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In this paper we define a Distributed Arbitrary Segment Tree (DAST), a distributed tree-like structure that layers the range query processing mechanism over public Distributed Hash Table (DHT) services. Compared with traditional segment trees, the arbitrary segment tree used by a DAST reduces the number of key-space segments that need to be maintained, which in turn results in fewer query operations and lower overheads. Moreover, considering that range queries often contain redundant entries that the clients do not need, we introduce the concept of accuracy of results (AoR) for range queries. We demonstrate that by adjusting AoR, the DHT operational overhead can be improved. DAST is implemented on a well-known public DHT service (OpenDHT) and validation through experimentation and supporting simulation is performed. The results demonstrate the effectiveness of DAST over exiting methods.