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In this paper, we study the problem of indexing multidimensional data in P2P networks based on distributed hash tables (DHTs). We advocate the indexing approach that superimposes a multidimensional index tree on top of a DHT - a paradigm that keeps the underlying DHT intact while being able to adapt to any DHT substrate. In this context, we identify several index design issues and propose a novel indexing scheme called multidimensional Lightweight Hash Tree (m-LIGHT). First, to preserve data locality, m-LIGHT employs a clever naming mechanism that gracefully maps a tree-based index into the DHT and contributes to high efficiency in both index maintenance and query processing. Second, to tackle the load balancing issue, m-LIGHT leverages a new data-aware splitting strategy that achieves optimal load balance under a fixed index size. We present detailed algorithms for processing complex queries over the m-LIGHT index. We also conduct an extensive performance evaluation of m-LIGHT in comparison with several state-of-the-art indexing schemes. The experimental results show that m-LIGHT substantially reduces index maintenance overhead and improves query performance in terms of both bandwidth consumption and response latency.