Abstract: Time intervals are often associated with tuples to represent their valid time in temporal relations, where overlap join is crucial for various kinds of queries. Many existing overlap join algorithms use indices based on tree structures such as quad-tree, B⁺-tree and interval tree. These algorithms usually have high CPU cost since deep path traversals are unavoidable, which makes them not so competitive as data-partition or plane-sweep based algorithms. This paper proposes an efficient overlap join algorithm based on a new two-layer flat index named as Overlap Interval Inverted Index (i.e., O2i Index). It uses an array to record the end points of intervals and approximates the nesting structures of intervals via two functions in the first layer, and the second layer uses inverted lists to trace all intervals satisfying the approximated nesting structures. With the help of the new index, the join algorithm only visits the must-be-scanned lists and skips all others. Analyses and experiments on both real and synthetic datasets show that the proposed algorithm is as competitive as the state-of-the-art algorithms.