Related papers: Packing Boundary-Anchored Rectangles and Squares
We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are…
A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.
We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on a line segment, a…
In this paper, we investigate the homothetic point enclosure problem: given a set $S$ of $n$ triangles with sides parallel to three fixed directions, find a data structure for $S$ that can report all the triangles of $S$ that contain a…
We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…
A quadratically constrained quadratic program (QCQP) is an optimization problem in which the objective function is a quadratic function and the feasible region is defined by quadratic constraints. Solving non-convex QCQP to global…
Let $B$ be a set of $n$ axis-parallel boxes in $\mathbb{R}^d$ such that each box has a corner at the origin and the other corner in the positive quadrant of $\mathbb{R}^d$, and let $k$ be a positive integer. We study the problem of…
We present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most…
A surface embedded in space, in such a way that each point has a neighborhood within which the surface is a terrain, projects to an immersed surface in the plane, the boundary of which is a self-intersecting curve. Under what circumstances…
We consider the problem of computing Shapley values for points in the plane, where each point is interpreted as a player, and the value of a coalition is defined by the area of usual geometric objects, such as the convex hull or the minimum…
The aim of the paper is to propose a bounded-error quantum polynomial time (BQP) algorithm for the max-bisection and the min-bisection problems. The max-bisection and the min-bisection problems are fundamental NP-hard problems. Given a…
We consider the problem of solving packing/covering LPs online, when the columns of the constraint matrix are presented in random order. This problem has received much attention and the main focus is to figure out how large the right-hand…
We study the Partial Degree Bounded Edge Packing (PDBEP) problem introduced in [5] by Zhang. They have shown that this problem is NP-Hard even for uniform degree constraint. They also presented approximation algorithms for the case when all…
We study new types of geometric query problems defined as follows: given a geometric set $P$, preprocess it such that given a query point $q$, the location of the largest circle that does not contain any member of $P$, but contains $q$ can…
The 2024 edition of the CG:SHOP Challenge focused on the knapsack polygonal packing problem. Each instance consists of a convex polygon known as the container and a multiset of items, where each item is a simple polygon with an associated…
We study the strip packing problem, a classical packing problem which generalizes both bin packing and makespan minimization. Here we are given a set of axis-parallel rectangles in the two-dimensional plane and the goal is to pack them in a…
Given a finite family of squares in the plane, the packing problem asks for the maximum number $\nu$ of pairwise disjoint squares among them, while the hitting problem for the minimum number $\tau$ of points hitting all of them. Clearly,…
Given a set of objects with durations (jobs) that cover a base region, can we schedule the jobs to maximize the duration the original region remains covered? We call this problem the sensor cover problem. This problem arises in the context…
We introduce the $(p,q)$-Fair Clustering problem. In this problem, we are given a set of points $P$ and a collection of different weight functions $W$. We would like to find a clustering which minimizes the $\ell_q$-norm of the vector over…
Let P be a set of n weighted points, Q be a set of m unweighted points in the plane, and k a non-negative integer. We consider the problem of computing a subset $Q'\subseteq Q$ with size at most k such that the sum of the weights of the…