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Fully Dynamic Maximal Independent Set with Sublinear in n Update Time [article]

Sepehr Assadi, Krzysztof Onak, Baruch Schieber, Shay Solomon
2018 arXiv   pre-print
The first fully dynamic algorithm for maintaining a maximal independent set (MIS) with update time that is sublinear in the number of edges was presented recently by the authors of this paper [Assadi et.al  ...  In this paper, we break this natural barrier and present the first fully dynamic (randomized) algorithm for maintaining an MIS with update time that is always sublinear in the number of vertices, namely  ...  We start with the simpler proof.  ... 
arXiv:1806.10051v1 fatcat:wjlcsv55sjhhfpl2og3oxtfs6e

Dynamic Geometric Data Structures via Shallow Cuttings

Timothy M. Chan
2020 Discrete & Computational Geometry  
We describe the first fully dynamic data structures with sublinear amortized update time for maintaining (i) the number of vertices or the volume of the convex hull of a 3D point set, (ii) the largest  ...  For example, we can now maintain the Euclidean minimum spanning tree of a 2D point set with O(log 6 n) amortized update time by using another reduction of Eppstein [18] combined with known results for  ...  For all these problems, the fully dynamic case has remained open. New results. 1. We present the first fully dynamic data structures with sublinear update time for Problems (i)-(iv).  ... 
doi:10.1007/s00454-020-00229-5 fatcat:265qnyzjkjfm5brlpwsra25o4e

Dynamic Geometric Data Structures via Shallow Cuttings [article]

Timothy M. Chan
2019 arXiv   pre-print
We describe the first fully dynamic data structures with sublinear amortized update time for maintaining (i) the number of vertices or the volume of the convex hull of a 3D point set, (ii) the largest  ...  The update times are near n^11/12 for (i) and (ii), n^7/8 for (iii) and (iv), and n^2/3 for (v).  ...  Thanks also to Mitchell Jones for discussions on range searching for points in convex position.  ... 
arXiv:1903.08387v1 fatcat:w6p24qkf75agdcogdyatg2535e

Worst-Case Efficient Dynamic Geometric Independent Set [article]

Jean Cardinal, John Iacono, Grigorios Koumoutsos
2021 arXiv   pre-print
with sublinear worst-case update time is possible.  ...  First, we develop a dynamic data structure which stores all objects and provides an approximate independent set when queried, with output-sensitive running time.  ...  Acknowledgments We would like to thank Timothy Chan and Qizheng He for pointing out an error in a previous version of this paper.  ... 
arXiv:2108.08050v4 fatcat:xce6fddysncixezglh5n7ph6km

Dynamic graph connectivity with improved worst case update time and sublinear space [article]

David Gibb, Bruce Kapron, Valerie King, Nolan Thorn
2015 arXiv   pre-print
This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space.  ...  In this paper, we shave off a factor of log n from that time, to O(log^4 n) per update.  ...  As an application, we show the first sublinear space dynamic 2-edge connectivity algorithm, which uses O(log 6 n) amortized update time, O(log n/ log log n) query time, and O(n log 2 n) words.  ... 
arXiv:1509.06464v1 fatcat:jsjqlzksjncadbqic63sxiqffe

Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms

Moab Arar, Shiri Chechik, Sarel Cohen, Cliff Stein, David Wajc, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
Specifically, our main result is a randomized fully-dynamic (2 + )-approximate integral matching algorithm with small polylog worst-case update time.  ...  We present a simple randomized reduction from fully-dynamic integral matching algorithms to fully-dynamic "approximately-maximal" fractional matching algorithms.  ...  Acknowledgements We thank Monika Henzinger for sharing a preprint of [15] with us, and Virginia Vassilevska Williams for sharing a preprint of [50] with us.  ... 
doi:10.4230/lipics.icalp.2018.7 dblp:conf/icalp/ArarCCSW18 fatcat:5sw6c6dv5ve5jfvkp7l6w3b2pi

Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms [article]

Moab Arar, Shiri Chechik, Sarel Cohen, Cliff Stein, David Wajc
2018 arXiv   pre-print
Specifically, our main result is a randomized fully-dynamic (2+ϵ)-approximate integral matching algorithm with small polylog worst-case update time.  ...  We present a simple randomized reduction from fully-dynamic integral matching algorithms to fully-dynamic "approximately-maximal" fractional matching algorithms.  ...  We thank Monika Henzinger for sharing a preprint of [14] with us, and Virginia Vassilevska Williams for sharing a preprint of [51] with us.  ... 
arXiv:1711.06625v2 fatcat:ibtgntip25dbretoruaww7nqby

More Dynamic Data Structures for Geometric Set Cover with Sublinear Update Time [article]

Timothy M. Chan, Qizheng He
2021 arXiv   pre-print
We present the first dynamic data structure that can maintain an O(1)-approximation in sublinear update time for set cover for axis-aligned squares in 2D.  ...  Previously, a dynamic geometric set cover data structure with sublinear update time was known only for unit squares by Agarwal, Chang, Suri, Xiao, and Xue [SoCG 2020].  ...  [3] , and another on dynamic geometric independent set by Henzinger, Neumann, and Wiese [23] . In this paper, we continue the study by Agarwal et al.  ... 
arXiv:2103.07857v1 fatcat:p7k66z65kvashaihrzrccayyue

