Efficient multi-dimensional data search has received much attention in centralized systems. However, its implementation in large-scale distributed systems is not a trivial job and remains to be a challenge. In this paper, SDI, a new succinct multi-dimensional balanced tree structure based on peer-to-peer technology, is presented. With SDI structure, the query efficiency can be bounded by O(log N). Compared with previous tree-based methods, SDI has extremely low maintenance cost. This is due to the carefully chosen finger links. Furthermore, new algorithms are designed for both point query and range query processing, which make SDI free from the root-bottleneck problem. Experimental results validate the efficiency and effectiveness of the proposed approach. Categories and Subject Descriptors C.2.4 [Distributed Systems]: Distributed applications; H.2.4 [Systems]: Query processing; H.2.m [Database Management]: Miscellaneous General Terms Algorithms, Experimentation, Design Keywords mul...