There are many applications in which users interactively access huge tree data by repeating set-based navigations. In this paper, we focus on label-specific/wildcard children/ descendant navigations. For efficient processing of these operations in huge data stored on a disk, we need a node ordering scheme that clusters nodes that are accessed together by these operations. In this paper, (1) we show there is no node order that is optimal for all these operations, (2) we propose two schemes, each of which is optimal only for some subset of them, and (3) we show that one of the proposed schemes can process all these operations with access to a constant-bounded number of regions on the disk without accessing irrelevant nodes.