Disjoint-Set Data Structure-Aided Structured Gaussian Elimination for Solving Sparse Linear Systems

Structured Gaussian elimination (SGE) is a class of methods for efficiently solving sparse linear systems. The key idea is to first triangulate the original linear systems. The maximum component (MC)-based strategies are widely used to implement the triangulation process. The most straightforward way to find the MC is through exhaustive search. Instead, in this letter, we propose to use a disjoint-set data structure (DSDS) to efficiently maintain the components. The extra storage and time complexity introduced by the DSDS are respectively linear to the number of unknowns and constraints involved in a linear system. Simulation results show that using the DSDS can be several times faster than doing the exhaustive search to find the components.