13 papers
FPTAS for Polygonal Multi-Robot Motion Planning
Sayan Bandyapadhyay, William Lochet, Saket Saurabh +1
We study multi-robot motion planning in a polygonal environment with polygonal robots. The setting of the problem consists of a polygonal domain with vertices and…
How to Fix a Broken Metric: A Linear Kernel, Tight Bounds, and Tree Metrics
Sayan Bandyapadhyay, William Lochet, Daniel Lokshtanov +4
Given a complete graph whose edge weights represent dissimilarities, Metric Violation Distance asks whether at most weights can be changed to form a metric. Motivated by metric…
Single-Exponential Algorithms for Directed Feedback Vertex Set on Planar Digraphs
Daniel Lokshtanov, Saket Saurabh, Jie Xue
We consider Directed Feedback Vertex Set on planar digraphs, parameterized by the solution size . We give a randomized algorithm with one-sided error running in time $(2+\sqrt5)…
Fine-Grained Bounds for Courcelle's Theorem
Daniel Lokshtanov, Fahad Panolan, Saket Saurabh +2
Courcelle's theorem states that there exists an algorithm that takes as input a graph of treewidth at most and a MSO formula , and determines whether satisfies i…
Parameterized Approximation of Rectangle Stabbing
Huairui Chu, Ajaykrishnan E S, Daniel Lokshtanov +4
In the Rectangle Stabbing problem, input is a set of axis-parallel rectangles and a set of axis parallel lines in the plane. The task is to find a minimum siz…
Robust Contraction Decomposition for Minor-Free Graphs and its Applications
Sayan Bandyapadhyay, William Lochet, Daniel Lokshtanov +6
We prove a robust contraction decomposition theorem for -minor-free graphs, which states that given an -minor-free graph and an integer , one can partition in polynomi…
Parameterized Approximation for Capacitated -Hitting Set with Hard Capacities
Daniel Lokshtanov, Abhishek Sahu, Saket Saurabh +2
The \textsc{Capacitated -Hitting Set} problem involves a universe with a capacity function and a collection of subsets…
Efficient Approximation of Fractional Hypertree Width
Viktoriia Korchemna, Daniel Lokshtanov, Saket Saurabh +2
We give two new approximation algorithms to compute the fractional hypertree width of an input hypergraph. The first algorithm takes as input -vertex -edge hypergraph of…
Subexponential Parameterized Algorithms for Hitting Subgraphs
Daniel Lokshtanov, Fahad Panolan, Saket Saurabh +2
For a finite set of graphs, the -Hitting problem aims to compute, for a given graph (taken from some graph class ) of vertices (and…
Bipartizing (Pseudo-)Disk Graphs: Approximation with a Ratio Better than 3
Daniel Lokshtanov, Fahad Panolan, Saket Saurabh +2
In a disk graph, every vertex corresponds to a disk in and two vertices are connected by an edge whenever the two corresponding disks intersect. Disk graphs form an…
An -Time Approximation Scheme for Geometric Many-to-Many Matching
Sayan Bandyapadhyay, Jie Xue
Geometric matching is an important topic in computational geometry and has been extensively studied over decades. In this paper, we study a geometric-matching problem, known as geo…
Enclosing Points with Geometric Objects
Timothy M. Chan, Qizheng He, Jie Xue
Let be a set of points in and be a set of geometric objects in , where . We study the problem of computing a…
Euclidean Bottleneck Steiner Tree is Fixed-Parameter Tractable
Sayan Bandyapadhyay, William Lochet, Daniel Lokshtanov +2
In the Euclidean Bottleneck Steiner Tree problem, the input consists of a set of points in called terminals and a parameter , and the goal is to compute a Ste…