We study a geometric hitting set problem involving unirectional rays and curves in the plane. We show that this problem is hard to approximate within a logarithmic factor even when the curves are convex polygonal x-monotone chains. Additionally, it is hard to approximate within a factor of 76 even when the curves are line segments with bounded slopes. Lastly, we demonstrate that the problem is ...

0

cover

Ice-core records show that climate changes in the past have been large, rapid, and synchronous over broad areas extending into low latitudes, with less variability over historical times. These ice-core records come from high mountain glaciers and the polar regions, including small ice caps and the large ice sheets of Greenland and Antarctica.

[1] We use 22 monthly GRACE (Gravity Recovery and Climate Experiment) gravity fields to estimate the linear trend in Greenland ice mass during 2002–2004. We recover a decrease in total ice mass of 82 ± 28 km of ice per year, consistent with estimates from other techniques. Our uncertainty estimate is dominated by the effects of GRACE measurement errors and errors in our post glacial rebound (PG...

15.

We construct a Π2 enumeration degree which is a strong minimal cover.

It has been known for more than 40 years that there are posets with planar cover graphs and arbitrarily large dimension. Recently, Streib and Trotter proved that such posets must have large height. In fact, all known constructions of such posets have two large disjoint chains with all points in one chain incomparable with all points in the other. Gutowski and Krawczyk conjectured that this feat...

An old question of Yates as to whether all minimal degrees have a strong minimal cover remains one of the longstanding problems of degree theory, apparently largely impervious to present techniques. We survey existing results in this area, focussing especially on some recent progress.

An equivalence graph is a vertex disjoint union of complete graphs. For a graph G, let eq(G) be the irdnimum number of equivalence subgraphs of G needed to cover all edges of G. Similarly, let cc(G) be the minimum number of complete subgraphs of G needed to cover all its edges. Let H be a graph on n vertices with ma,'dmal degree _~d (and minimal degree --~ 1), and let G=I~ be its complement. We...