Three-layer bubble-sorting-based nonManhattan channel routing

Abstract

It is well known that a nonManhattan channel router can use fewer routing tracks, and is never worse than a Manhattan router in a channel. To my knowledge, a three-layer bubblesorting-based nonManhattan channel routing problem is always solved by the solution in a two-layer bubble-sorting-based nonManhattan channel routing problem. Recently, an O͑kn 2 ͒ heuristic algorithm [Chaudhary et al. 1991] and an O͑k 2 n͒ optimal algorithm [Chen et al. 1994] have been proposed, where k is the number of two-layer routing tracks and n is the number of terminals in a bubble-sorting-based nonManhattan channel. In this paper we propose an optimal three-layer bubble-sorting-based nonManhattan routing algorithm to minimize the number of three-layer routing tracks. Furthermore, the time complexity of this optimal algorithm is proven to be in O͑hn͒ time, where h is the number of three-layer routing tracks and n is the number of terminals in a bubble-sorting-based nonManhattan channel.

Channel routing for integrated optics

“…Our channel routing technique is based on non-Manhattan routing grids and positional net sorting. We draw inspirations from a sorting-based channel router [14], [15] that has the useful property of being minimal in terms of crossings. However, the original sort-router formulation suffers from a number of unaddressed limitations and detrimental side-effects that make it impractical for optical routing.…”

“…Such routing grids can more suitably represent waveguide curves, and provides greater routing flexibility in the absence of multiple routing layers. The work of [14], [15], also described in textbook [34], investigates a non-Manhattan grid channel router based on sorting. The nets of a channel are assigned numerical indexes, and routing is performed by sorting the nets in a finite number of permutations.…”

“…However, the original sorting-based channel routing solutions presented in [14], [15] have drawbacks that make them impractical. Below, we describe the limitations of the sort routers of [14], [15]; these limitations motivate the design of our own sorting-based channel router, specifically designed for integrated optics.…”

“…Two sorting techniques are presented in [14], [15]: swapsorting and bubble-sorting. The swap-based router swaps positions of pairs of adjacent nets if they are out-of-order.…”

“…Channel routing techniques are therefore needed that minimize waveguide crossings and bends. Drawing inspirations from sortingbased routing techniques [14], [15], we present an efficient solution for channel routing of integrated optical waveguides that minimizes signal loss as a function of waveguide crossings and bends within the channel.…”