Data series indexes are necessary for managing and analyzing the increasing amounts of data series collections that are nowadays available. These indexes support both exact and approximate similarity search, with approximate search providing high-quality results within milliseconds, which makes it very attractive for certain modern applications. Reducing the pre-processing (i.e., index building) time and improving the accuracy of search results are two major challenges. DSTree and the iSAX index family are state-of-the-art solutions for this problem. However, DSTree suffers from long index building times, while iSAX suffers from low search accuracy. In this paper, we identify two problems of the iSAX index family that adversely affect the overall performance. First, we observe the presence of a proximity-compactness trade-off related to the index structure design (i.e., the node fanout degree), significantly limiting the efficiency and accuracy of the resulting index. Second, a skewed data distribution will negatively affect the performance of iSAX. To overcome these problems, we propose Dumpy, an index that employs a novel multi-ary data structure with an adaptive node splitting algorithm and an efficient building workflow. Furthermore, we devise Dumpy-Fuzzy as a variant of Dumpy which further improves search accuracy by proper duplication of series. To fully leverage the potential of modern hardware including multicore CPUs and Solid State Drives (SSDs), we parallelize Dumpy to DumpyOS with sophisticated indexing and pruning-based querying algorithms. An optimized approximate search algorithm, DumpyOS-F which prominently improves the search accuracy without violating the index, is also proposed.