On bounded block decomposition problems for under-specified systems of equations

When solving a system of equations, it can be beneficial not to solve it in its entirety at once, but rather to decompose it into smaller subsystems that can be solved in order. Based on a bisimplicial graph representation we analyze the parameterized complexity of two problems central to such a decomposition: The Free Square Block problem related to finding smallest subsystems that can be solved separately, and the Bounded Block Decomposition problem related to determining a decomposition where the largest subsystem is as small as possible. We show both problems to be W[1]-hard. Finally we relate these problems to crown structures and settle two open questions regarding them using our results

Scene Modeling Based on Constraint System Decomposition Techniques

We present a new approach to 3D scene modeling based on geometric constraints. Contrary to the existing methods, we can quickly obtain 3D scene models that respect the given constraints exactly. Our system can describe a large variety of linear and non-linear constraints in a flexible way. To deal wit