This thesis deals with the rectilinear crossing minimization problem, which is NP-hard [BD93]. More precisely, we propose a heuristic for computing a straight-line drawing of a general graph G which realizes a small rectilinear crossing number. Inspired by Gutwenger et al. [GMW05], we pursue an approach which extracts a planar subgraph that includes as many edges of G as possible and iterativel...

In this paper, we present an algorithm, called selforganization assisted placement (SOAP), for circuit placement in arbitrarily shaped regions, including two-dimensional rectilinear regions, nonplanar surfaces of three-dimensional objects, and three-dimensional volumes. SOAP is based on a learning algorithm for neural networks proposed by Kohonen [l], called self-organization, which adjusts the...

Given a set P of terminals in the plane and a partition of P into k subsets P1, . . . , Pk, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree Ti connecting the terminals in each set Pi (i = 1, . . . , k) and a top-level tree Ttop connecting the trees T1, . . . , Tk. The goal is to minimize the total length of all trees. This problem arises naturally in the design of lo...

In part II of this group of papers, the control of the gait of a biped robot during rectilinear walk was considered. The modeling approach and simulation, using Kane’s method with implementation leveraged by Autolev, a symbolic computational environment that is complementary, was discussed in part I. Performing turns during the walk is technically more complex than the rectilinear case and dese...