Design an electronic mouse trap for agriculture area

This paper explains the issues on the increasing of mice in agriculture area. The electronic mousetrap is being improved as it can catch more than a mouse with maximum of five. The device has a LCD to display a message of “Awaiting Mouse” and “Mouse Trapped”. Then, the LED light will remain light up after the door has been closed. The LED were function as an alert to the owner to know either there is a mouse or not inside the trap. The LED will turn off once the mouse is release. In the project, the main part of the circuit consists of PIR sensors and LCD display. The coding is designed by using Arduino.Keywords: PIR sensor; Arduino; LCD; mousetrap; LE

Proportional Contact Representations of 4-connected Planar Graphs

Abstract. In a contact representation of a planar graph, vertices are represented by interior-disjoint polygons and two polygons share a non-empty common boundary when the corresponding vertices are adjacent. In the weighted version, a weight is assigned to each vertex and a contact representation is called proportional if each polygon realizes an area proportional to the vertex weight. In this paper we study proportional contact representations of 4-connected internally triangulated planar graphs. The best known lower and upper bounds on the polygonal complexity for such graphs are 4 and 8, respectively. We narrow the gap between them by proving the existence of a representation with complexity 6. We then disprove a 10-year old conjecture on the existence of a Hamiltonian canonical cycle in a 4-connected maximal planar graph, which also implies that a previously suggested method for constructing proportional contact representations of complexity 6 for these graphs will not work. Finally we prove that it is NP-complete to decide whether a 4-connected planar graph admits a contact representation using only rectangles.

Planar Preprocessing for Spring Embedders

Abstract. Spring embedders are conceptually simple and produce straight-line drawings with an undeniable aesthetic appeal, which explains their prevalence when it comes to automated graph drawing. However, when drawing planar graphs, spring embedders often produce non-plane drawings, as edge crossings do not factor into the objective function being minimized. On the other hand, there are fairly straight-forward algorithms for creating plane straight-line drawings for planar graphs, but the resulting layouts generally are not aesthetically pleasing, as vertices are often grouped in small regions and edges lengths can vary dramatically. It is known that the initial layout influences the output of a spring embedder, and yet a random layout is nearly always the default. We study the effect of using various plane initial drawings as an inputs to a spring embedder, measuring the percent improvement in reducing crossings and in increasing node separation, edge length uniformity, and angular resolution.

Edge-Weighted Contact Representations of Planar Graphs

We study contact representations of edge-weighted planar graphs, where vertices are rectangles or rectilinear polygons and edges are polygon contacts whose lengths represent the edge weights. We show that for any given edge-weighted planar graph whose outer face is a quadrangle, that is internally triangulated and that has no separating triangles we can construct in linear time an edge-proportional rectangular dual if one exists and report failure otherwise. For a given combinatorial structure of the contact representation and edge weights interpreted as lower bounds on the contact lengths, a corresponding contact representation that minimizes the size of the enclosing rectangle can be found in linear time.If the combinatorial structure is not fixed, we prove NP-hardness of deciding whether a contact representation with bounded contact lengths exists. Finally, we give a complete characterization of the rectilinear polygon complexity required for representing biconnected internally triangulated graphs: For outerplanar graphs complexity 8 is sufficient and necessary, and for graphs with two adjacent or multiple non-adjacent internal vertices the complexity is unbounded

Orthogonal cartograms with few corners per face

We give an algorithm to create orthogonal drawings of 3-connected 3-regular planar graphs such that each interior face of the graph is drawn with a prescribed area. This algorithm produces a drawing with at most 12 corners per face and 4 bends per edge, which improves the previous known result of 34 corners per face