The concept of rectangle-of-influence (RI) drawings is old and well-studied in the area of graph drawing. A graph has such a drawing if we can assign points to its vertices such that for every edge (v, w) the supporting rectangle (i.e., the minimal closed axis-aligned rectangle R(v, w) containing v and w) contains no other points. In the original setup, the graph had to have an edge for every p...

A rectangular drawing of a planar graph G is in which vertices are mapped to grid points, edges horizontal and vertical straight-line segments, faces drawn as rectangles. Sometimes this latter constraint relaxed for the outer face. In paper, we study drawings have unit length. We show complexity dichotomy problem deciding existence unit-length drawing, depending on whether face must also be rec...

It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single non-overlapping piece by cutting along grid edges defined by coordinate planes through every vertex.

Visual coverage is one of the most important quality indexes for depicting the usability of an individual camera or camera network. It is the basis for camera network deployment, placement, coverage-enhancement, planning, etc. Precision and efficiency are critical influences on applications, especially those involving several cameras. This paper proposes a new method to efficiently estimate sup...

A straight-line drawing of a plane graph is called an open rectangle-ofinfluence drawing if there is no vertex in the proper inside of the axis-parallel rectangle defined by the two ends of every edge. In an inner triangulated plane graph, every inner face is a triangle although the outer face is not necessarily a triangle. In this paper, we first obtain a sufficient condition for an inner tria...

A proximity drawing of a graph is a straight-line drawing where adjacent vertices are represented by points that are deemed to be close according to some proximity measure. A rectangle of innuence drawing is a proximity drawing where the measure is based on the concept of rectangle of innuence. Given two points u and v, the rectangle of innuence of u and v is the axis-aligned rectangle having u...

This paper presents an algorithm for finding edge-disjoint paths in a given plane grid bounded by two nested rectangles. A pair of vertices on the boundary of the same rectangle are designated as terminals for each of the paths. The number of terminals lying on each boundary vertex is determined by the degree of the boundary vertex. Every vertex of degree 2 has either 0 or 2 terminals lying on ...

Prototypes for automated spatial layout in architecture focus on approaches, which define occupiable space as an orthogonal 2D-grid and use algorithms to allocate each rectangle of the grid to a particular function. However, these approaches are limiting the design to orthogonal spatial layouts. Based on SAT solving techniques, the prototype presented in this paper proposes a methodology for au...

With ever-new technologies emerging also the amount of information to be stored and processed is growing exponentially and is believed to be always at the limit. In contrast, however, huge resources are available in the IT sector alike e.g. the renewable energy sector, which are often even not at all used. This under-usage bares any rational especially in the IT sector where e.g. virtualisation...

In this paper we introduce a new drawing style of a plane graph G called a box-rectangular drawing. It is defined to be a drawing of G on an integer grid such that every vertex is drawn as a rectangle, called a box, each edge is drawn as either a horizontal line segment or a vertical line segment, and the contour of each face is drawn as a rectangle. We establish a necessary and sufficient cond...