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Register a new userScheduling for Weighted Flow and Completion Times in Reconfigurable Networks
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Added by
Michael Dinitz
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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New optical technologies offer the ability to reconfigure network topologies dynamically, rather than setting them once and for all. This is true in both optical wide area networks (optical WANs) and in datacenters, despite the many differences between these two settings. Because of these new technologies, there has been a surge of both practical and theoretical research on algorithms to take advantage of them. In particular, Jia et al. [INFOCOM 17] designed online scheduling algorithms for dynamically reconfigurable topologies for both the makespan and sum of completion times objectives. In this paper, we work in the same setting but study an objective that is more meaningful in an online setting: the sum of flow times. The flow time of a job is the total amount of time that it spends in the system, which may be considerably smaller than its completion time if it is released late. We provide competitive algorithms for the online setting with speed augmentation, and also give a lower bound proving that speed augmentation is in fact necessary. As a side effect of our techniques, we also improve and generalize the results of Jia et al. on completion times by giving an $O(1)$-competitive algorithm for arbitrary sizes and release times even when nodes have different degree bounds, and moreover allow for the weighted sum of completion times (or flow times).
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We discuss one of the most fundamental scheduling problem of processing jobs on a single machine to minimize the weighted flow time (weighted response time). Our main result is a $O(log P)$-competitive algorithm, where $P$ is the maximum-to-minimum processing time ratio, improving upon the $O(log^{2}P)$-competitive algorithm of Chekuri, Khanna and Zhu (STOC 2001). We also design a $O(log D)$-competitive algorithm, where $D$ is the maximum-to-minimum density ratio of jobs. Finally, we show how to combine these results with the result of Bansal and Dhamdhere (SODA 2003) to achieve a $O(log(min(P,D,W)))$-competitive algorithm (where $W$ is the maximum-to-minimum weight ratio), without knowing $P,D,W$ in advance. As shown by Bansal and Chan (SODA 2009), no constant-competitive algorithm is achievable for this problem.
We propose a method for reconfiguring a relay node for polarization encoded quantum key distribution (QKD) networks. The relay can be switched between trusted and untrusted modes to adapt to different network conditions, relay distances, and security requirements. This not only extends the distance over which a QKD network operates but also enables point-to-multipoint (P2MP) network topologies. The proposed architecture centralizes the expensive and delicate single-photon detectors (SPDs) at the relay node with eased maintenance and cooling while simplifying each user node so that it only needs commercially available devices for low-cost qubit preparation.
We give a 1.488-approximation for the classic scheduling problem of minimizing total weighted completion time on unrelated machines. This is a considerable improvement on the recent breakthrough of $(1.5 - 10^{-7})$-approximation (STOC 2016, Bansal-Srinivasan-Svensson) and the follow-up result of $(1.5 - 1/6000)$-approximation (FOCS 2017, Li). Bansal et al. introduced a novel rounding scheme yielding strong negative correlations for the first time and applied it to the scheduling problem to obtain their breakthrough, which resolved the open problem if one can beat out the long-standing $1.5$-approximation barrier based on independent rounding. Our key technical contribution is in achieving significantly stronger negative correlations via iterative fair contention resolution, which is of independent interest. Previously, Bansal et al. obtained strong negative correlations via a variant of pipage type rounding and Li used it as a black box.
Inter-datacenter networks connect dozens of geographically dispersed datacenters and carry traffic flows with highly variable sizes and different classes. Adaptive flow routing can improve efficiency and performance by assigning paths to new flows according to network status and flow properties. A popular approach widely used for traffic engineering is based on current bandwidth utilization of links. We propose an alternative that reduces bandwidth usage by up to at least 50% and flow completion times by up to at least 40% across various scheduling policies and flow size distributions.
Modern networks run middleboxes that offer services ranging from network address translation and server load balancing to firewalls, encryption, and compression. In an industry trend known as Network Functions Virtualization (NFV), these middleboxes run as virtual machines on any commodity server, and the switches steer traffic through the relevant chain of services. Network administrators must decide how many middleboxes to run, where to place them, and how to direct traffic through them, based on the traffic load and the server and network capacity. Rather than placing specific kinds of middleboxes on each processing node, we argue that server virtualization allows each server node to host all middlebox functions, and simply vary the fraction of resources devoted to each one. This extra flexibility fundamentally changes the optimization problem the network administrators must solve to a new kind of multi-commodity flow problem, where the traffic flows consume bandwidth on the links as well as processing resources on the nodes. We show that allocating resources to maximize the processed flow can be optimized exactly via a linear programming formulation, and to arbitrary accuracy via an efficient combinatorial algorithm. Our experiments with real traffic and topologies show that a joint optimization of node and link resources leads to an efficient use of bandwidth and processing capacity. We also study a class of design problems that decide where to provide node capacity to best process and route a given set of demands, and demonstrate both approximation algorithms and hardness results for these problems.
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