The Steiner tree problem requires to nd a shortest tree connecting a given set of terminal points in a metric space. We suggest a better and fast heuristic for the Steiner problem in graphs and in rectilinear plane. This heuristic nds a Steiner tree at most 1.757 and 1.267 times longer than the optimal solution in graphs and rectilinear plane, respectively.

We propose variable rectilinear interpolation (VRI) as an alternative method for device characterization. Based on a rectilinear structure, this algorithm constructs a mapping with non-uniform nodes placed to maximize informational entropy while meeting the pre-defined error tolerance threshold. In this paper we describe the VRI algorithm and structure; followed by an example in which we charac...

We consider the generalized minimum Manhattan network problem (GMMN). The input to this problem is a set R of n pairs of terminals, which are points in R. The goal is to find a minimum-length rectilinear network that connects every pair in R by a Manhattan path, that is, a path of axis-parallel line segments whose total length equals the pair’s Manhattan distance. This problem is a generalizati...

This paper is a commentary on the work of Butt and Cavalier [2], a paper that was published in an earlier issue of this journal. With the aid of an example problem, we demonstrate that the set of gridlines proposed by them to nd the rectilinear least cost path between two points in the presence of convex polygonal congested regions is inadequate. We proceed to prove its adequacy for the case of...

Routing is a phase in the physical design of Electronic Circuits. The main aim of routing in VLSI design is to interconnect the cells that have been assigned positions as a solution of the placement problem. The problem of finding Rectilinear SteinerMinimal Tree (RSMT) is one of the fundamental problems in the field of Electronic Design Automation. The obstacle avoiding rectilinear Steiner mini...

In a proportional contact representation of a planar graph, each vertex is represented by a simple polygon with area proportional to a given weight, and edges are represented by adjacencies between the corresponding pairs of polygons. In this paper we study proportional contact representations that use rectilinear polygons without wasted areas (white space). In this setting, the best known algo...

Path instability of a rising bubble is complex phenomenon. In many industrial applications, bubbles encounter walls, and the interactions between wall have significant impact on flow physics. A single near vertical was experimentally observed to follow bouncing trajectory. To investigate near-wall dynamics bubbles, 3D numerical simulations were performed based volume fluid (VOF) method using op...

In lateral interception tasks balls converging onto the same interception location via different trajectories give rise to systematic differences in the kinematics of hand movement. While it is generally accepted that this angle-of-approach effect reflects the prospective (on-line) control of movement, controversy exists with respect to the information used to guide the hand to the future inter...

The embedding problem for a class of graphs called rectilinear graphs is discussed. These graphs have applications in many VLSI Layout Problems. An interesting topological characterization of these graphs lead to efficient algorithms for recognizing and embedding rectilinear graphs which are embeddable on the plane.

This paper is a commentary on the work of Butt and Cavalier (Socio-Econ. Plann. Sci. 31(2) (1997) 103), a paper that was published in an earlier issue of this journal. With the aid of an example problem, we demonstrate that the set of gridlines proposed by them to find the rectilinear least cost path between two points in the presence of convex polygonal congested regions is inadequate. We proc...