Distributed Verification and Hardness of Distributed Approximation

STOC 2011 (Invited and accepted to SICOMP)
Distributed Verification and Hardness of Distributed Approximation
Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, Roger Wattenhofer, Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, Roger Wattenhofer
Abstract

We study the verification problem in distributed networks, stated as follows. Let H be a subgraph of a network G where each vertex of G knows which edges incident on it are in H. We would like to verify whether H has some properties, e.g., if it is a tree or if it is connected (every node knows in the end of the process whether H has the specified property or not). We would like to perform this verification in a decentralized fashion via a distributed algorithm. The time complexity of verification is measured as the number of rounds of distributed communication.

In this paper we initiate a systematic study of distributed verification, and give almost tight lower bounds on the running time of distributed verification algorithms for many fundamental problems such as connectivity, spanning connected subgraph, and s-t cut verification.

We then show applications of these results in deriving strong unconditional time lower bounds on the hardness of distributed approximation for many classical optimization problems including minimum spanning tree, shortest paths, and minimum cut.

Many of these results are the first non-trivial lower bounds for both exact and approximate distributed computation and they resolve previous open questions. Moreover, our unconditional lower bound of approximating minimum spanning tree (MST) subsumes and improves upon the previous hardness of approximation bound of Elkin [STOC 2004] as well as the lower bound for (exact) MST computation of Peleg and Rubinovich [FOCS 1999]. Our result implies that there can be no distributed approximation algorithm for MST that is significantly faster than the current exact algorithm, for any approximation factor.

Our lower bound proofs show an interesting connection between communication complexity and distributed computing which turns out to be useful in establishing the time complexity of exact and approximate distributed computation of many problems.

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Astro: A Predictive Model for Anomaly Detection and Feedback-based Scheduling on Hadoop

Chaitali Gupta, Mayank Bansal, Tzu-Cheng Chuang, Ranjan Sinha, Sami Ben-romdhane

The sheer growth in data volume and Hadoop cluster size make it a significant challenge to diagnose and locate problems in a production-level cluster environment efficiently and within a short period of time. Often times, the distributed monitoring systems are not capable of detecting a problem well in advance when a large-scale Hadoop cluster starts to deteriorate i n performance or becomes unavailable. Thus, inc o m i n g workloads, scheduled between the time when cluster starts to deteriorate and the time when the problem is identified, suffer from longer execution times. As a result, both reliability and throughput of the cluster reduce significantly. In this paper, we address this problem by proposing a system called Astro, which consists of a predictive model and an extension to the Hadoop scheduler. The predictive model in Astro takes into account a rich set of cluster behavioral information that are collected by monitoring processes and model them using machine learning algorithms to predict future behavior of the cluster. The Astro predictive model detects anomalies in the cluster and also identifies a ranked set of metrics that have contributed the most towards the problem. The Astro scheduler uses the prediction outcome and the list of metrics to decide whether it needs to move and reduce workloads from the problematic cluster nodes or to prevent additional workload allocations to them, in order to improve both throughput and reliability of the cluster. The results demonstrate that the Astro scheduler improves usage of cluster compute resources significantly by 64.23% compared to traditional Hadoop. Furthermore, the runtime of the benchmark application reduced by 26.68% during the time of anomaly, thus improving the cluster throughput.

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