Drawing algorithms for survivable telecommunication networks.

Abstract

Visualizing survivable telecommunication networks on the screen has proven to be useful and helpful for the network designers. In fact, they can easily identify rings, perceive the interaction between rings, and then rapidly spot possible problems. Given a ring cover of survivable telecommunication networks, we provide three techniques for drawing a ring cover: the inside drawing, the outside drawing and the mixed drawing. In chapter 1, we will introduce the problem and present some basic definitions related to our subject. In chapter 2, we will present the inside drawing algorithm which consists of drawing each ring inside another one. In chapter 3, we will deal with the outside drawing algorithm in which rings are drawn outside others. In chapter 4, we will describe the mixed drawing algorithm which consists of drawing rings outside or inside each other. Finally, a conclusion and open problems for future work will be presented in chapter 5. We should mention that all these drawings should respect many criteria in order to preserve the readability of the drawing. These criteria are as follows: Rings must be easily identifiable within the picture, no crossing is acceptable and the resolution rule should be respected. As in most of the graph drawing algorithms, the area used for the drawing is very important. Our proposed algorithms produce drawings that require $O(n\sp2)$ area, where n is the number of nodes in the ring cover.