Lower bounds for matroid optimization problems with a linear constraint
I Doron-Arad, A Kulik, H Shachnai - 51st International Colloquium …, 2024 - drops.dagstuhl.de
We study a family of matroid optimization problems with a linear constraint (MOL). In these
problems, we seek a subset of elements which optimizes (ie, maximizes or minimizes) a …
problems, we seek a subset of elements which optimizes (ie, maximizes or minimizes) a …
Determinantal sieving
We introduce a new, remarkably powerful tool to the toolbox of algebraic FPT algorithms,
determinantal sieving. Given a polynomial P (x 1,…, xn) over a field 𝔽 of characteristic 2, on …
determinantal sieving. Given a polynomial P (x 1,…, xn) over a field 𝔽 of characteristic 2, on …
Tight lower bounds for weighted matroid problems
I Doron-Arad, A Kulik, H Shachnai - arXiv preprint arXiv:2307.07773, 2023 - arxiv.org
In this paper we derive tight lower bounds resolving the hardness status of several
fundamental weighted matroid problems. One notable example is budgeted matroid …
fundamental weighted matroid problems. One notable example is budgeted matroid …
Leveraging Fixed-Parameter Tractability for Robot Inspection Planning
Y Mizutani, DC Salomao, A Crane, M Bentert… - arXiv preprint arXiv …, 2024 - arxiv.org
Autonomous robotic inspection, where a robot moves through its environment and inspects
points of interest, has applications in industrial settings, structural health monitoring, and …
points of interest, has applications in industrial settings, structural health monitoring, and …
Hamiltonicity, Path Cover, and Independence Number: An FPT Perspective
The connection between Hamiltonicity and the independence numbers of graphs has been
a fundamental aspect of Graph Theory since the seminal works of the 1960s. This paper …
a fundamental aspect of Graph Theory since the seminal works of the 1960s. This paper …
Finding longer cycles via shortest colourful cycle
A Björklund, T Husfeldt - arXiv preprint arXiv:2408.03699, 2024 - arxiv.org
We consider the parameterised $ k, e $-Long Cycle problem, in which you are given an $ n
$-vertex undirected graph $ G $, a specified edge $ e $ in $ G $, and a positive integer $ k …
$-vertex undirected graph $ G $, a specified edge $ e $ in $ G $, and a positive integer $ k …
Two-sets cut-uncut on planar graphs
We study the following Two-Sets Cut-Uncut problem on planar graphs. Therein, one is given
an undirected planar graph $ G $ and two sets of vertices $ S $ and $ T $. The question is …
an undirected planar graph $ G $ and two sets of vertices $ S $ and $ T $. The question is …
An algorithmic version of the Hajnal--Szemer\'edi theorem
L Gan, J Han, J Hu - arXiv preprint arXiv:2307.08056, 2023 - arxiv.org
We prove the following algorithmic version of the classical Hajnal--Szemer\'edi Theorem in
graph theory. Given $ r, c, n\in\mathbb {N} $ such that $ n\in r\mathbb N $, let $ G $ be an $ n …
graph theory. Given $ r, c, n\in\mathbb {N} $ such that $ n\in r\mathbb N $, let $ G $ be an $ n …
Computing paths of large rank in planar frameworks deterministically
A framework consists of an undirected graph $ G $ and a matroid $ M $ whose elements
correspond to the vertices of $ G $. Recently, Fomin et al.[SODA 2023] and Eiben et …
correspond to the vertices of $ G $. Recently, Fomin et al.[SODA 2023] and Eiben et …
Determining fixed-length paths in directed and undirected edge-weighted graphs
D Hambly, R Lewis, P Corcoran - 2024 - orca.cardiff.ac.uk
In this paper, we examine the N P-hard problem of identifying fixed-length st paths in edge-
weighted graphs–that is, a path of a desired length k from a source vertex s to a target vertex …
weighted graphs–that is, a path of a desired length k from a source vertex s to a target vertex …