Related papers: Ranking Unit Squares with Few Visibilities
The general position problem in graphs is to find the maximum number of vertices that can be selected such that no three vertices lie on a common shortest path. The mutual-visibility problem in graphs is to find the maximum number of…
A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph.…
We present conjectured candidates for the least perimeter partition of a disc into $N \le 10$ regions which take one of two possible areas. We assume that the optimal partition is connected, and therefore enumerate all three-connected…
The Searchlight Scheduling Problem was first studied in 2D polygons, where the goal is for point guards in fixed positions to rotate searchlights to catch an evasive intruder. Here the problem is extended to 3D polyhedra, with the guards…
We explore the connection between the rank of a polynomial and the singularities of its vanishing locus. We first describe the singularity of generic polynomials of fixed rank. We then focus on cubic surfaces. Cubic surfaces with isolated…
We consider the problem of mirror invisibility for plane sets. Given a circle and a finite number of unit vectors (defining the directions of invisibility) such that the angles between them are commensurable with $\pi$, for any $\varepsilon…
We prove that a smooth surface, non of general type, in projective four-space, which lies on a quartic hypersurface with isolated singularities has degree at most 27 (in fact we prove a slightly more general result).
We consider the planar two-center problem for a convex polygon: given a convex polygon in the plane, find two congruent disks of minimum radius whose union contains the polygon. We present an $O(n\log n)$-time algorithm for the two-center…
Ranking or assessing centrality in multivariate and non-Euclidean data is difficult because there is no canonical order and many depth notions become computationally fragile in high-dimensional or structured settings. We introduce a…
In this paper we will examine unions of oriented and non-oriented unit squares in same plane and measure the ratio of perimeter to area of these unions. In 1998, T. Keleti published the conjecture that this ratio never exceeds 4. We outline…
In the symmetric rendezvous problem two players follow the same (randomized) strategy to visit one of $n$ locations in each time step $t=0,1,2,\dots$. Their goal is to minimize the expected time until they visit the same location and thus…
In this work, we deal with rank-constrained integer least-squares optimization problems arising in low-rank matrix factorization related applications. We propose a solution for constrained integer least-squares problem subject to equality,…
A positive integer $n$ is said to be $k$-layered if its divisors can be partitioned into $k$ sets with equal sum. In this paper, we start the systematic study of these class of numbers. In particular, we state some algorithms to find some…
We prove the computational intractability of rotating and placing $n$ square tiles into a $1 \times n$ array such that adjacent tiles are compatible--either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as…
Many approximation algorithms and heuristic algorithms to find a fair clustering have emerged. In this paper we define a new and natural variant of fair clustering problem and design a polynomial time algorithm to compute an optimal fair…
For three decades, carrier-phase observations have been used to obtain the most accurate location estimates using global navigation satellite systems (GNSS). These estimates are computed by minimizing a nonlinear mixed-integer least-squares…
Least square estimators for graphical models for cardinal paired comparison data with and without covariates are rigorously analyzed. Novel, graph--based, necessary and sufficient conditions that guarantee strong consistency, asymptotic…
This paper considers affine analogues of the isoperimetric inequality in the sense of piecewise linear topology. Given a closed polygon P embedded in R^d having n edges, we give upper and lower bounds for the minimal number of triangles…
The investigation of the relation among the distances of an arbitrary point in the Euclidean space $\mathbb{R}^n$ to the vertices of a regular $n$-simplex in that space has led us to the study of simplices having a regular facet. Calling an…
A new way of constructing fusion bases (i.e., the set of inequalities governing fusion rules) out of fusion elementary couplings is presented. It relies on a polytope reinterpretation of the problem: the elementary couplings are associated…