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 O^(n)
Nearby in the stack
and
O~(1)
respectively. The fastest known deterministic worst-case update time algorithms for achieving approximation ratio
(2−δ)
(for any
δ>0
) and
(2+ε)
were both shown by Roghani et al. [2021] with update times
O(n3/4)
and
Oε(n)
respectively. We close the gap between worst-case and amortized algorithms for the two approximation ratios as the best deterministic amortized update times for the problem are
Oε(n)
and
O~(1)
which were shown in Bernstein and Stein [SODA'2021] and Bhattacharya and Kiss [ICALP'2021] respectively. In order to achieve both results we explicitly state a method implicitly used in Nanongkai and Saranurak [STOC'2017] and Bernstein et al. [arXiv'2020] which allows to transform dynamic algorithms capable of processing the input in batches to a dynamic algorithms with worst-case update time. Independent Work: Independently and concurrently to our work Grandoni et al. [arXiv'2021] has presented a fully dynamic algorithm for maintaining a
(3/2+ε)
-approximate maximum matching with deterministic worst-case update time