63 citations · 220 across the 18 of their papers we have counts for
6 papers · 1 filter
Weight Balancing on Boundaries
Luis Barba, Otfried Cheong, Michael Gene Dobbins +8
Given a polygonal region containing a target point (which we assume is the origin), it is not hard to see that there are two points on the perimeter that are antipodal, that is, wh…
Fence patrolling by mobile agents with distinct speeds
Akitoshi Kawamura, Yusuke Kobayashi
Suppose we want to patrol a fence (line segment) using k mobile agents with given speeds v_1, ..., v_k so that every point on the fence is visited by an agent at least once in ever…
A lower bound on opaque sets
Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi +1
It is proved that the total length of any set of countably many rectifiable curves, whose union meets all straight lines that intersect the unit square U, is at least 2.00002. This…
Generalized Semimagic Squares for Digital Halftoning
Akitoshi Kawamura
Completing Aronov et al.'s study on zero-discrepancy matrices for digital halftoning, we determine all (m, n, k, l) for which it is possible to put mn consecutive integers on an m-…
Distance k-Sectors Exist
Keiko Imai, Akitoshi Kawamura, Jiří Matoušek +2
The bisector of two nonempty sets P and Q in a metric space is the set of all points with equal distance to P and to Q. A distance k-sector of P and Q, where k is an integer, is a…
Zone Diagrams in Euclidean Spaces and in Other Normed Spaces
Akitoshi Kawamura, Jiří Matoušek, Takeshi Tokuyama
Zone diagram is a variation on the classical concept of a Voronoi diagram. Given n sites in a metric space that compete for territory, the zone diagram is an equilibrium state in t…