Related papers: An Optimal Algorithm for Half-plane Hitting Set

Given a separation oracle for a convex set $K \subset \mathbb{R}^n$ that is contained in a box of radius $R$, the goal is to either compute a point in $K$ or prove that $K$ does not contain a ball of radius $\epsilon$. We propose a new…

Given two sets $S$ and $T$ of points in the plane, of total size $n$, a {many-to-many} matching between $S$ and $T$ is a set of pairs $(p,q)$ such that $p\in S$, $q\in T$ and for each $r\in S\cup T$, $r$ appears in at least one such pair.…

This paper studies the problem of enumerating all maximal collinear subsets of size at least three in a given set of $n$ points. An algorithm for this problem, besides solving degeneracy testing and the exact fitting problem, can also help…

We consider the problem of finding k centers for n weighted points on a real line. This (weighted) k-center problem was solved in O(n log n) time previously by using Cole's parametric search and other complicated approaches. In this paper,…

The hitting set problem is a well-known NP-hard optimization problem in which, given a set of elements and a collection of subsets, the goal is to find the smallest selection of elements, such that each subset contains at least one element…

Let $P$ and $S$ be two disjoint sets of $n$ and $m$ points in the plane, respectively. We consider the problem of computing a Steiner tree whose Steiner vertices belong to $S$, in which each point of $P$ is a leaf, and whose longest edge…

In this paper, we first consider the subpath convex hull query problem: Given a simple path $\pi$ of $n$ vertices, preprocess it so that the convex hull of any query subpath of $\pi$ can be quickly obtained. Previously, Guibas, Hershberger,…

We propose faster algorithms for the following three optimization problems on $n$ collinear points, i.e., points in dimension one. The first two problems are known to be NP-hard in higher dimensions. 1- Maximizing total area of disjoint…

In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…

Given a set $P$ of $n$ points and a set $S$ of $m$ weighted disks in the plane, the disk coverage problem asks for a subset of disks of minimum total weight that cover all points of $P$. The problem is NP-hard. In this paper, we consider a…

The authors recently gave an $n^{O(\log\log n)}$ time membership query algorithm for properly learning decision trees under the uniform distribution (Blanc et al., 2021). The previous fastest algorithm for this problem ran in $n^{O(\log…

We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a * b rectangles such that the sum of the weights of the points in P…

We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…

This paper addresses the single-item lot sizing problem with a 1-breakpoint all-units quantity discount in a monotonic setting where the purchase prices are non-increasing over the planning horizon. For this case, we establish several novel…

Let $\mathcal{P}$ be a set of $h$ pairwise-disjoint polygonal obstacles with a total of $n$ vertices in the plane. We consider the problem of building a data structure that can quickly compute an $L_1$ shortest obstacle-avoiding path…

Given a set $S$ of $m$ point sites in a simple polygon $P$ of $n$ vertices, we consider the problem of computing the geodesic farthest-point Voronoi diagram for $S$ in $P$. It is known that the problem has an $\Omega(n+m\log m)$ time lower…

Given a point $s$ and a set of $h$ pairwise disjoint polygonal obstacles of totally $n$ vertices in the plane, we present a new algorithm for building an $L_1$ shortest path map of size O(n) in $O(T)$ time and O(n) space such that for any…

We present an $n\Delta^{O(k^2)}$ time algorithm to obtain an optimal solution for $1$-dimensional cutting stock problem: the bin packing problem of packing $n$ items onto unit capacity bins under the restriction that the number of item…

We present an implementation of a recent algorithm to compute shortest-path trees in unit disk graphs in $O(n\log n)$ worst-case time, where $n$ is the number of disks. In the minimum-separation problem, we are given $n$ unit disks and two…

The distributed single-source shortest paths problem is one of the most fundamental and central problems in the message-passing distributed computing. Classical Bellman-Ford algorithm solves it in $O(n)$ time, where $n$ is the number of…