Finding all maximum non-crossing subsets of nets using dynamic programming

Abstract

Current algorithms of the dynamic programming or longest increasing subsequence with the time complexity of O(n2) or O(nlogn) can only find one maximum non-crossing subset of nets even if there is more than one with the same length. In order to traverse all possible ones in the VLSI (Very Large Integration Circuits) wire routing, a dynamic programming algorithm is adopted and modified to calculate the length of maximum non-crossing subsets. For this purpose, an adjacent list is created for the traverse and a recursive function is used to output all maximum non-crossing subsets of nets. The effectiveness of the algorithm with a time complexity of O(n2) is illustrated through the theoretical analysis and experimental results of corresponding C++ program. © 2011 Springer-Verlag Berlin Heidelberg.