You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Repair performance in hierarchical data centers is often bottlenecked by cross-rack network transfer. Recent theoretical results show that the cross-rack repair traffic can be minimized through repair layering, whose idea is to partition a repair operation into inner-rack and cross-rack layers. However, how repair layering should be implemented and deployed in practice remains an open issue. In this paper, we address this issue by proposing a practical repair layering framework called DoubleR. We design two families of practical double regenerating codes (DRC), which not only minimize the cross-rack repair traffic, but also have several practical properties that improve state-of-the-art regenerating codes. We implement and deploy DoubleR atop Hadoop Distributed File System (HDFS), and show that DoubleR maintains the theoretical guarantees of DRC and improves the repair performance of regenerating codes in both node recovery and degraded read operations.

Cited Abstract(s):
[1]: To reduce storage overhead, cloud file systems are transitioning from replication to erasure codes. This process has revealed new dimensions on which to evaluate the performance of different coding schemes: the amount of data used in recovery and when performing degraded reads. We present an algorithm that finds the optimal number of codeword symbols needed for recovery for any XOR-based erasure code and produces recovery schedules that use a minimum amount of data. We differentiate popular erasure codes based on this criterion and demonstrate that the differences improve I O performance in practice for the large block sizes used in cloud file systems. Several cloud systems [15, 10] have adopted Reed-Solomon (RS) codes, because of their generality and their ability to tolerate larger numbers of failures. We define a new class of rotated Reed-Solomon codes that perform degraded reads more efficiently than all known codes, but otherwise inherit the reliability and performance properties of Reed-Solomon codes.

[2]: Erasure codes such as Reed-Solomon (RS) codes are being extensively deployed in data centers since they offer significantly higher reliability than data replication methods at much lower storage overheads. These codes however mandate much higher resources with respect to network bandwidth and disk IO during reconstruction of data that is missing or otherwise unavailable. Existing solutions to this problem either demand additional storage space or severely limit the choice of the system parameters. In this paper, we present "Hitchhiker", a new erasure-coded storage system that reduces both network traffic and disk IO by around 25 to 45 during reconstruction of missing or otherwise unavailable data, with no additional storage, the same fault tolerance, and arbitrary flexibility in the choice of parameters, as compared to RS-based systems. Hitchhiker 'rides' on top of RS codes, and is based on novel encoding and decoding techniques that will be presented in this paper. We have implemented Hitchhiker in the Hadoop Distributed File System (HDFS). When evaluating various metrics on the data-warehouse cluster in production at Facebook with real-time traffic and workloads, during reconstruction, we observe a 36 reduction in the computation time and a 32 reduction in the data read time, in addition to the 35 reduction in network traffic and disk IO. Hitchhiker can thus reduce the latency of degraded reads and perform faster recovery from failed or decommissioned machines.
Some erasure codes aim to minimize I O (i.e., the amount of data read from storage) during repair. For example, Rotated RS codes [1] and Hitchhiker [2] propose new parity constructions that send fewer blocks in a single-node failure repair.