Summary
A routing problem is given by a planar graph G= (V, E) with a given embedding into the plane and a set Ne of nets. A net is a pair of points on the boundary of the infinite face. The goal is to find a set of pairwise edge-disjoint paths connecting the terminals of the various nets. We assume that the degree of every vertex not on the boundary of the infinite face is even and call such routing problems half-even. We show that one can decide in time O(bn) whether a half-even problem is solvable and that a solution can be constructed in time O(n 2). Here n=¦V¦ and b is the number of vertices on the boundary of the infinite face. If the routing problem is even, i.e. every cut has even free capacity, and G is a subgraph of the planar grid then a solution can be found in time O(n 3/2).
Similar content being viewed by others
References
Frank, A.: Disjoint paths in a rectilinear grid. Combinatorica 2, 4 (1982)
Frank, A.: Edge Disjoint Paths in Planar Graphs. J. Comb. Theory, Ser. B (To appear)
Hassin, R.: On Multicommodity Flows in Planar Graphs. Networks, 14, 225–235 (1984)
Kaufmann, M., Mehlhorn, K.: Generalized Switchbox Routing. ICALP 85, Lect. Notes Comput. Sci. 195, 328–337 (1985)
Lengauer, Th., Mehlhorn, K.: Four Results on the Complexity of VLSI Computations, in Advances in Computing research, Vol. 2. (F.P. Preparata ed.); pp. 1–22. Greenwich: JAI Press 1984
Matsumoto, K., Nishizeki, T., Saito, N.: An efficient algorithm for finding multi-commodity flows in planar graphs, SICOMP (To appear)
Mehlhorn, K.: Data Structures and Efficient Algorithms Vol.2: Graph Algorithms and NP-completeness, EATCS Monographs in Theoretical Computer Science. Berlin, Heidelberg, New York: Springer 1984
Mehlhorn, K., Preparata, F.P.: Routing through a rectangle. J. Assoc. Comput. Mach. 33, 60–85 (1986)
Nishezeki, T., Saito, N., Suzuki, K.: A Linear Time Routing Algorithm for Couvet Grids, IEEE Trans. CAD, 4, 1 (1985)
Okamura, H., Seymour, P.D.: Multicommodity flows in planar graphs, J. Comb. Theory, Ser. B 31, 75–81 (1983)
Preparata, F.P., Lipski, W. Jr.: Optimal three-layer channel routing. IEEE Trans. Comput. C-33, 5, 427–437 (1984)
Rivest, R.L., Baratz, A.E., Miller, G.: Provably good channel routing algorithms, Proc. CMU Conf. VLSI Syst. Comput., 151–159 (1981)
Author information
Authors and Affiliations
Additional information
This research was supported by the Deutsche Forschungsgemeinschaft, SFB 124, VLSI-Entwurfsmethoden und Parallelität. Part of it was done while the second author was visiting SIEMENS A.G., ZTI VENUS
Rights and permissions
About this article
Cite this article
Becker, M., Mehlhorn, K. Algorithms for routing in planar graphs. Acta Informatica 23, 163–176 (1986). https://doi.org/10.1007/BF00289496
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00289496