An Improved KM Algorithm for Computing Structural Index of DAE System

This paper proposes an improved KM algorithm to computing the structural index of linear time-invariant Differential Algebraic Equation (DAE) systems. The problem is of practical significance in index reduction based on structural index of DAE system and combinatorial relaxation theory. This improved KM algorithm combines greedy idea and classical KM algorithm. It first computes matches as much as possible using greedy technology, and then call KM algorithm to search the matches for the unmatched vertices during the step of greedy technology. The improved KM algorithm reduces the running time bound by a factor of r, the number of matches searched using greedy algorithm. Generally, the time complexity is O(r²+(n-r)n²), the optimal time is O(n²).