A Fixed Parameter Tractable Approximation Scheme for the Optimal Cut Graph of a Surface

Given a graph $G$ cellularly embedded on a surface $\Sigma$ of genus $g$, a cut graph is a subgraph of $G$ such that cutting $\Sigma$ along $G$ yields a topological disk. We provide a fixed parameter tractable approximation scheme for the problem of computing the shortest cut graph, that is, for any $\varepsilon >0$, we show how to compute a $(1+ \varepsilon)$ approximation of the shortest cut graph in time $f(\varepsilon, g)n^3$. Our techniques first rely on the computation of a spanner for the problem using the technique of brick decompositions, to reduce the problem to the case of bounded tree-width. Then, to solve the bounded tree-width case, we introduce a variant of the surface-cut decomposition of Ru\'e, Sau and Thilikos, which may be of independent interest

Control and optimization methods for traffic signal control in large-scale congested urban road networks

The problem of designing real-time traffic signal control strategies for large-scale congested urban road networks via suitable application of control and optimization methods is considered. Three alternative methodologies are proposed, all based on the store-and-forward modeling (SFM) paradigm. The first methodology results in a linear multivariable feedback regulator derived through the formulation of the problem as a linear-quadratic (LQ) optimal control problem. The second methodology leads to an open-loop constrained quadratic optimal control problem whose numerical solution is achieved via quadratic-programming (QP). Finally, the third methodology leads to an open-loop constrained nonlinear optimal control problem whose numerical solution is effectuated by use of a feasible-direction algorithm. A simulation-based investigation of the signal control problem for a large-scale urban network using these methodologies is presented. Results demonstrate the efficiency and real-time feasibility of the developed generic control methods