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When Algorithms for Maximal Independent Set and Maximal Matching Run in Sublinear Time

Schieber, and Shay Solomon . Fully dynamic maximal independent set with sublinear update time . In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018 , Los Angeles, CA, USA ... , June 25-29, 2018 , pages 815 - 826 , 2018 . Sepehr Assadi , Krzysztof Onak, Baruch Schieber, and Shay Solomon . Fully Dynamic Maximal Independent Set with Sublinear in n Update Time . In Proceedings of

Improved Dynamic Graph Coloring

, 1999. Moses Charikar and Shay Solomon. Fully dynamic almost-maximal matching: Breaking the polynomial barrier for worst-case time bounds. arXiv preprint arXiv:1711.06883, 2017. Richard Cole and Uzi ... number and min-3lin-deletion . In Proc. 33rd ICALP , pages 226 - 237 , 2006 . T. Kopelowitz , R. Krauthgamer , E. Porat, and Shay Solomon . Orienting fully dynamic graphs with worst-case time bounds . In

Fully Dynamic Almost-Maximal Matching: Breaking the Polynomial Worst-Case Time Barrier

Mark N. Wegman . Universal classes of hash functions . In Proc. 9th STOC , pages 106 - 112 , 1977 . Moses Charikar and Shay Solomon . Fully dynamic almost-maximal matching: Breaking the polynomial ... . Overmars . A balanced search tree with O (1) worstcase update time . Acta Inf. , 26 ( 3 ): 269 - 277 , 1988 . Ofer Neiman and Shay Solomon . Simple deterministic algorithms for fully dynamic maximal matching

Local Algorithms for Bounded Degree Sparsifiers in Sparse Graphs

-dimensional Euclidean space . In Proc. of 9th SOCG , pages 53 - 62 , 1993 . Int. J. Comput . Geometry Appl. , 7 ( 4 ): 297 - 315 , 1997 . Michael Elkin and Shay Solomon . Optimal euclidean spanners: Really ... Annual IEEE Symposium on Foundations of Computer Science, FOCS 2009, October 25-27 , 2009 , Atlanta, Georgia, USA, pages 3 - 12 , 2009 . Ofer Neiman and Shay Solomon . Simple deterministic algorithms for

Fully Dynamic MIS in Uniformly Sparse Graphs

, Cambridge, Massachusetts , USA 2 Shay Solomon 3 Baruch Schieber IBM Research, TJ Watson Research Center , Yorktown Heights, New York , USA We consider the problem of maintaining a maximal independent set ... Schieber, and Shay Solomon . Fully dynamic maximal independent set with sublinear update time . In Proc. 50th Annual ACM SIGACT Symposium on Theory of Computing , STOC, 2018 . 3 We note that the length of

Low-Light Trees, and Tight Lower Bounds for Euclidean Spanners

We show that for every n-point metric space M and positive integer k, there exists a spanning tree T with unweighted diameter O(k) and weight w(T)=O(k⋅n 1/k )⋅w(MST(M)), and a spanning tree T′ with weight w(T′)=O(k)⋅w(MST(M)) and unweighted diameter O(k⋅n 1/k ). These trees also achieve an optimal maximum degree. Furthermore, we demonstrate that these trees can be constructed...