Abstract-If the data density of magnetic disks is to continue its current 30-50% annual growth, new recording techniques are required. Among the actively considered options, shingled writing is currently the most attractive one because it is the easiest to implement at the device level. Shingled write recording trades the inconvenience of the inability to update in-place for a much higher data density by a using a different write technique that overlaps the currently written track with the previous track. Random reads are still possible on such devices, but writes must be done largely sequentially.In this paper, we discuss possible changes to disk-based data structures that the adoption of shingled writing will require. We first explore disk structures that are optimized for large sequential writes with little or no sequential writing, even of metadata structures, while providing acceptable read performance. We also examine the usefulness of non-volatile RAM and the benefits of object-based interfaces in the context of shingled disks. Finally, through the analysis of recent device traces, we demonstrate the surprising stability of written device blocks, with general purpose workloads showing that more than 93% of device blocks remain unchanged over a day, and that for more specialized workloads less than 0.5% of a shingled-write disk's capacity would be needed to hold randomly updated blocks.

Abstract-We present a two-dimensional RAID architecture that is specifically tailored to the needs of archival storage systems. Our proposal starts with a fairly conventional twodimensional RAID architecture where each disk belongs to exactly one horizontal and one vertical RAID level 4 stripe. Once the array has been populated, we add a superparity device that contains the exclusive OR of all the contents of all horizontal-or vertical-parity disks. The new organization tolerates all triple disk failures and nearly all quadruple and quintuple disk failures. As a result, it provides mean times to data loss (MTTDLs) more than a hundred times better than those of sets of RAID level 6 stripes with equal capacity and similar parity overhead. 1

Abstract-Disk failure rates vary so widely among different makes and models that designing storage solutions for the worst case scenario is a losing proposition. The approach we propose here is to design our storage solutions for the most probable case while incorporating in our design the option of adding extra redundancy when we find out that its disks are less reliable than expected. To illustrate our proposal, we show how to increase the reliability of existing twodimensional disk arrays with n 2 data elements and 2n parity elements by adding n additional parity elements that will mirror the contents of half the existing parity elements. Our approach offers the three advantages of being easy to deploy, not affecting the complexity of parity calculations, and providing a five-year reliability of 99.999 percent in the face of catastrophic levels of data loss where the array would lose up to a quarter of its storage capacity in a year.

Abstract-As we move towards data centers at the exascale, the reliability challenges of such enormous storage systems are daunting. We demonstrate how such systems will suffer substantial annual data loss if only traditional reliability mechanisms are employed. We argue that the architecture for exascale storage systems should incorporate novel mechanisms at or below the object level to address this problem. Our argument for such a research focus is that focusing solely on the device level will not scale, and in this study we analytically evaluate how rapidly this problem manifests.

Abstract. In this paper, we investigate the quotient semilattice R/M of the r.e. degrees modulo the cappable degrees. We first prove the R/M counterpart of the Friedberg-Muchnik theorem. We then show that minimal elements and minimal pairs are not present in R/M. We end with a proof of the R/M counterpart to Sack's splitting theorem.0. Introduction. The set of all r.e. degrees is made into an upper semilattice (with 0 and 1) in a natural way: namely, the reducibility relation between r.e. sets induces a partial ordering on degrees, for which it is readily shown that finite suprema always exist. This semilattice structure, denoted "7 ", has been extensively studied.Earliest results stress the richness and the uniformity of 7. For instance, the Friedberg-Muchnik theorem states that there exists an incomparable pair in 7