Suppose that we are given two independent sets Ib and Ir of a graph such that |Ib| = |Ir|, and imagine that a token is placed on each vertex in Ib. Then, the sliding token problem is to determine… (More)

We provide an implementation of an algorithm that, given a triangulated planar graph with <i>m</i> edges, returns a simple cycle that is a 3/4-balanced separator consisting of at most &sqrt;8<i>m</i>… (More)

We prove a conjecture of Aanjaneya, Bishnu, and Pal that the maximum number of diffuse reflections needed for a point light source to illuminate the interior of a simple polygon with n walls is bn/2c… (More)

What is the largest cube or sphere that a given rectangular piece of paper can wrap? This natural problem, which has plagued giftwrappers everywhere, remains very much unsolved. Here we introduce new… (More)

The tangram and Sei Shōnagon Chie no Ita are popular dissection puzzles consisting of seven pieces. Each puzzle can be formed by identifying edges from sixteen identical right isosceles triangles. It… (More)

We present a PTAS for computing the maximum a posteriori assignment on Pairwise Markov Random Fields with non-negative weights in planar graphs. This algorithm is practical and not far behind… (More)