Speedup Graph Processing by Graph Ordering

The CPU cache performance is one of the key issues to efficiency in database systems. It is reported that cache miss latency takes a half of the execution time in database systems. To improve the CPU cache performance, there are studies to support searching including cache-oblivious, and cache-conscious trees. In this paper, we focus on CPU speedup for graph computing in general by reducing the CPU cache miss ratio for different graph algorithms. The approaches dealing with trees are not applicable to graphs which are complex in nature. In this paper, we explore a general approach to speed up CPU computing, in order to further enhance the efficiency of the graph algorithms without changing the graph algorithms (implementations) and the data structures used. That is, we aim at designing a general solution that is not for a specific graph algorithm, neither for a specific data structure. The approach studied in this work is graph ordering, which is to find the optimal permutation among all nodes in a given graph by keeping nodes that will be frequently accessed together locally, to minimize the CPU cache miss ratio. We prove the graph ordering problem is NP-hard, and give a basic algorithm with a bounded approximation. To improve the time complexity of the basic algorithm, we further propose a new algorithm to reduce the time complexity and improve the efficiency with new optimization techniques based on a new data structure. We conducted extensive experiments to evaluate our approach in comparison with other 9 possible graph orderings (such as the one obtained by METIS) using 8 large real graphs and 9 representative graph algorithms. We confirm that our approach can achieve high performance by reducing the CPU cache miss ratios.