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Private decision tree evaluation (PDTE) allows a decision tree holder to run a secure protocol with a feature provider. By running the protocol, the feature provider will learn a classification result. Nothing more is revealed to either party. In most existing PDTE protocols, the required communication grows exponentially with the tree's depth $d$, which is highly inefficient for large trees. This shortcoming motivated us to design a sublinear PDTE protocol with $O(d)$ communication complexity. The core of our construction is a shared oblivious selection (SOS) functionality, allowing two parties to perform a secret-shared oblivious read operation from an array. We provide two SOS protocols, both of which achieve sublinear communication and propose optimizations to further improve their efficiency. Our sublinear PDTE protocol is based on the proposed SOS functionality and we prove its security under a semi-honest adversary. We compare our protocol with the state-of-the-art, in terms of communication and computation, under various network settings. The performance evaluation shows that our protocol is practical and more scalable over large trees than existing solutions.