By N. Benvenuto, et al.,

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**Extra resources for Algorithms for Comm. Systs and Their Applns**

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A. M. Turing [Tur36] introduced a mathematical model of computers, called a Turing machine, and showed that such an unsolvable problem does exist. A typical example is the socalled halting problem: given a computer program with its input, will it ever halt? Turing proved that there is no algorithm that solves correctly all instances of this problem within finite time. Thus there exist problems for which there is no algorithm. However, all of the problems discussed in this book have algorithms. TEAM LinG - Live, Informative, Non-cost and Genuine !

L(a) partitions E into a spanning tree T and a set B of back edges. T and B are drawn by solid and dotted lines in Fig. 3, where the numbers next to vertices are levels. Fig. 3 BFS: tree edges and back edges. TEAM LinG - Live, Informative, Non-cost and Genuine ! 3 we have seen two data structures to represent a graph: an adjacencey matrix representation and a list representation. The two plane graphs in Figs. 4(a) have the same adjacency matrix representation as illustrated in Fig. l(b). This implies that the two graphs in Fig.

Clearly We are now ready to describe the drawing algorithm. First we draw G3 by a triangle as follows. Set P(u1) = (O,O), P ( V Z = ) (2,O), P(u3) = (1, l),and L ( Q ) = {ui} for i = 1,2,3. (See Fig. ) Assume that k - 1 23 and we have embedded Gk-1 in such a way that the following conditions hold: ( e l ) P ( q ) = (0,O) and P(u2) = ( 2 k - 6,O); (e2) z ( w 1 ) < ~ ( w z <) . . < ~ ( w t )where , Co(Gk-l) = w l , w 2 , . . , w t , w1 = u1 and wt = 712; and (e3) each edge (wi,wi+l) on Co(Gk-l) is drawn by a straight line having slope either fl or -1, as illustrated in Fig.

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