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Fully-Dynamic Graph Sparsifiers Against an Adaptive Adversary [article]

Aaron Bernstein, Jan van den Brand, Maximilian Probst Gutenberg, Danupon Nanongkai, Thatchaphol Saranurak, Aaron Sidford, He Sun
2020 arXiv   pre-print
Designing dynamic graph algorithms against an adaptive adversary is a major goal in the field of dynamic graph algorithms.  ...  While a few such algorithms are known for spanning trees, matchings, and single-source shortest paths, very little was known for an important primitive like graph sparsifiers.  ...  There exists a fully dynamic algorithm that maintains for any weighted graph an e ǫ -approximate spectral sparsifier against an adaptive adversary.  ... 
arXiv:2004.08432v3 fatcat:2qr27k6ionfapogo66hn2aohpm

Rounding Dynamic Matchings Against an Adaptive Adversary [article]

David Wajc
2020 arXiv   pre-print
We present a new dynamic matching sparsification scheme. From this scheme we derive a framework for dynamically rounding fractional matchings against adaptive adversaries.  ...  Plugging in known dynamic fractional matching algorithms into our framework, we obtain numerous randomized dynamic matching algorithms which work against adaptive adversaries (the first such algorithms  ...  Cohen, Bernhard Haeupler, Roie Levin, Seffi Naor and the anonymous reviewers for comments on an earlier draft of this paper, which helped improve its presentation.  ... 
arXiv:1911.05545v2 fatcat:w32zxkzbbjchnevsykrsb7ryim

Fast Dynamic Cuts, Distances and Effective Resistances via Vertex Sparsifiers [article]

Li Chen, Gramoz Goranci, Monika Henzinger, Richard Peng, Thatchaphol Saranurak
2020 arXiv   pre-print
/3) amortized time against an oblivious adversary, and Õ(m^3/4) time against an adaptive adversary. (2) An incremental data structure that maintains O(1)-approximate shortest path in n^o(1) time per operation  ...  The key tool behind result (1) is the dynamic maintenance of an algorithmic construction due to Madry [FOCS' 10], which partitions a graph into a collection of simpler graph structures (known as j-trees  ...  6.16 works only against an oblivious adversary, so we need a dynamic cut sparsifier that works against an adaptive advesray.  ... 
arXiv:2005.02368v1 fatcat:rnksl5fksjfrxixq4n2pdxutcy

Deterministic Dynamic Matching In Worst-Case Update Time [article]

Peter Kiss
2021 arXiv   pre-print
We present deterministic algorithms for maintaining a (3/2 + ϵ) and (2 + ϵ)-approximate maximum matching in a fully dynamic graph with worst-case update times Ô(√(n)) and Õ(1) respectively.  ...  [arXiv'2021] has presented a fully dynamic algorithm for maintaining a (3/2 + ϵ)-approximate maximum matching with deterministic worst-case update time O_ϵ(√(n)).  ...  Our reduction requires an update time blow-up of Ô (1) or Õ (1) and is deterministic or randomized against an adaptive adversary respectively.  ... 
arXiv:2108.10461v3 fatcat:dnd5pgkw3ra4pg2m7n2pdk5lry

On Fully Dynamic Graph Sparsifiers

Ittai Abraham, David Durfee, Ioannis Koutis, Sebastian Krinninger, Richard Peng
2016 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)  
Third, we apply our dynamic sparsifier algorithm to obtain a fully dynamic algorithm for maintaining a (1 + ϵ)-approximation to the value of the maximum flow in an unweighted, undirected, bipartite graph  ...  Second, we give a fully dynamic algorithm for maintaining a (1 ±ϵ) -cut sparsifier with worst-case update time poly(n, ϵ^-1). Both sparsifiers have size n · poly(n, ϵ^-1).  ...  Thus, the full dynamic update process of all data structures takes O(poly(log n, −1 )) time per dynamic update ofG.  ... 
doi:10.1109/focs.2016.44 dblp:conf/focs/AbrahamDKKP16 fatcat:tu35ze66lncbdbg32fjv63az5u

The Expander Hierarchy and its Applications to Dynamic Graph Algorithms [article]

Gramoz Goranci, Harald Räcke, Thatchaphol Saranurak, Zihan Tan
2020 arXiv   pre-print
This decomposition is more robust against updates and better captures the clustering structure of graphs.  ...  The key idea behind these results is a fully dynamic algorithm for maintaining a tree flow sparsifier, a notion introduced by Räcke [FOCS'02] for constructing competitive oblivious routing schemes. (2)  ...  They also extend the algorithm to work against an adaptive adversary while supporting updates and queries inÕ(m 3/4 ) time.  ... 
arXiv:2005.02369v2 fatcat:mnl3635ea5d55int3kbdmfnj2a

Maintaining an EDCS in General Graphs: Simpler, Density-Sensitive and with Worst-Case Time Bounds [article]

Fabrizio Grandoni, Chris Schwiegelshohn, Shay Solomon, Amitai Uzrad
2021 arXiv   pre-print
In their breakthrough ICALP'15 paper, Bernstein and Stein presented an algorithm for maintaining a (3/2+ϵ)-approximate maximum matching in fully dynamic bipartite graphs with a worst-case update time of  ...  an oblivious adversary) one can achieve a much better (still polynomial) update time for approximation slightly below 2 [Behnezhad, Lacki and Mirrokni, SODA'20].  ...  assumption: Via a randomized algorithm against an adaptive adversary [Waj20, BHN16] and via a deterministic algorithm but with an amortized update time bound [BK21, BHN16] .  ... 
arXiv:2108.08825v1 fatcat:x4gz5uiwvba3bb5mslhrhhyi54

