Many engineers are exposed to binary data. These can be files or data exchanged over network links. When involved in the verification and validation of systems that deal with specific protocols or binary data storage, it is often tedious to analyse the hexadecimal dumps in order to find specific parameters of interest. Despite detailed protocol specifications, it takes a lot of manual effort to inspect byte after byte. This is not only a laborious work, but it is also very error-prone, especially when messages are very complex, contain mixtures of big- and little-endianess, timestamps, ASCII, Unicode, base-64 images, calibrated data and others... Furthermore, when having large amount of data, it isn't straight forward to extract all the parameters of interest for offline data correlation or analysis. Last, but not least, there is today no generic test tool that allows to autonomously interpret and respond to any protocol written over the Internet Transmission Control Protocol (TCP/IP). Indeed, many various file formats and protocols exist, but writing a new tool for each of them, by having the format definitions hard-coded, is not always very efficient. A lot of time and money is wasted as people keep re-inventing the wheel again and again. Gepetto (the GEneric Processing Editing and Testing TOol) tries to provide a solution to this problematic.

Let P be a d-dimensional n-point set. A Tverberg partition of P is a partition of P into r sets P1, ..., Pr such that the convex hulls ch(P1), ..., ch(Pr) have non-empty intersection. A point in the intersection of the convex hulls is called a Tverberg point of depth r for P. A classic result by Tverberg implies that there always exists a Tverberg partition of size n/(d+1), but it is not known how to find such a partition in polynomial time. Therefore, approximate solutions are of interest.

We study several canonical decision problems arising from some well-known theorems from combinatorial geometry. Among others, we show that computing the minimum size of a Caratheodory set and a Helly set and certain decision versions of the hs cut problem are W[1]-hard (and NP-hard) if the dimension is part of the input. This is done by fpt-reductions (which are actually ptime-reductions) from the d-Sum problem. Our reductions also imply that the problems we consider cannot be solved in time n^{o(d)} (where n is the size of the input), unless the Exponential-Time Hypothesis (ETH) is false. The technique of embedding d-Sum into a geometric setting is conceptually much simpler than direct fpt-reductions from purely combinatorial W[1]-hard problems (like the clique problem) and has great potential to show (parameterized) hardness and (conditional) lower bounds for many other problems.