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Fully dynamic maximal matching in O(log n) update time [article]

Surender Baswana, Manoj Gupta, Sandeep Sen
2016 arXiv   pre-print
In contrast, we can maintain a factor two approximate maximum matching in O(log n) expected time per update as a direct corollary of the maximal matching scheme.  ...  Our data structure is randomized that takes O(log n) expected amortized time for each edge update where n is the number of vertices in the graph.  ...  This leads to a fully dynamic algorithm for maximal matching which achieves expected amortized O(log n) update time per edge insertion or deletion.  ... 
arXiv:1103.1109v4 fatcat:w4vprjmwqzcvrdtn5zwblsjssu

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

Surender Baswana, Manoj Gupta, Sandeep Sen
2011 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science  
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.  ...  Our data structure is randomized that takes O(log n) expected amortized time for each edge update where n is the number of vertices in the graph.  ...  This leads to a fully dynamic algorithm for maximal matching which achieves expected amortized O(log n) update time per edge insertion or deletion.  ... 
doi:10.1109/focs.2011.89 dblp:conf/focs/BaswanaGS11 fatcat:77frtcv62jel3btmdu2iw25pyi

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

Surender Baswana, Manoj Gupta, Sandeep Sen
2015 SIAM journal on computing (Print)  
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.  ...  Our data structure is randomized that takes O(log n) expected amortized time for each edge update where n is the number of vertices in the graph.  ...  This leads to a fully dynamic algorithm for maximal matching which achieves expected amortized O(log n) update time per edge insertion or deletion.  ... 
doi:10.1137/130914140 fatcat:fadpjoe3bfc5nchei5wdxk5fvi

Fully Dynamic Maximal Matching in Constant Update Time [article]

Shay Solomon
2016 arXiv   pre-print
Baswana, Gupta and Sen [FOCS'11] showed that fully dynamic maximal matching can be maintained in general graphs with logarithmic amortized update time.  ...  In this paper, we resolve the question in the affirmative, by presenting a randomized algorithm for maintaining maximal matching in general graphs with constant amortized update time.  ...  A fundamental challenge is to efficiently maintain a maximal matching in a fully dynamic setting.  ... 
arXiv:1604.08491v1 fatcat:gkt3g6hbvjfell3qs42sneapsq

Fully Dynamic Matching: Beating 2-Approximation in Δ^ϵ Update Time [article]

Soheil Behnezhad, Jakub Łącki, Vahab Mirrokni
2019 arXiv   pre-print
In fully dynamic graphs, we know how to maintain a 2-approximation of maximum matching extremely fast, that is, in polylogarithmic update time or better.  ...  update time O(Δ^ϵ+polylog n), where Δ is the maximum degree.  ...  Acknowledgements Soheil Behnezhad thanks Mahsa Derakhshan, MohammadTaghi Hajiaghayi, Cliff Stein and Madhu Sudan for their collaboration in [6] and Sepehr Assadi for many helpful discussions and pointers  ... 
arXiv:1911.01839v1 fatcat:cx76uc4ljregzoz65fpmh3lvfa

Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time [article]

Franziska Eberle, Nicole Megow, Lukas Nölke, Bertrand Simon, Andreas Wiese
2021 arXiv   pre-print
More precisely, we handle the arrival and departure of individual items or knapsacks during the execution of the algorithm with worst-case update time polylogarithmic in the number of items.  ...  We investigate this problem and special cases thereof in the context of dynamic algorithms and design data structures that efficiently maintain near-optimal knapsack solutions for dynamically changing  ...  Fully dynamic approximate maximum matching and minimum vertex cover in O(log 3 n) worst case update time. In SODA, pages 470-489. SIAM, 2017. 11 S. Bhattacharya, M. Henzinger, and D. Nanongkai.  ... 
arXiv:2007.08415v3 fatcat:hs7o2xmqirah5iqpsh42voguvu

Deterministic Dynamic Matching in O(1) Update Time

Sayan Bhattacharya, Deeparnab Chakrabarty, Monika Henzinger
2019 Algorithmica  
(in: Proceedings of the ACM-SIAM symposium on discrete algorithms (SODA), 2015); it had an approximation ratio of (2 + ε) and an amortized update time of O(log n/ε 2 ).  ...  We present a new deterministic fully dynamic algorithm that maintains a O(1)-approximate minimum vertex cover and maximum fractional matching, with an amortized update time of O(1).  ...  [6] whose amortized update time was O( f · log(m + n)); we trade-off O( f ) in the approximation factor with O(log n) in the update time.  ... 
doi:10.1007/s00453-019-00630-4 fatcat:vqgsq4gghjablm43jzq75nlho4

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

Fully-Dynamic Minimum Spanning Forest with Improved Worst-Case Update Time [article]

