We consider the problem of computing the q-gram profile of a string T of size N compressed by a context-free grammar with n production rules. We present an algorithm that runs in O(N ↵) expected time and uses O(n+kT,q) space, where N ↵  qn is the exact number of characters decompressed by the algorithm and kT,q  N ↵ is the number of distinct q-grams in T . This simultaneously matches the curr...

Properties of Pisot numbers have long been of interest. One line of questioning, initiated by Erdős, Joó and Komornik in 1990, is the determination of l(q) for Pisot numbers q, where l(q) = inf(|y| : y = 0 + 1q + · · ·+ nq, i ∈ {±1, 0}, y 6= 0). Although the quantity l(q) is known for some Pisot numbers q, there has been no general method for computing l(q). This paper gives such an algorithm. ...

We consider the problem of triangle guarding (4-guarding) a simple, 2D polygon Q. A polygon Q is 4-guarded if every point q of Q is contained in the convex hull of some three guards that can all see q. This rather odd condition approximates a desire, for example, to see all sides of q or to locate (via triangulation) q from at least two angularly well-separated views. If we restrict the guards ...

In [1], Feng et al. propose a polynomial time approximation algorithm for a novel maximum edge coloring problem which arises from the field of wireless mesh networks [2]. The problem is about coloring all the edges in a graph and finding a coloring solution which uses the maximum number of colors with the constraint, for every vertex in the graph, all the edges incident to it are colored with n...

The pivot algorithm is a Markov Chain Monte Carlo algorithm for simulating the selfavoiding walk. At each iteration a pivot which produces a global change in the walk is proposed. If the resulting walk is self-avoiding, the new walk is accepted; otherwise, it is rejected. Past implementations of the algorithm required a time O(N) per accepted pivot, where N is the number of steps in the walk. W...