Fully Dynamic Maximal Independent Set with Sublinear Update Time [article]

Sepehr Assadi and Krzysztof Onak and Baruch Schieber and Shay Solomon
2018 arXiv   pre-print
A maximal independent set (MIS) can be maintained in an evolving m-edge graph by simply recomputing it from scratch in O(m) time after each update.  ...  But can it be maintained in time sublinear in m in fully dynamic graphs? We answer this fundamental open question in the affirmative.  ...  An O(m 3/)-Update-Time Dynamic Algorithm We present our fully dynamic algorithm for maintaining a maximal independent set in this section and prove Theorem 1.  ... 
arXiv:1802.09709v1 fatcat:3xgikdusczdqnbxzxvij2ib4gq

Improved Algorithms for Fully Dynamic Maximal Independent Set [article]

Yuhao Du, Hengjie Zhang
2018 arXiv   pre-print
Maintaining maximal independent set in dynamic graph is a fundamental open problem in graph theory and the first sublinear time deterministic algorithm was came up by Assadi, Onak, Schieber and Solomon  ...  We have two main contributions in this paper. We present a new simple deterministic algorithm with O(m^2/3√( m)) amortized update time, which improves the previous best result.  ...  If one algorithm A will force one vertex w to be in MIS permanently, then A cannot solve the fully dynamic maximal independent set problem in O(m 1/2−ǫ ) amortized time for any constant ǫ, unless the OMv  ... 
arXiv:1804.08908v1 fatcat:yk7nqdga75gddnsex27m3d2mr4

Online Energy Management Strategy Design for Smart Meter Privacy Against FHMM-based NILM

Yang You, Tobias J. Oechtering
2020 2020 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm)  
With certain specific assumptions, the derived online energy management strategy is shown to have a sublinear dynamic regret and a sublinear dynamic fit, which means our proposed online algorithm has the  ...  asymptotic performance with the optimal offline dynamic benchmark.  ...  The authors in [23] show that by iteratively apply the above updating rules, an OCO problem in the same form with ( 14 ) but with time-invariant action set can be solved with sublinear dynamic regret  ... 
doi:10.1109/smartgridcomm47815.2020.9302973 fatcat:qtctydaiybb3ljxm5ridnh3hum

Fully Dynamic MIS in Uniformly Sparse Graphs

Krzysztof Onak, Baruch Schieber, Shay Solomon, Nicole Wein, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
We consider the problem of maintaining a maximal independent set (MIS) in a dynamic graph subject to edge insertions and deletions.  ...  Recently, Assadi, Onak, Schieber and Solomon (STOC 2018) showed that an MIS can be maintained in sublinear (in the dynamically changing number of edges) amortized update time.  ...  This data structure is fully dynamic with polylogarithmic amortized update time.  ... 
doi:10.4230/lipics.icalp.2018.92 dblp:conf/icalp/OnakSSW18 fatcat:bkult7l4evc77elewtbajiefta

Enumeration in Data Management (Dagstuhl Seminar 19211)

Endre Boros, Benny Kimelfeld, Reinhard Pichler, Nicole Schweikardt, Michael Wagner
2019 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 19211 "Enumeration in Data Management".  ...  In addition, we aimed to build and disseminate a toolkit for data-centric enumeration problems, including algorithmic techniques, proof techniques, and important indicator problems.  ...  [1] (i.e., enumerating the maximal independent sets for succinct graph representations) cannot lead to a polynomial delay algorithm assuming the Strong Exponential Time Hypothesis (SETH).  ... 
doi:10.4230/dagrep.9.5.89 dblp:journals/dagstuhl-reports/BorosKPS19 fatcat:gfir76niqfhmno2hpj563cwwqe

Fully Dynamic Maximal Matching in $O(\log n)$ Update Time

Surender Baswana, Manoj Gupta, Sandeep Sen
2015 SIAM journal on computing (Print)  
For a graph with n vertices and m edges, they give an O((n + m) 0.7072 ) update time algorithm which is sublinear only for a sparse graph.  ...  In contrast, we can maintain a factor two approximate maximum matching in O(log n) expected amortized time per update as a direct corollary of the maximal matching scheme.  ...  FULLY DYNAMIC ALGORITHM WITH EXPECTED AMORTIZED O( √ n) TIME PER UPDATE The algorithm maintains a partition of the set of vertices into two levels.  ... 
doi:10.1137/130914140 fatcat:fadpjoe3bfc5nchei5wdxk5fvi

Dynamic Graph Algorithms with Batch Updates in the Massively Parallel Computation Model [article]

Krzysztof Nowicki, Krzysztof Onak
2021 arXiv   pre-print
They work in the most restrictive memory regime, in which local memory per machine is strongly sublinear in the number of graph vertices.  ...  Our algorithms can process batches of updates of size Θ(S), for Minimum Spanning Forest and 2-Edge Connected Components, and Θ(S^1-ε), for Maximal Matching, in O(1) rounds, where S is the local memory  ...  Need of Algorithms for Dynamic Data Sets: In the strongly sublinear memory regime we don't know any efficient 3 algorithms for neither the Maximal Matching problem or the Minimum Spanning Forest problem  ... 
arXiv:2002.07800v2 fatcat:ukkaha5mrfd5bghlqtlx7cnduq
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