A 2 + approximation algorithm for the k-MST problem - download pdf or read online

By Arora S., Karakostas G.

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Wood, Lower Bounds for 3-D Drawings, JGAA, 7(1) 33–77 (2003) 67 [14] S. Even and G. Granot, Rectilinear planar drawings with few bends in each edge. Tech. Rep. 797, Computer Science Department, Technion, Israel Inst. , 1994. [15] H. Koike, An application of three-dimensional visualization to objectoriented programming. In T. Catarci, M. F. Costabile, and S. , Proc. Advanced Visual Interfaces (AVI ’92), vol. 36 of Series in Comput. , pp. 180–192, World Scientific, 1992. [16] H. Koike, The role of another spatial dimension in software visualization.

Let x and y be the other two vertices in K6 \ M2 . Each of the chordal 2-paths axc, ayc, bxd and byd have at least two bends by Observation 6, giving a total of at least 8 = 12 − 2j bends. This completes the proof. We now prove a lower bound of seven on the number of bends in drawings of K6 \ M3 , the octahedron graph. The drawing of K6 \ M3 obtained from the drawing of K6 illustrated in Figure 17 by deleting the two 2-bend edges and the 0-bend edge has eight bends. We conjecture that every drawing of K6 \ M3 has at least eight bends.

The Incremental algorithm, as stated in [21], only works for simple graphs, however with a suitable modification it also works for multigraphs [A. Papakostas, private communication, 1998]. D. Wood, Lower Bounds for 3-D Drawings, JGAA, 7(1) 33–77 (2003) 39 a number of introductory results concerning 0-bend drawings of cycles. These results are used to prove our lower bounds on the total number of bends in drawings of complete graphs and graphs obtained from complete graphs by deleting a matching, which are established in Section 3.

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A 2 + approximation algorithm for the k-MST problem by Arora S., Karakostas G.

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