53 citations · 112 across the 26 of their papers we have counts for
13 papers · 1 filter
The Two-Squirrel Problem and Its Relatives
Sergey Bereg, Yuya Higashikawa, Naoki Katoh +3
In this paper, we start with a variation of the star cover problem called the Two-Squirrel problem. Given a set of points in the plane, and two sites and , comp…
Optimal Placement of Base Stations in Border Surveillance using Limited Capacity Drones
S. Bereg, J. M. Díaz-Báñez, M. Haghpanah +8
Imagine an island modeled as a simple polygon with vertices whose coastline we wish to monitor. We consider the problem of building the minimum number of refueling stations…
Constructing Order Type Graphs using an Axiomatic Approach
Sergey Bereg, Mohammadreza Haghpanah
A given order type in the plane can be represented by a point set. However, it might be difficult to recognize the orientations of some point triples. Recently, Aichholzer \etal \c…
On Maximum-Sum Matchings of Points
Sergey Bereg, Oscar Chacón-Rivera, David Flores-Peñaloza +3
Huemer et al. (Discrete Mathematics, 2019) proved that for any two point sets and with , the perfect matching that matches points of with points of , and ma…
Balanced partitions of 3-colored geometric sets in the plane
Sergey Bereg, Matias Korman, Rodrigo I. Silveira +6
Let be a finite set of geometric objects partitioned into classes or \emph{colors}. A subset is said to be \emph{balanced} if contains the same amount of e…
On balanced 4-holes in bichromatic point sets
S. Bereg, J. M. Díaz-Báñez, R. Fabila-Monroy +5
Let be a point set in the plane in general position such that each of its elements is colored either red or blue, where and denote the points colored red and th…