Recently, it was proved that triangle-free intersection graphs of n line segments in the plane can have chromatic number as large as (log log n). Essentially the same construction produces (log log n)-chromatic triangle-free intersection graphs of a variety of other geometric shapes—those belonging to any class of compact arcconnected sets in R2 closed under horizontal scaling, vertical scaling...

In this paper we consider several instances of the k-center on a line problem where the goal is, given a set of points S in the plane and a parameter k ≥ 1, to find k disks with centers on a line l such that their union covers S and the maximum radius of the disks is minimized. This problem is a constraint version of the well-known k-center problem in which the centers are constrained to lie in...

We study stochastic combinatorial optimization problems where the objective is to minimize expected maximum load (a.k.a. makespan). In this framework, we have a set of n tasks and m resources, each task j uses some subset resources. Tasks random sizes $$X_j$$ , our goal non-adaptively select t over all on any resource i total size selected that use i. For example, when resources are points inte...

We examine the space requirement for the classic linesegment intersection problem. Using so-called implicit data structures, we show how to make the standard sweep-line algorithm run in O((n+ k) log n) time with only O(log n) extra space, where n is the number of line segments and k is the number of intersections. If division is allowed and input can be destroyed, the algorithm can run in O((n ...

Abstract We combine our dynamical modeling black-hole mass measurements from the Lick AGN Monitoring Project 2016 sample with measured cross-correlation time lags and line widths to recover individual scale factors, f , used in traditional reverberation-mapping analyses. extend by including prior results Code for Reverberation Modeling of Emission Lines ( caramel ) studies that have utilized me...

It is shown that for every subdivision of the d-dimensional Euclidean space, d ≥ 2, into n convex cells, there is a straight line that stabs at least Ω((log n/ log log n)1/(d−1)) cells. In other words, if a convex subdivision of d-space has the property that any line stabs at most k cells, then the subdivision has at most exp(O(kd−1 log k)) cells. This bound is best possible apart from a consta...