This paper presents an optimal constraint graph generation algorithm for graph-based one-dimensional layout compaction. The first published algorithm for this problem was the shadow-propagation algorithm. However, without sophisticated implementation of a shadow-front, complexity of the algorithm could fall into O(n2), where n is the number of layout objects. Although our algorithm, called the enhanced plane-sweep based graph generation algorithm, is an extension of the shadow-propagation algorithm, such a drawback is resolved by introducing an enhanced plane-sweep technique. The algorithm maintains multiple shadow-fronts simultaneously by storing them in a work-list called previous-boundary. Since a balanced search tree is selected for implementation of the worklist, total complexity of the algorithm is O(n log n) which is optimal. Experimental results show that the enhanced plane-sweep based graph generation algorithm runs in almost linear time with respect to the number of layout objects and is faster than the perpendicular plane-sweep algorithm which is also optimal in terms of time complexity.

An autonatic layout scheme dedicated to bipolar analog modules is described. A layout model is settled in such a way that the VCC/GND line is laid out on top/bottom edge of a rectangular region, within which the whole elements are placed and interconnected. According to this simple modeling, a layout scheme can be constructed of a series of the following algorithms: First clustering is executed for partitioning a given circuit into clusters, each having connections with VCC and GND lines, and then linear ordering is applied to clusters so as to be placed in a one-dimensional array. After a relative placement of circuits elements in each cluster, a block compactor is implemented by means of packing blocks in each cluster into an idle space, and then a detailed router is conducted to attain 100% interconnection. Finally a layout compactor is invoked to pack all layout patterns into a rectangle of the minimum possible area. A number of implementation results are also shown to reveal the practicability of the proposed analog module generator.