An Equally-Split Bin Packing Problem.

We investigate the equally-split bin packing problem (ESBP), which is inspired by a service placement scenario in cloud computing. In this problem, given a set of items, a set of bins already in use, and an infinite number of new bins, one is asked to pack the items using as few bins as possible. Unlike the traditional bin packing problem, ESBP requires that each item must be split equally into at least two pieces, and the pieces of an item must be placed into different bins. We tackle this problem both theoretically and practically. We prove that ESBP is NP-hard and cannot be approximated within a factor better than 4/3 unless P = NP. On the positive side, we propose two algorithms with asymptotic approximation ratios at most e/(e-1)≈ 1.582 . We also propose a heuristic algorithm, which not only minimizes the number of bins used but also reduces the total number of item pieces. We compared these three algorithms and two other methods on a dataset from Alibaba. The experimental result shows that our heuristic algorithm has the best overall performance.