Methods and apparatus provide for, at each of plural calculation timings, associating pieces of position information indicating the positions of objects in a virtual space at the calculation timing with leaves and creates a complete binary tree in which position information reflecting pieces of the position information of child nodes is associated with an internal node, and a node shuffling section that shuffles 2·2n (n≥1) child nodes regarding each group of 2n nodes on the basis of the position information associated with each of the 2·2n child nodes belonging to the 2n nodes in each layer sequentially from the immediately-upper layer of the lowermost layer in the complete binary tree; and carrying out collision determination between objects by using the complete binary tree resulting from the shuffling by the node shuffling section.