Software bugs are inevitable in software-defined networking control software, and troubleshooting is a tedious, time-consuming task. In this paper we discuss how to improve control software troubleshooting by presenting a technique for automatically identifying a minimal sequence of inputs responsible for triggering a given bug, without making assumptions about the language or instrumentation of the software under test. We apply our technique to five open source SDN control platforms---Floodlight, NOX, POX, Pyretic, ONOS---and illustrate how the minimal causal sequences our system found aided the troubleshooting process.

A fast algorithm is presented for computing the growth distance between a pair of convex objects in three-dimensional space. The growth distance is a measure of both separation and penetration between objects. When the objects are polytopes represented by their faces, the growth distance is determined by the solution of a linear program (LP). The article presents an approach to the solution of the LP. Under appropriate conditions, the computational time is very small and does not depend on the total number of faces of the objects. Compared to the existing algorithm for growth distance, there is a time reduction of several orders of magnitude. This increase in speed is achieved by exploiting two resources: adjacency of the object faces and the computational coherence induced by incremental motions of the objects, Computational experiments show that the performance of the algorithm is in the same range as the fastest codes for the computation of the Euclidean separation distance.

This paper introduces a novel heuristic roadmap method for path planning, one that is inspired by the Voronoi diagram concept, but easily applicable to general configuration spaces. The roadmap is formed by connecting the local maxima of a clearance function which is defined using distance functions. Reaching the roadmap from any free configuration is achieved by applying the continuous active-set optimization algorithm to the maximization of the clearance function. Preliminary experiments with the new roadmap algorithm point to its potential utility in solving practical path planning problems.

A fast algorithm is presented for computing the growth distance between a pair of convex objects in three dimensional space. The growth distance has been introduced by Ong et al. (1996) as a measure of both separation and penetration between objects. This article presents an approach to the growth distance computation using geometrical consideration. Under appropriate conditions, the computational time is very small and does not depend on the total number of faces of the objects. This increase in speed comes from the use of information on the adjacency of faces of the objects. Such adjacency information is particularly useful for object undergoing incremental motion. Computational experiments provided shows that the performance of the algorithm is in the same range as the known fastest Euclidean distance code.