Since some computation in reachability Query Preserving Graph Compression （QPGC） algorithm are redundant， a high-performance compression strategy was proposed. In the stage of solving the vertex sets of ancestors and descendants， an algorithm named TSB （Topological Sorting Based algorithm for solving ancestor and descendant sets） was proposed for common graph data. Firstly， the vertices of the graph data were topological sorted. Then， the vertex sets were solved in the order or backward order of the topological sequence， avoiding the redundant computation caused by the ambiguous solution order. And an algorithm based on graph aggregation operation was proposed for graph data with short longest path， namely AGGB （AGGregation Based algorithm for solving ancestor and descendant sets）， so the vertex sets were able to be solved in a certain number of aggregation operations. In the stage of solving reachability equivalence class， a Piecewise Statistical Pruning （PSP） algorithm was proposed. Firstly， piecewise statistics of ancestors and descendants sets were obtained and then the statistics were compared to achieve the coarse matching， and some unnecessary fine matches were pruned off. Experimental results show that compared with QPGC algorithm： in the stage of solving the vertex sets of ancestors and descendants， TSB and AGGB algorithm have the performance averagely increased by 94.22% and 90.00% respectively on different datasets； and in the stage of solving the reachability equivalence class， PSP algorithm has the performance increased by more than 70% on most datasets. With the increasing of the dataset， using TSB and AGGB cooperated with PSP has the performance improved by nearly 28 times. Theoretical analysis and simulation results show that the proposed strategy has less redundant computation and faster compression speed compared to QPGC.