Related papers: Examination of saturation coverage of polygons usi…
In the maximum independent set of convex polygons problem, we are given a set of $n$ convex polygons in the plane with the objective of selecting a maximum cardinality subset of non-overlapping polygons. Here we study a special case of the…
We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…
We determine putative optimal packings of regular spherical polygons via optimization on smooth manifolds. For several cases, we establish maximality by extending the Lov\'asz theta number to Cayley graphs on the special orthogonal group…
This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this…
Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that…
Random sequential adsorption of linear and square particles with excluded volume interaction is studied numerically on planar lattices considering Gaussian distributions of lateral sizes of the incident particles, with several values of the…
In this paper, we study a layered random access scheme based on non-orthogonal multiple access (NOMA) to improve the throughput of multichannel ALOHA. At a receiver, successive interference cancellation (SIC) is carried out across layers to…
With the advent of autonomous robots with two- and three-dimensional scanning capabilities, classical visibility-based exploration methods from computational geometry have gained in practical importance. However, real-life laser scanning of…
Understanding the dynamic adsorption of colloidal particles at fluid interfaces is essential for applications ranging from emulsion stabilization to interfacial assembly of functional materials. Adsorption dynamics is often described…
This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with…
The problem of covering random points in a plane with sets of a given shape has several practical applications in communications and operations research. One especially prominent application is the coverage of randomly-located points of…
In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…
We study the two-dimensional geometric knapsack problem for convex polygons. Given a set of weighted convex polygons and a square knapsack, the goal is to select the most profitable subset of the given polygons that fits non-overlappingly…
In conventional radar, the transmission of the same waveform is repeated after a predefined interval of time called pulse-repetition-interval (PRI). This technique helps to estimate the range and Doppler shift of targets and suppress…
Spatial join processing techniques that identify intersections between complex geometries (e.g., polygons) commonly follow a two-step filter-and-refine pipeline. The filter step evaluates the query predicate on the minimum bounding…
We consider the problem of finding all enclosing rectangles of minimum area that can contain a given set of rectangles without overlap. Our rectangle packer chooses the x-coordinates of all the rectangles before any of the y-coordinates. We…
We study approximability of subdense instances of various covering problems on graphs, defined as instances in which the minimum or average degree is Omega(n/psi(n)) for some function psi(n)=omega(1) of the instance size. We design new…
A reversible adsorption-desorption parking process in one dimension is studied. An exact solution for the equilibrium properties is obtained. The coverage near saturation depends logarithmically on the ratio between the adsorption rate,…
The present paper reports a novel behavior involving regular polygons with n sides and filled to varying degrees with granular materials. These are comprised of a set of hollow polygons produced on a 3D printer, and a single larger hollow…
Test set with redundancy is one of the focuses in recent bioinformatics research. Set cover greedy algorithm (SGA for short) is a commonly used algorithm for test set with redundancy. This paper proves that the approximation ratio of SGA…