 2016. 21 Søren Dahlgaard. On the hardness of partially dynamic graph problems and connections to diameter.  ... 
arXiv:1703.01638v1 fatcat:udwtdffcebbijku3zkctq4x4ii

A Bi-level Nested Sparse Optimization for Adaptive Mechanical Fault Feature Detection

Han Zhang, Xuefeng Chen, Xiaoli Zhang, Xinrong Zhang
2020 IEEE Access  
The proposed BiNOSP can perfectly approximate the oracle MSE without any real feature information, and further provides a reliable way to obtain the optimal hyper-parameter sets for the maximum performance  ...  Denoising is a permanent topic and there are various denoisers proposed in the fault diagnosis of industrial systems.  ...  The core idea of SRFD is to explore the sparsity prior of fault feature signal in an elaborately designed transformation space, and then reconstruct the target feature through optimization strategy [16  ... 
doi:10.1109/access.2020.2968726 fatcat:6v4654yaavgpxdngysf2qjk4nu
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