Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such "local" parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code. ] linear code C over the field F q is said to have locality r if this symbol can be recovered by accessing at most r other code symbols of code C. Equivalently, for any coordinate i, there exists a row in the parity-check matrix of the code of Hamming weight at most r + 1, whose support includes i. An (r, d) code was defined as a systematic linear code C having minimum distance d, where all k message symbols have locality r. It was shown that the minimum distance of an (r, d) code is upper bounded by

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Situatedness of development processes is a key issue in both the software engineering and the method engineering communities, as there is a strong felt need for process prescriptions to be adapted to the situation at hand. The assumption of the process modelling approach presented in this paper is that process prescriptions shall be selected according to the actual situation at hand i.e. dynamically in the course of the process.The paper focuses on a multi-model view of process modelling which supports this dynamicity. The approach builds on the notion of a labelled graph of intentions and strategies called a map as well as its associated guidelines. The map is a navigational structure which supports the dynamic selection of the intention to be achieved next and the appropriate strategy to achieve it whereas guidelines help in the operationalization of the selected intention. The paper presents the map and guidelines and exemplifies the approach with the CREWS-L'Ecritoire * method for requirements engineering. I IntroductionProcess engineering is considered today as a key issue by both the software engineering and information systems engineering communities. Recent interest in process engineering is part of the shift of focus from the product to the process view of systems development. The belief of the software engineering community is that as a result of improved development processes [Dow93], [Arm93] and [Jar94]. there shall be both, improved productivity of the software systems industry and improved systems quality, The focus has been to increase the level of formality of process models in order to make possible their enactment in Process Centred Software Environments [Fin94] was put in to allow process models to respond to these departures. One approach was to assume prescriptive models and then, modify them to accommodate real processes. This modification could be achieved in two ways. First the extent of deviations from the prescription that could be allowed was modelled as constraints [Cug95,Cug96,Cug98].Any actual deviation that satisfied the constraint was therefore manageable and the process enactment mechanism could handle it. This way of handling deviations took the prescriptive approach to its logical conclusion : it prescribed the deviations allowed in a prescription. The second way of handling deviations is to allow changes to be made in the prescription as and when they are needed [Dow94, SiS96, Jac92, Fin94, Ban93, Bel94]. Thus, a dynamic change of the basic prescription is allowed.In recent years, the information systems community has concentrated on the need for adapting and extending existing methods to meet the changing needs of practice.Method engineering [Wel92], [Har94] represents the effort to improve the usefulness of systems development methods by creating an adaptation framework whereby methods are created to match specific organisational situations. This improvement has been attempted at two levels. At a global level, it deals with determining the project contingency factors...

In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated to small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan et al, in which recovery from a single erasure is considered. By studying the Generalized Hamming Weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Turán graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from 2 erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case.

Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node, regenerating codes seek to minimize the amount of data downloaded for node repair, while codes with locality attempt to minimize the number of helper nodes accessed. In this paper, we provide several constructions for a class of vector codes with locality in which the local codes are regenerating codes, that enjoy both advantages. We derive an upper bound on the minimum distance of this class of codes and show that the proposed constructions achieve this bound. The constructions include both the cases where the local regenerating codes correspond to the MSR as well as the MBR point on the storage-repair-bandwidth tradeoff curve of regenerating codes.

We argue that ERP installations are difficult to align to specific requirements of the enterprise because of the low level at which ERP functionality is described. We raise this level from a functional description to a goal-oriented one. We use SAP R/3 to illustrate this. A SAP goal expresses the task that a SAP function carries out and abstracts away from the performance of this task. Since a SAP goal can be achieved in many ways, we introduce the notion of SAP strategies. We organise goals and strategies as a directed graph called a map. We illustrate the map with the Materials Management Module of SAP. In order to evaluate and compare the use of the map with the functional approach, we develop an evaluation framework. The evaluation and comparison is presented. The materials management map is then used to align the SAP module to the stores and purchase department of an academic institute.

We study a generalization of the setting of regenerating codes, motivated by applications to storage systems consisting of clusters of storage nodes. There are n clusters in total, with m nodes per cluster. A data file is coded and stored across the mn nodes, with each node storing α symbols. For availability of data, we require that the file be retrievable by downloading the entire content from any subset of k clusters. Nodes represent entities that can fail. We distinguish between intra-cluster and inter-cluster bandwidth (BW) costs during node repair. Node-repair in a cluster is accomplished by downloading β symbols each from any set of d other clusters, dubbed remote helper clusters, and also up to α symbols each from any set of surviving nodes, dubbed local helper nodes, in the host cluster. We first identify the optimal trade-off between storage-overhead and inter-cluster repair-bandwidth under functional repair, and also present optimal exact-repair code constructions for a class of parameters. The new tradeoff is strictly better than what is achievable via space-sharing existing coding solutions, whenever > 0. We then obtain sharp lower bounds on the necessary intra-cluster repair BW to achieve optimal trade-off. Under functional repair, random linear network codes (RLNCs) simultaneously optimize usage of both inter-and intra-cluster repair BW; simulation results based on RLNCs suggest optimality of the bounds on intra-cluster repair-bandwidth. Our bounds reveal the interesting fact that, while it is beneficial to increase the number of local helper nodes in order to improve the storage-vs-inter-cluster-repair-BW trade-off, increasing not only increases intra-cluster BW in the host-cluster, but also increases the intra-cluster BW in the remote helper clusters. We also analyze resilience of the clustered storage system against passive eavesdropping by providing file-size bounds and optimal code constructions.

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