Fully Dynamic Electrical Flows: Sparse Maxflow Faster Than Goldberg-Rao [article]

Yu Gao, Yang P. Liu, Richard Peng
2021 arXiv   pre-print
We give an algorithm for computing exact maximum flows on graphs with m edges and integer capacities in the range [1, U] in O(m^3/2 - 1/328log U) time.  ...  Our algorithm revolves around dynamically maintaining the augmenting electrical flows at the core of the interior point method based algorithm from [Mądry JACM '16].  ...  While we do not build a Checker that works against fully adaptive adversaries, we allow for a small amount of adaptivity.  ... 
arXiv:2101.07233v2 fatcat:2ycw53yixbbqtkqvyke7eizbq4

Faster Maxflow via Improved Dynamic Spectral Vertex Sparsifiers [article]

Jan van den Brand, Yu Gao, Arun Jambulapati, Yin Tat Lee, Yang P. Liu, Richard Peng, Aaron Sidford
2021 arXiv   pre-print
A procedure for turning algorithms for estimating a sequence of vectors under updates from an oblivious adversary to one that tolerates adaptive adversaries via the Gaussian-mechanism from differential  ...  A direct reduction from detecting edges with large energy in dynamic electric flows to dynamic spectral vertex sparsifiers. 3.  ...  these dynamic algorithms to work against an adaptive adversary.  ... 
arXiv:2112.00722v1 fatcat:v5fv24yzpbdrzlkeso4ofz5haq

Fast Deterministic Fully Dynamic Distance Approximation [article]

Jan van den Brand, Sebastian Forster, Yasamin Nazari
2022 arXiv   pre-print
In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees.  ...  In particular, we obtain improved dynamic algorithms that, given an unweighted and undirected graph G=(V,E) undergoing edge insertions and deletions, and a parameter 0 < ϵ≤ 1, maintain (1+ϵ)-approximations  ...  hold with high probability against an adaptive adversary.  ... 
arXiv:2111.03361v2 fatcat:qzxfmf2znzcjhlsfckrxispe5i

Series Editorial: Inauguration Issue of the Series on Machine Learning in Communications and Networks

Geoffrey Y. Li, Walid Saad, Ayfer Ozgur, Peter Kairouz, Zhijin Qin, Jakob Hoydis, Zhu Han, Deniz Gunduz, Jaafar Elmirghani
2021 IEEE Journal on Selected Areas in Communications  
The paper proposed an end-to-end deep learning structure with adaptive depth, which could be adjusted for different tasks.  ...  The fine-tuning of the learned CTP is achieved so that the proposed design is adaptive to dynamic channel conditions without requiring training from scratch.  ... 
doi:10.1109/jsac.2020.3036785 fatcat:pdmsdg6zrreqzgqye3qrj5f3na

Maximum Flow and Minimum-Cost Flow in Almost-Linear Time [article]

Li Chen, Rasmus Kyng, Yang P. Liu, Richard Peng, Maximilian Probst Gutenberg, Sushant Sachdeva
2022 arXiv   pre-print
We give an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with m edges and polynomially bounded integral demands, costs, and capacities in m^1+o(1) time.  ...  Our algorithm builds the flow through a sequence of m^1+o(1) approximate undirected minimum-ratio cycles, each of which is computed and processed in amortized m^o(1) time using a new dynamic graph data  ...  Instead of modelling our IPM as giving rise to a fully-dynamic problem against an adaptive adversary, the promise that the witness circulation can always be written as f * − f lets us express the IPM with  ... 
arXiv:2203.00671v2 fatcat:hwdtmht5mjc4fn73pb3zg5tyte

Dynamic Spanning Forest with Worst-Case Update Time: Adaptive, Las Vegas, and O(n^1/2-ϵ)-Time [article]

Danupon Nanongkai, Thatchaphol Saranurak
2017 arXiv   pre-print
To the best of our knowledge, our algorithms are among a few non-trivial randomized dynamic algorithms that work against adaptive adversaries.  ...  Our algorithms guarantee worst-case update time and work against an adaptive adversary, meaning that an edge update can depend on previous outputs of the algorithms.  ...  The dynamic SF algorithm by Henzinger and King [17] works against adaptive adversaries by exactly doing this.  ... 
arXiv:1611.03745v2 fatcat:3ov2ucwrrnd5jf2stms3qhq5ze

2020 Index IEEE Transactions on Image Processing Vol. 29

2020 IEEE Transactions on Image Processing  
Chen, Z., +, TIP 2020 5431-5446 Online Tensor Sparsifying Transform Based on Temporal Superpixels From Compressive Spectral Video Measurements. Online Alternate Generator Against Adversarial Attacks.  ...  Shi, W., +, TIP 2020 375-388 Image Super-Resolution as a Defense Against Adversarial Attacks.  ... 
doi:10.1109/tip.2020.3046056 fatcat:24m6k2elprf2nfmucbjzhvzk3m

Dynamic Maintenance of Low-Stretch Probabilistic Tree Embeddings with Applications [article]

Sebastian Forster, Gramoz Goranci, Monika Henzinger
2020 arXiv   pre-print
We obtain a trade-off between amortized update time and expected stretch against an oblivious adversary.  ...  We give the first non-trivial fully dynamic probabilistic tree embedding algorithm for weighted graphs undergoing edge insertions and deletions.  ...  so as to make the decremental LDD algorithm fast, i.e., the centers are chosen by a fully adaptive adversary.  ... 
arXiv:2004.10319v2 fatcat:uevdd7dx75avpbtivcc4oh5j34
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