Hardness of Token Swapping on Trees

no code implementations • 11 Mar 2021 • Oswin Aichholzer, Erik D. Demaine, Matias Korman, Jayson Lynch, Anna Lubiw, Zuzana Mas, Mikhail Rudoy, Virginia Vassilevska Williams, Nicole Wein

We also show limitations on approximation of sequential token swapping on trees: we identify a broad class of algorithms that encompass all three known polynomial-time algorithms that achieve the best known approximation factor (which is $2$) and show that no such algorithm can achieve an approximation factor less than $2$.

Motion Planning Data Structures and Algorithms Computational Complexity

Fine-Grained Complexity and Algorithms for the Schulze Voting Method

no code implementations • 5 Mar 2021 • Krzysztof Sornat, Virginia Vassilevska Williams, Yinzhan Xu

We prove a similar connection between the so called Dominating Pairs problem and the problem of finding a winner in the Schulze method.

Open-Ended Question Answering

Algorithms, Reductions and Equivalences for Small Weight Variants of All-Pairs Shortest Paths

no code implementations • 11 Feb 2021 • Timothy M. Chan, Virginia Vassilevska Williams, Yinzhan Xu

We also give new algorithms for variants of #APSP in unweighted graphs, as well as a near-optimal $\tilde{O}(n^3)$-time algorithm for the original #APSP problem in unweighted graphs.

Data Structures and Algorithms Computational Complexity