SETH vs Approximation

A Rubinstein, VV Williams - ACM SIGACT News, 2019 - dl.acm.org
Our story is about hardness of problems in P, but its roots begin with two algorithmic
approaches that have been developed to cope with NP-hard problems: approximation …

Tight conditional lower bounds for approximating diameter in directed graphs

M Dalirrooyfard, N Wein - Proceedings of the 53rd Annual ACM SIGACT …, 2021 - dl.acm.org
Among the most fundamental graph parameters is the Diameter, the largest distance
between any pair of vertices in a graph. Computing the Diameter of a graph with m edges …

Settling SETH vs. approximate sparse directed unweighted diameter (up to (NU) NSETH)

R Li - Proceedings of the 53rd Annual ACM SIGACT …, 2021 - dl.acm.org
We prove several tight results on the fine-grained complexity of approximating the diameter
of a graph. First, we prove that, for any ε> 0, assuming the Strong Exponential Time …

Approximation algorithms for min-distance problems in dags

M Dalirrooyfard, J Kaufmann - arXiv preprint arXiv:2106.02120, 2021 - arxiv.org
The min-distance between two nodes $ u, v $ is defined as the minimum of the distance from
$ v $ to $ u $ or from $ u $ to $ v $, and is a natural distance metric in DAGs. As with the …

Constant approximation of min-distances in near-linear time

S Chechik, T Zhang - 2022 IEEE 63rd Annual Symposium on …, 2022 - ieeexplore.ieee.org
In a weighed directed graph G=(V,E,ω) with m edges and n vertices, we are interested in its
basic graph parameters such as diameter, radius and eccentricities, under the nonstandard …

On Diameter Approximation in Directed Graphs

A Abboud, M Dalirrooyfard, R Li… - arXiv preprint arXiv …, 2023 - arxiv.org
Computing the diameter of a graph, ie the largest distance, is a fundamental problem that is
central in fine-grained complexity. In undirected graphs, the Strong Exponential Time …

Approximating Min-Diameter: Standard and Bichromatic

A Berger, J Kaufmann, VV Williams - arXiv preprint arXiv:2308.08674, 2023 - arxiv.org
The min-diameter of a directed graph $ G $ is a measure of the largest distance between
nodes. It is equal to the maximum min-distance $ d_ {min}(u, v) $ across all pairs $ u, v\in V …

Finding Patterns, Short Cycles and Long Shortest Paths in Graphs

M Dalirrooyfard - 2022 - dspace.mit.edu
This thesis is about finding useful structures in a graph using fast algorithms, or showing that
no such fast algorithms exist using popular fine-grained hypotheses from the field of Fine …

[PDF][PDF] Low obstacles avoidance for lower limb exoskeletons

E Trombin - 2022 - thesis.unipd.it
Powered lower limb exoskeletons (LLEs) are innovative wearable robots that allow
independent walking in people with severe gait impairments, or even to augment lower limb …

Algorithms and Hardness for Approximating the Diameter of a Graph

NS Wein - 2021 - dspace.mit.edu
The diameter of a graph is one of the most basic and fundamental attributes of a graph. It is
defined as the distance between the pair of vertices that is the farthest apart. The diameter of …