Consider a communication setup consisting of two terminals, each with access to one of two correlated sources. The terminals can swap information and both terminals want to reconstruct a deterministic function of the two sources under the requirements that reconstructions at the two terminals must satisfy average distortion constraints and the two reconstructions must be identical with high probability. In this paper, we develop an achievability and a converse to the problem assuming discrete memoryless sources. Furthermore, we demonstrate that our bounds are separately tight for a few special cases of the problem.

We consider the problem of stragglers in distributed computing systems. Stragglers, which are compute nodes that unpredictably slow down, often increase the completion times of tasks. One common approach to mitigating stragglers is work replication, where only the first completion among replicated tasks is accepted, discarding the others. However, discarding work leads to resource wastage. In this article, we propose a method for exploiting the work completed by stragglers rather than discarding it. The idea is to increase the granularity of the assigned work, and to increase the frequency of worker updates. We show that the proposed method reduces the completion time of tasks via experiments performed on a simulated cluster as well as on Amazon EC2 with Apache Hadoop.

We present the problem of two-terminal source coding with Common Sum Reconstruction (CSR). Consider two terminals, each with access to one of two correlated sources. Both terminals want to reconstruct the sum of the two sources under some average distortion constraint, and the reconstructions at two terminals must be identical with high probability. In this paper, we develop inner and outer bounds to the achievable rate distortion region of the CSR problem for a doubly symmetric binary source. We employ existing achievability results for Steinberg's common reconstruction and Wyner-Ziv's source coding with side information problems, and an achievability result for the lossy version of Körner-Marton's modulo-two sum computation problem.

Elasticity is offered by cloud service providers to exploit under-utilized computing resources. The low-cost elastic nodes can leave and join any time during the computation cycle. The possibility of elastic events occurring together with the problem of slow nodes, referred to as stragglers, increases the uncertainty of the system, leading to computation delay. Recent results have shown that coded computing can be used to reduce the negative effect of elasticity and stragglers. In this paper, we propose two hierarchical coded elastic computing schemes that can further speed up the system by exploiting stragglers and effectively allocating tasks among available nodes. In our simulations, our scheme realizes 45% improvement in average finishing time compared to the state-of-the-art coded elastic computing scheme.

We consider decentralized consensus optimization when workers sample data from non-identical distributions and perform variable amounts of work due to slow nodes known as stragglers. The problem of non-identical distributions and the problem of variable amount of work have been previously studied separately. In our work we analyse them together under a unified system model. We propose to combine worker outputs weighted by the amount of work completed by each. We prove convergence of the proposed method under perfect consensus, assuming straggler statistics are independent and identical across all workers for all iterations. Our numerical results show that under approximate consensus the proposed method outperforms the non-weighted scheme for both convex and non-convex objective functions.