Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance

We present two on-line algorithms for maintaining a topological order of a directed $n$-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles $m$ arc additions in $O(m^{3/2})$ time. For sparse graphs ($m/n = O(1)$), this bound improves the best previous bound by a logarithmic factor, and is tight to within a constant factor among algorithms satisfying a natural {\em locality} property. Our second algorithm handles an arbitrary sequence of arc additions in $O(n^{5/2})$ time. For sufficiently dense graphs, this bound improves the best previous bound by a polynomial factor. Our bound may be far from tight: we show that the algorithm can take $\Omega(n^2 2^{\sqrt{2\lg n}})$ time by relating its performance to a generalization of the $k$-levels problem of combinatorial geometry. A completely different algorithm running in $\Theta(n^2 \log n)$ time was given recently by Bender, Fineman, and Gilbert. We extend both of our algorithms to the maintenance of strong components, without affecting the asymptotic time bounds.Comment: 31 page

A Computational Algebra Approach to the Reverse Engineering of Gene Regulatory Networks

This paper proposes a new method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is time-discrete deterministic dynamical systems, with a finite set of states for each of the variables. The simplest examples of such models are Boolean networks, in which variables have only two possible states. The use of a larger number of possible states allows a finer discretization of experimental data and more than one possible mode of action for the variables, depending on threshold values. Furthermore, with a suitable choice of state set, one can employ powerful tools from computational algebra, that underlie the reverse-engineering algorithm, avoiding costly enumeration strategies. To perform well, the algorithm requires wildtype together with perturbation time courses. This makes it suitable for small to meso-scale networks rather than networks on a genome-wide scale. The complexity of the algorithm is quadratic in the number of variables and cubic in the number of time points. The algorithm is validated on a recently published Boolean network model of segment polarity development in Drosophila melanogaster.Comment: 28 pages, 5 EPS figures, uses elsart.cl

Low Power Depth Estimation of Rigid Objects for Time-of-Flight Imaging

Depth sensing is useful in a variety of applications that range from augmented reality to robotics. Time-of-flight (TOF) cameras are appealing because they obtain dense depth measurements with minimal latency. However, for many battery-powered devices, the illumination source of a TOF camera is power hungry and can limit the battery life of the device. To address this issue, we present an algorithm that lowers the power for depth sensing by reducing the usage of the TOF camera and estimating depth maps using concurrently collected images. Our technique also adaptively controls the TOF camera and enables it when an accurate depth map cannot be estimated. To ensure that the overall system power for depth sensing is reduced, we design our algorithm to run on a low power embedded platform, where it outputs 640x480 depth maps at 30 frames per second. We evaluate our approach on several RGB-D datasets, where it produces depth maps with an overall mean relative error of 0.96% and reduces the usage of the TOF camera by 85%. When used with commercial TOF cameras, we estimate that our algorithm can lower the total power for depth sensing by up to 73%