This paper concerns proving almost tight (super-polynomial) running times, for achieving desired approximation ratios for various problems. To illustrate the question we study, let us consider the Set-Cover problem with n elements and m sets. Now we specify our goal to approximate Set-Cover to a factor of (1 − α) lnn, for a given parameter 0 < α < 1. What is the best possible running time for a...

We consider a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a given vertex-weighted undirected graph. Since it is included by the Steiner tree activation problem, the problem admits an O(logn)-approximation algorithm in g...

Vertebrate herbivores and fire are known to be important drivers of vegetation dynamics in African savannas. It is of particular importance to understand how changes in herbivore population density, especially of elephants, and fire frequency will affect the amount of tree cover in savanna ecosystems, given the critical importance of tree cover for biodiversity, ecosystem function, and human we...

We introduce the notion of sofic tree-shifts which corresponds to symbolic dynamical systems of infinite trees accepted by finite tree automata. We show that, contrary to shifts of infinite sequences, there is no unique minimal deterministic irreducible tree automaton accepting an irreducible sofic tree-shift, but that there is a unique synchronized one, called the Shannon cover of the tree-shi...

Recommended Citation Jones, Christine L., "Comparing remote sensing and ground-based methods of quantifying cover type and carbon storage in an urban forest", Master's report, 2011 2 This report, " Comparing remote sensing and ground-based methods of quantifying cover type and carbon storage in an urban forest " , is hereby approved in partial fulfillment of the requirements for the Degree of M...

The cover time of a graph is the time it takes for a random walk on it to visit all vertices. This note shows that for any tree on n vertices, the probability that the cover time of the tree is linear in n is exponentially small in n. This is true for any starting vertex.

Let Fn q be a vector space of dimension n over the finite field Fq . A q-analog of a Steiner system (also known as a q-Steiner system), denoted Sq(t,k,n), is a set S of k-dimensional subspaces of Fn q such that each t-dimensional subspace of Fn q is contained in exactly one element of S . Presently, q-Steiner systems are known only for t = 1, and in the trivial cases t = k and k= n. In this pap...

In this article, we study the behaviour of dynamic programming methods for the tree edit distance problem, such as [4] and [2]. We show that those two algorithms may be described in a more general framework of cover strategies. This analysis allows us to define a new tree edit distance algorithm, that is optimal for cover strategies.