The \(k\)-Set consensus problem with weight consideration
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In the cloud computing environment, files are duplicated into several copies for storage at different locations to increase their access efficiency and fault tolerance. However, there may exist malicious processors in the cloud computing environment. How to ensure that fault-free processors coordinate to find appropriate locations to store these duplicated files without influence from malicious processors is an important issue. In this paper, we propose a consensus algorithm to assist fault-free processors in reaching a consensus on where to store the duplicated files in the presence of malicious processors. In this paper, we will extend the classical consensus problem to a new type of consensus problem called the \(k\)-Set consensus problem with weight consideration (\(k\)-SetW problem). This problem is integrated with the concepts of weight and \(k\)-Set. In other words, each processor in this problem is allowed to have multiple initial values (i.e., the expected locations for the duplicated files) and set the weight for each initial value. The weighted value shows the processor’s preference for an initial value. Regarding the consensus, this problem does not require agreement among all fault-free processors on a single consensus value. It allows coexistence of multiple consensus values as long as the number of consensus values is not greater than \(k\) (i.e., the maximum number of duplicated files). By solving the \(k\)-SetW problem, we can help fault-free processors determine the locations for storing the duplicates of at most \(k\) copies based on their preferences in the presence of malicious processors.
KeywordsDistributed system Malicious fault Fault-tolerant K-Set consensus problem Weight
C. F. Cheng’s research was sponsored by the National Science Council of Taiwan, ROC, under Grant NSC102-2221-E-032-026.
- 1.White T (2009) Hadoop: the definitive guide, MapReduce for the cloud. O’Reilly Media, New YorkGoogle Scholar
- 2.Afrati FN, Ullman JD (2011) Optimizing multiway joins in a map-reduce environment. IEEE Trans Knowl Data Eng 23(9)Google Scholar
- 3.Jiang D, Tung AKH, Chen G (2011) MAP-JOIN-REDUCE: toward scalable and efficient data analysis on large clusters. IEEE Trans Knowl Data Eng 23(9)Google Scholar
- 4.Attiya H, Welch J (2004) Distributed computing—fundamentals, simulation and advanced topics, 2nd edn. Wiley, New York, pp 414Google Scholar
- 6.Silberschatz A, Galvin PB, Gagne G (2009) Operating system concepts, 8th edn. Wiley, New YorkGoogle Scholar
- 10.Parvedy PR, Raynal M, Travers C (2005) Decision optimal early-stopping \(k\)-set agreement in synchronous systems prone to send omission failures. In: Proceedings of the 11th Pacific Rim international symposium on dependable computingGoogle Scholar
- 12.Garg VK, Bridgman J (2011) The weighted Byzantine agreement problem. In: Proceedings of the IEEE parallel and distributed processing symposiumGoogle Scholar
- 13.Berman P, Garay JA (1989) Asymptotically optimal distributed consensus. Proceedings of the international colloquium on automata, languages and programming, CopenhagenGoogle Scholar
- 14.Berman P, Garay JA, Perry KJ (1989) Towards optimal distributed consensus. In: Proceedings of the annual symposium on foundations of computer science, pp 410–415Google Scholar
- 19.Ma ZS, Krings AW (2011) Dynamic hybrid fault modeling and extended evolutionary game theory for reliability, survivability and fault tolerance analyses. IEEE Trans Reliab 60(1)Google Scholar