Algorithms for Balanced Graph Bi-partitioning

Graph partitioning has been widely applied in cloud computing, data centres, virtual machine scheduling, hardware/software co-design, and VLSI circuit design, etc. The general graph partitioning problem is known to be NP-hard. This paper investigates how to partition the vertex set of an undirected weighted graph into two disjoint subsets, such that the total vertex-weights of the two subsets are nearly equal, and the total weight of the edges connecting the two subsets is minimized. A heuristic algorithm is proposed to initialize an approximate bi-partition such that the total vertex-weight of each subset is close to that of the other. The proposed algorithm constructs a subset by selecting a group of neighbouring vertices with the highest gain from the original graph for inclusion into the subset. A customized tabu search is proposed to further refine the initial partition, which minimizes the communication cost and keeps partition balanced. Experimental results show that the proposed algorithms outperform the state-of-the-art on the public benchmarks, with the improvement of up to 79% for certain cases.