The hitting set problem is one of the fundamental problems in combinatorial optimization
and is well-studied in offline setup. We consider the online hitting set problem, where only …

Online algorithms are crucial for real-time decision-making and adaptability across diverse
fields, such as operations research, computer science, and combinatorics. These algorithms …

We revisit a natural variant of geometric set cover, called minimum-membership geometric
set cover (MMGSC). In this problem, the input consists of a set $ S $ of points and a set …

Abstract Let B=(b1,…, bn} be a set of n axis-aligned boxes in ℝ d where d≥ 2 is a constant.
The piercing problem is to compute a smallest set of points N∪ ℝ d that hits every box in B …

We consider the online version of the piercing set problem, where geometric objects arrive
one by one, and the online algorithm must maintain a valid piercing set for the already …

Abstract In the Maximum Independent Set of Hyperrectangles problem, we are given a set of
n (possibly overlapping) d-dimensional axis-aligned hyperrectangles, and the goal is to find …

In the Maximum Independent Set of Hyperrectangles problem, we are given a set of $ n
$(possibly overlapping) $ d $-dimensional axis-aligned hyperrectangles, and the goal is to …

VC-dimension and $\varepsilon $-nets are key concepts in Statistical Learning Theory.
Intuitively, VC-dimension is a measure of the size of a class of sets. The famous $\varepsilon …

We study the problem of stabbing rectilinear polygons, where we are given $ n $ rectilinear
polygons in the plane that we want to stab, ie, we want to select horizontal line segments …

We study rectangle stabbing problems in which we are given n axis-aligned rectangles in
the plane that we want to stab, that is, we want to select line segments such that for each …