Related papers: FPTAS for barrier covering problem with equal circ…
We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An…
This work addresses the finite-time enclosing control problem where a set of followers are deployed to encircle and rotate around multiple moving targets with a predefined spacing pattern in finite time. A novel distributed and continuous…
Let $S$ be a planar point set in general position, and let $\mathcal{P}(S)$ be the set of all plane straight-line paths with vertex set $S$. A flip on a path $P \in \mathcal{P}(S)$ is the operation of replacing an edge $e$ of $P$ with…
This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…
A perfect straight-line matching $M$ on a finite set $P$ of points in the plane is a set of segments such that each point in $P$ is an endpoint of exactly one segment. $M$ is non-crossing if no two segments in $M$ cross each other. Given a…
We consider the parity problem in one-dimensional, binary, circular cellular automata: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. It is easy to…
We show that for $m$ points and $n$ lines in the real plane, the number of distinct distances between the points and the lines is $\Omega(m^{1/5}n^{3/5})$, as long as $m^{1/2}\le n\le m^2$. We also prove that for any $m$ points in the…
The paper presents two edge grouping algorithms for finding a closed contour starting from a particular edge point and enclosing a fixation point. Both algorithms search a shortest simple cycle in \textit{an angularly ordered graph} derived…
In the packing-constrained point covering problem, PC^2, one seeks configurations of points in the plane that cannot all be covered by a packing arrangement of unit disks. We consider in particular the problem of finding the minimum number…
We establish tight bounds for beacon-based coverage problems, and improve the bounds for beacon-based routing problems in simple rectilinear polygons. Specifically, we show that $\lfloor \frac{n}{6} \rfloor$ beacons are always sufficient…
Let $\mathscr O$ be a set of $n$ disjoint obstacles in $\mathbb{R}^2$, $\mathscr M$ be a moving object. Let $s$ and $l$ denote the starting point and maximum path length of the moving object $\mathscr M$, respectively. Given a point $p$ in…
A permutation may be represented by a collection of paths in the plane. We consider a natural class of such representations, which we call tangles, in which the paths consist of straight segments at 45 degree angles, and the permutation is…
A graph is rectilinear planar if it admits a planar orthogonal drawing without bends. While testing rectilinear planarity is NP-hard in general (Garg and Tamassia, 2001), it is a long-standing open problem to establish a tight upper bound…
Given $n$ intervals on a line $\ell$, we consider the problem of moving these intervals on $\ell$ such that no two intervals overlap and the maximum moving distance of the intervals is minimized. The difficulty for solving the problem lies…
Let P be a set of n points in the Euclidean plane and let O be the origin point in the plane. In the k-tour cover problem (called frequently the capacitated vehicle routing problem), the goal is to minimize the total length of tours that…
We determine the conditions resulting from equating the area sums of alternative sectors in a circle generated by four, two, and three straight lines, respectively, that connect opposite points on its circumference while passing through a…
We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason - the problem of "super…
Subtrajectory clustering is an important variant of the trajectory clustering problem, where the start and endpoints of trajectory patterns within the collected trajectory data are not known in advance. We study this problem in the form of…
Consider the scattering of a time-harmonic plane wave by heterogeneous media consisting of linear or nonlinear point scatterers and extended obstacles. A generalized Foldy-Lax formulation is developed to take fully into account of the…
Given a graph with edge costs and vertex profits and given a budget B, the Orienteering Problem asks for a walk of cost at most B of maximum profit. Additionally, each profit may be given with a time window within it can be collected by the…