function that produces a layout of a graph G on the plane. We consider the problem of assigning text labels to every edge of the graph such that the quality of the labeling assignment is optimal. This problem has been first encountered in automated cartography and has been referred to as the Line Feature Label Placement (LFLP) problem. Even though much effort has been devoted over the last 15 years in the area of automated drawing of maps, the Edge Label Placement (ELP) problem has received tittle attention. In this paper we investigate computational complexity issues of the ELP problem, which have been open up to the present time. Specifically we prove that the ELP problem is NP-Hard.
Abstract. Let G(V, E) be a graph, and let/7 be the drawing of G on the plane. We consider the problem of assigning text labels to every edge of G such that the quality of the label assignment is optimal. This problem has been first encountered in automated cartography. Even though much effort has been devoted over the last 15 years in the area of automated drawing of maps, the Edge Label Placement (ELP) problem remains essentially unsolved. In this paper we investigate the ELP problem. We present an algorithm for the ELP problem more suitable for hierarchical drawings of graphs, but it can be adopted to many different drawing styles and still remain effective. Also, we present experimental results of our algorithm that indicate its effectiveness.
The automatic placement of text or symbol labels corresponding to graphical features is critical in several application areas such as cartography, geographical information systems, and graph drawing. In this paper we present a general framework for solving the problem of assigning text or symbol labels to a set of graphical features in two dimensional drawings or maps. Our approach does not favor the labeling of one type of graphical feature (such as a node, edge, or area) over another. Additionally, the labels are allowed to have arbitrary size and orientation. We also present a fast and simple technique, based on the general framework, for assigning labels to edges of graph drawings. We have implemented our techniques and have performed extensive experimentation on hierarchical and orthogonal drawings of graphs. The resulting label assignments are very practical and indicate the effectiveness of our approach.
The automatic placement of text or symbol labels corresponding to graphical objects is critical in several application areas such as Cartography, Geographical Information Systems, and Graph Drawing. In this paper we present a general framework for solving the problem of assigning text or symbol labels to a set of graphical features in two dimensional drawings or maps. Our approach does not favor the labeling of one type of graphical feature (such as a node, edge, or area) over another. Additionally, the labcls arc allowed to have arbitrary size and orientation. We have applied our framework to drawings of graphs. We have implemented our techniques and have performed extensive experimentation on hierarchical and orthogonal drawings of graphs. The resulting label assignments are very practical and indicate the effectiveness of our approach.
In this research, experimental studies were based on drilling with solid carbide tools and the material used was Al7075. The study primarily focused on investigating the effects of machining parameters (cutting speed, feed rate, diameter of the tool) on the thrust force (F z ) and the cutting torque (M z ) when drilling an Al7075 workpiece. The experimental data were analyzed using the response surface methodology (RSM) with an aim to identify the significant factors on the development of both the F z and M z . The application of the mathematical models provided favorable results with an accuracy of 3.4% and 4.7%, for the F z and the M z , respectively. Analysis of variance (ANOVA) was applied in order to examine the effectiveness of the model, and both mathematical models were established and validated. The equations derived proved to be very precise when a set of validation tests were executed. The importance of the factors' influence over the responses was also presented. Both the diameter of the cutting and the feed rate were found to be the factors of high significance, while cutting speed did not affect considerably the F z and M z in the experiments performed.
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