A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection size is the number of edges connecting the two sets. Finding the bisection of minimum size is NP-hard. We present an algorithm that nds a bisection that is within O(p n log n) of optimal. No sublinear approximation ratio for bisection was previously known.

The minimum feature size of a planar straight-line graph is the minimum distance between a vertex and a nonincident edge. When a polygon is partitioned into a mesh, the degradation is the ratio of original to final minimum feature size. We show that some planar straight-line graphs cannot be triangulated with constant degradation, even with an unbounded number of Steiner points and triangles. T...

Let n > 4 be a natural number, and let K be a set K ⊆ [n] := {1, 2, . . . , n}. We study the problem to find the smallest possible size of a maximal family A of subsets of [n] such that A contains only sets whose size is in K, and A 6⊆ B for all {A,B} ⊆ A, i.e. A is an antichain. We present a general construction of such antichains for sets K containing 2, but not 1. If 3 ∈ K our construction a...

Raising the minimum age of legal access to tobacco products may reduce smoking initiation and save lives. In a national telephone survey (2014-2015), US adolescents aged 13 to 17 years (N = 1,125; response rate, 66%) were asked about raising the age of legal access to tobacco products and randomized to hear one of 3 ages (19, 20, or 21 y). Most adolescents, across all US regions, favored raisin...

Previous research documents a substantive, positive, correlation between the minimum legal drinking age (MLDA) and birth outcomes. Using an improved empirical framework, we reach a different conclusion: there is little or no relationship between the minimum legal drinking age and the health of infants born to young mothers. We do, however, find that MLDA policies are associated with the sex rat...