Formerly extensive on the Volcanic Plateau, frost flat heathland dominated by monoao (Dracophyllum subulatum ) is now reduced to fragments. It is threatened by mouse-ear hawkweed (Hieracium pilosella) at the only major site where it is likely to survive indefinitely (Rangitaiki Conservation Area). In the past, fire has perpetuated monoao on frost flats, but in future it may accelerate the sprea...

The Anthropocene is a geological epoch marked by major human influences on processes in the atmosphere, biosphere, hydrosphere and geosphere. One of the most dramatic features of the Anthropocene is the massive alteration of the Earth's vegetation, including forests. Here we investigate the role of topography in shaping human impacts on tree cover from local to global scales. We show that human...

We study graph orientations that minimize the entropy of the in-degree sequence. The problem of finding such an orientation is an interesting special case of the minimum entropy set cover problem previously studied by Halperin and Karp (Theoret. Comput. Sci., 2005) and by the current authors (Algorithmica, to appear). We prove that the minimum entropy orientation problem is NP-hard even if the ...

A tree cover of a graph is a collection of subgraphs such that each vertex is a part of at least one subgraph and each subgraph is a tree. The bounded tree cover problem (BTC) finds a tree cover with minimum number of trees of bounded weight. This paper considers several generalized versions of BTC. The first problem deals with graphs having multiple metric weight functions. Strong and weak tre...

Introduction: During trips the imposed costs are aggravated due to time and financial limits, not being familiar with treatment centers that are covered by the insurances and charges for accommodation. Insurance, especially supplementary treatment services insurance can be an appropriate solution to decrease these costs. These kinds of insurances cover a range of services inclu...

In the previous lecture we covered polynomial time reductions and approximation algorithms for vertex cover and set cover problems. By reductions we showed that SAT, 3SAT, Independent Set, Vertex Cover, Integer Programming, and Clique problems are NP-Hard. In this lecture we will continue to cover approximation algorithms for maximum coverage and metric TSP problems. We will also cover Strong N...

We consider the problem of computing minimum geometric hitting sets in which, given a set of geometric objects and a set of points, the goal is to compute the smallest subset of points that hit all geometric objects. The problem is known to be strongly NP-hard even for simple geometric objects like unit disks in the plane. Therefore, unless P=NP, it is not possible to get Fully Polynomial Time ...

Graph orientations with low out-degree are one of several ways to efficiently store sparse graphs. If the graphs allow for insertion and deletion of edges, one may have to flip the orientation of some edges to prevent blowing up the maximum out-degree. We use arboricity as our sparsity measure. With an immensely simple greedy algorithm, we get parametrized trade-off bounds between outdegree and...

This study examines experimentally, in situ, the influence of four scales of heterogeneity (0, 1, 10, 100 mm) and the hierarchical combination of those scales of heterogeneity (0 + 1 + 10, 0 + 1 + 100, 0 + 10 + 100, 0 + 1 + 10 + 100 mm) on the early establishment of a sessile marine littoral epibenthic community. The study was carried out in St. Andrews, New Brunswick (Canada) from July to Octo...