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Faster Algorithms for Text-to-Pattern Hamming Distances

The exact algorithms use a novel combination of hashing, bit-packed FFT, and recursion, and prove a fine-grained equivalence between the exact Text-to-Pattern Hamming Distances problem and a range-restricted, counting version of 3 SUM.
IEEE (opens in a new tab)

Beyond 2-Approximation for k-Center in Graphs

The first set of results show that one can beat the multiplicative factor of $2$ in undirected unweighted graphs if one is willing to allow additional small additive error, obtaining $(2-\varepsilon,O(1))$ approximations.
arXiv (opens in a new tab)

All-Pairs Shortest Paths with Few Weights per Node

New algorithms are presented that can tolerate any sublinear number of distinct weights per node d ≤ n1−є, whereas previous work could only handle d ≤ n1/2−є in subcubic time, promoting the understanding of the APSP hypothesis showing that the hardest instances must exhaust a linear number of weights per node.
ACM (opens in a new tab)

Listing 6-Cycles

A simple algorithm is given that lists $t$ (non-induced) $6-cycles in an $n$-node undirected graph in $\tilde O(n^2+t)$ time, which nearly matches the fastest known algorithm for detecting a $6$-cycle in $O(n2) $ time by Yuster and Zwick (1997).
arXiv (opens in a new tab)

Improved Roundtrip Spanners, Emulators, and Directed Girth Approximation

This paper focuses on developing fast algorithms for roundtrip spanners and related problems, and gives an $\tilde{O}(mn^{1/3})$-time algorithm that 4-approximation of a directed graph, which is near-optimal for dense graphs.
arXiv (opens in a new tab)
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