Wiring knock-knee layouts: A global approach

Abstract

We present a global approach to solve the three-layer wirability problem for knock-knee layouts. In general, the problem is $\mathcal{N}\mathcal{P}$-complete. Only for very restricted classes of layouts polynomial three-layer wiring algorithms are known up to now. In this paper we show that for a large class of layouts a three-layer wiring can be constructed by solving a path problem in a special class of graphs or a two-satisfiability problem, and thus may be wired efficiently. Moreover, it is shown that a minimum stretching of the layout into a layout belonging to this class can be found by solving a clique cover problem in an interval graph. This problem is polynomially solvable as well. Altogether, the method also yields a good heuristic for the three-layer wirability problem for knock-knee layouts.

Part of this work was done while Majid Sarrafzadeh, Dorothea Wagner and Frank Wagner were with the LEONARDO FIBONACCI INSTITUTE for the Foundations of Computer Science, Trento, Italy. Majid Sarrafzadeh also acknowledges the National Science Foundation for supporting this research in part under grant MIP-8921540. Dorothea Wagner and Karsten Weihe acknowledge the Deutsche Forschungsgemeinschaft for supporting this research under grant Mö 446/1-3.