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Robust optimization is a widely studied area in operations research, where the algorithm takes as input a range of values and outputs a single solution that performs well for the entire range. Specifically, a robust algorithm aims to minimizeregret, defined as the maximum difference between the solution’s cost and that of an optimal solution in hindsight once the input has been realized. For graph problems inP, such as shortest path and minimum spanning tree, robust polynomial-time algorithms that obtain a constant approximation on regret are known. In this paper, we study robust algorithms for minimizing regret inNP-hard graph optimization problems, and give constant approximations on regret for the classical traveling salesman and Steiner tree problems. 

This article presentsuniversalalgorithms for clustering problems, including the widely studiedk-median,k-means, andk-center objectives. The input is a metric space containing allpotentialclient locations. The algorithm must selectkcluster centers such that they are a good solution foranysubset of clients that actually realize. Specifically, we aim for lowregret, defined as the maximum over all subsets of the difference between the cost of the algorithm’s solution and that of an optimal solution. A universal algorithm’s solutionSolfor a clustering problem is said to be an α , β-approximation if for all subsets of clientsC^′, it satisfiessol(C^′) ≤ α ċopt(C′) + β ċmr, whereopt(C′ is the cost of the optimal solution for clients (C′) andmris the minimum regret achievable by any solution. Our main results are universal algorithms for the standard clustering objectives ofk-median,k-means, andk-center that achieve (O(1),O(1))-approximations. These results are obtained via a novel framework for universal algorithms using linear programming (LP) relaxations. These results generalize to other ℓ_p-objectives and the setting where some subset of the clients arefixed. We also give hardness results showing that (α, β)-approximation is NP-hard if α or β is at most a certain constant, even for the widely studied special case of Euclidean metric spaces. This shows that in some sense, (O(1),O(1))-approximation is the strongest type of guarantee obtainable for universal clustering. 

Low latency is a requirement for a variety of interactive network applications. The Internet, however, is not optimized for latency. We thus explore the design of wide-area networks that move data at nearly the speed of light in vacuum. Our cISP design augments the Internet’s fiber with free-space microwave wireless connectivity over paths very close to great-circle paths. cISP addresses the fundamental challenge of simultaneously providing ultra-low latency while accounting for numerous practical factors ranging from transmission tower availability to packet queuing. We show that instantiations of cISP across the United States and Europe would achieve mean latencies within 5% of that achievable using great-circle paths at the speed of light, over medium and long distances. Further, using experiments conducted on a nearly-speed-of-light algorithmic trading network, together with an analysis of trading data at its end points, we show that microwave networks are reliably faster than fiber networks even in inclement weather. Finally, we estimate that the economic value of such networks would substantially exceed their expense. 

Interactive mobile applications like web browsing and gaming are known to benefit significantly from low latency networking, as applications communicate with cloud servers and other users’ devices. Emerging mobile channel standards have not met these needs: general-purpose channels are greatly improving bandwidth but empirically offer little improvement for common latency-sensitive applications, and ultra-low-latency channels are targeted at only specific applications with very low bandwidth requirements. We explore a different direction for wireless channel design: utilizing two channels – one high bandwidth, one low latency – simultaneously for general-purpose applications. With a focus on web browsing, we design fine-grained traffic steering heuristics that can be implemented in a shim layer of the host network stack, effectively exploiting the high bandwidth and low latency properties of both channels. In the special case of 5G’s channels, our experiments show that even though URLLC offers just 0.2% of the bandwidth of eMBB, the use of both channels in parallel can reduce page load time by 26% to 59% compared to delivering traffic exclusively on eMBB. We believe this approach may benefit applications in addition to web browsing, may offer service providers incentives to deploy low latency channels, and suggests a direction for the design of future wireless channels. 

There is a rich body of literature on measuring and optimizing nearly every aspect of the web, including characterizing the structure and content of web pages, devising new techniques to load pages quickly, and evaluating such techniques. Virtually all of this prior work used a single page, namely the landing page (i.e., root document, "/"), of each web site as the representative of all pages on that site. In this paper, we characterize the differences between landing and internal (i.e., non-root) pages of 1000 web sites to demonstrate that the structure and content of internal pages differ substantially from those of landing pages, as well as from one another. We review more than a hundred studies published at top-tier networking conferences between 2015 and 2019, and highlight how, in light of these differences, the insights and claims of nearly two-thirds of the relevant studies would need to be revised for them to apply to internal pages. Going forward, we urge the networking community to include internal pages for measuring and optimizing the web. This recommendation, however, poses a non-trivial challenge: How do we select a set of representative internal web pages from a web site? To address the challenge, we have developed Hispar, a "top list" of 100,000 pages updated weekly comprising both the landing pages and internal pages of around 2000 web sites. We make Hispar and the tools to recreate or customize it publicly available. 

Robust optimization is a widely studied area in operations research, where the algorithm takes as input a range of values and outputs a single solution that performs well for the entire range. Specifically, a robust algorithm aims to minimize regret, defined as the maximum difference between the solution’s cost and that of an optimal solution in hindsight once the input has been realized. For graph problems in P, such as shortest path and minimum spanning tree, robust polynomial-time algorithms that obtain a constant approximation on regret are known. In this paper, we study robust algorithms for minimizing regret in NP-hard graph optimization problems, and give constant approximations on regret for the classical traveling salesman and Steiner tree problems.