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This work introduces novel polynomial algorithms for processing top-k queries in uncertain databases under the generally adopted model of x-relations. An x-relation consists of a number of x-tuples, and each x-tuple randomly instantiates into one tuple from one or more alternatives. Our results significantly improve the best known algorithms for top-k query processing in uncertain databases, in terms of both runtime and memory usage. In the single-alternative case, the new algorithms are 2 to 3 orders of magnitude faster than the previous algorithms. In the multialternative case, we introduce the first-known polynomial algorithms, while the current best algorithms have exponential complexity in both time and space. Our algorithms run in near linear or low polynomial time and cover both types of top-k queries in uncertain databases. We provide both the theoretical analysis and an extensive experimental evaluation to demonstrate the superiority of the new approaches over existing solutions.