Christian Wulff-Nilsen
2016 arXiv   pre-print
An immediate corollary of our result is the first Las Vegas data structure for fully-dynamic connectivity where each update is handled in worst-case time polynomially faster than Theta(n^1/2) w.h.p.; this  ...  Each update is supported in O(n^1/2 - c) expected worst-case time for some constant c > 0 and this worst-case bound holds with probability at least 1 - n^-d where d is a constant that can be made arbitrarily  ...  Then there is a fully-dynamic MSF structure with worst-case update time O(log 3 n + U (m, n) log n + ⌈lg m⌉ i=0 1 2 i P (min{m, 2 i log n}, min{n, 2 i log n})) for an n-vertex dynamic graph in which the  ... 
arXiv:1611.02864v2 fatcat:7hjj53c6qjec7ljmxxdiwqi5na

Fully dynamic 3/2 approximate maximum cardinality matching in O(√(n)) update time [article]

Manas Jyoti Kashyop, N.S. Narayanaswamy
2018 arXiv   pre-print
We present a randomized algorithm to maintain a maximal matching without 3 length augmenting paths in the fully dynamic setting.  ...  Over any sequence of t edge insertions and deletions presented by an oblivious adversary, the total update time of our algorithm is O(t√(n)) in expectation and O(t√(n) + n n) with high probability.  ...  Acknowledgement: We thank Sumedh Tirodkar for pointing out an error in our earlier draft.  ... 
arXiv:1810.01073v2 fatcat:hk4tzj7a5zar5kouym6nurtidm

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

Soheil Behnezhad, Mahsa Derakhshan, MohammadTaghi Hajiaghayi, Cliff Stein, Madhu Sudan
2019 arXiv   pre-print
Our algorithm is randomized and, per update, takes O(log^2 Δ·log^2 n) expected time.  ...  Furthermore, the algorithm can be adjusted to have O(log^2 Δ·log^4 n) worst-case update-time with high probability. Here, n denotes the number of vertices and Δ is the maximum degree in the graph.  ...  There is a data structure to maintain a random-order lexicographically first maximal matching against an oblivious adversary in a fully-dynamic graph that per update, takes O(log 2 ∆ · log 2 n) expected  ... 
arXiv:1909.03478v1 fatcat:hzibtxt6enhxxc27sxxe6uv54i

Deterministic Fully Dynamic Approximate Vertex Cover and Fractional Matching in O(1) Amortized Update Time [article]

Sayan Bhattacharya and Deeparnab Chakrabarty and Monika Henzinger
2016 arXiv   pre-print
We present a new deterministic fully dynamic algorithm that maintains a O(1)-approximate minimum vertex cover and maximum fractional matching, with an amortised update time of O(1).  ...  Our results also extend to a fully dynamic O(f^3)-approximate algorithm with O(f^2) amortized update time for the hypergraph vertex cover and fractional hypergraph matching problems, where every hyperedge  ...  (2+ δ )-approximate vertex cover and maximum matching in O(log n/δ 2 )-amortized update time.  ... 
arXiv:1611.00198v2 fatcat:s3x5lmcx4na3lhetb56x3eruqq

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
In this paper, we shave off a factor of log n from that time, to O(log^4 n) per update.  ...  This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space.  ...  W.h.p., fully dynamic 2-edge connectivity can be maintained in O(log 6 n) amortized time per update and O(log n/ log log n) per query using space O(n log 2 n) words, over a polynomial length sequence of  ... 
arXiv:1509.06464v1 fatcat:jsjqlzksjncadbqic63sxiqffe

Dynamic Suffix Array with Sub-linear update time and Poly-logarithmic Lookup Time [article]

Amihood Amir, Itai Boneh
2021 arXiv   pre-print
For an input query i∈ [1... n], our data structure reports SA_S[i] in O(log^5(n)) time.  ...  For an input query i∈ [1... n], our data structure reports the i'th entry in the inverted suffix array in O(log^4(n)) time.  ...  Acknowledgements We warmly thank Eylon Yogev for assistance with the presentation and the organization of the results presented in this manuscript.  ... 
arXiv:2112.12678v1 fatcat:vyhkhb4iafak7egvs6clpbapte

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
Our first algorithm is Monte Carlo and guarantees an O(n^0.4+o(1)) worst-case update time, where the o(1) term hides the O(√( n/ n)) factor.  ...  Our second algorithm is Las Vegas and guarantees an O(n^0.49306) worst-case update time with high probability.  ...  The term o(1) = O( log log n/ log n) in both preprocessing and update time.  ... 
arXiv:1611.03745v2 fatcat:3ov2ucwrrnd5jf2stms3qhq5ze
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