On the Restrictive Channel Thickness Estimation

Channel routing is an important phase of physical design of LSI and VLSI chips. The channel routing method was first proposed by Akihiro Hashimoto and James Stevens [1]. The method was extensively studied by many authors and applied to different technologies. At present there are known many effective heuristic algorithms for channel routing. A. LaPaugh [2] proved that the restrictive routing problem is NP-complete. In this paper we prove that for every positive integer k there is a restrictive channel C for which τ(C) > φ(HG)+L(VG)+k, where τ(C) is the thickness of the channel, φ(HG) is clique number of the horizontal constraints graph HG and L(V G) is the length of the longest directed path in the vertical constraints graph VG.