On some fine-grained questions in algorithms and complexity

VV Williams - Proceedings of the international congress of …, 2018 - World Scientific
In recent years, a new “fine-grained” theory of computational hardness has been developed,
based on “fine-grained reductions” that focus on exact running times for problems …

Recent advances in fully dynamic graph algorithms–a quick reference guide

K Hanauer, M Henzinger, C Schulz - ACM Journal of Experimental …, 2022 - dl.acm.org
In recent years, significant advances have been made in the design and analysis of fully
dynamic algorithms. However, these theoretical results have received very little attention …

Dynamic matching with better-than-2 approximation in polylogarithmic update time

S Bhattacharya, P Kiss, T Saranurak, D Wajc - Journal of the ACM, 2024 - dl.acm.org
We present dynamic algorithms with polylogarithmic update time for estimating the size of
the maximum matching of a graph undergoing edge insertions and deletions with …

Breaking the cubic barrier for all-pairs max-flow: Gomory-hu tree in nearly quadratic time

A Abboud, R Krauthgamer, J Li… - 2022 IEEE 63rd …, 2022 - ieeexplore.ieee.org
In 1961, Gomory and Hu showed that the All-Pairs Max-Flow problem of computing the max-
flow between all n\2 pairs of vertices in an undirected graph can be solved using only n-1 …

Dynamic dynamic time war**

K Bringmann, N Fischer, I van der Hoog… - Proceedings of the 2024 …, 2024 - SIAM
Abstract The Dynamic Time War** (DTW) distance is a popular similarity measure for
polygonal curves (ie, sequences of points). It finds many theoretical and practical …

Rounding dynamic matchings against an adaptive adversary

D Wajc - Proceedings of the 52nd Annual ACM SIGACT …, 2020 - dl.acm.org
We present a new dynamic matching sparsification scheme. From this scheme we derive a
framework for dynamically rounding fractional matchings against adaptive adversaries …

Near-optimal fully dynamic densest subgraph

S Sawlani, J Wang - Proceedings of the 52nd Annual ACM SIGACT …, 2020 - dl.acm.org
We give the first fully dynamic algorithm which maintains a (1− є)-approximate densest
subgraph in worst-case time poly (log n, є− 1) per update. Dense subgraph discovery is an …

Fast dynamic cuts, distances and effective resistances via vertex sparsifiers

L Chen, G Goranci, M Henzinger… - 2020 IEEE 61st …, 2020 - ieeexplore.ieee.org
We present a general framework of designing efficient dynamic approximate algorithms for
optimization problems on undirected graphs. In particular, we develop a technique that …

Tree edit distance cannot be computed in strongly subcubic time (unless APSP can)

K Bringmann, P Gawrychowski, S Mozes… - ACM Transactions on …, 2020 - dl.acm.org
The edit distance between two rooted ordered trees with n nodes labeled from an alphabet
Ʃ is the minimum cost of transforming one tree into the other by a sequence of elementary …

Fredman's Trick Meets Dominance Product: Fine-Grained Complexity of Unweighted APSP, 3SUM Counting, and More

TM Chan, V Vassilevska Williams, Y Xu - Proceedings of the 55th …, 2023 - dl.acm.org
In this paper we carefully combine Fredman's trick [SICOMP'76] and Matoušek's approach
for dominance product [IPL'91] to obtain powerful results in fine-grained complexity. Under …