Algorithms for Constructing Overlay Networks For Live Streaming

We present a polynomial time approximation algorithm for constructing an overlay multicast network for streaming live media events over the Internet. The class of overlay networks constructed by our algorithm include networks used by Akamai Technologies to deliver live media events to a global audience with high fidelity. We construct networks consisting of three stages of nodes. The nodes in the first stage are the entry points that act as sources for the live streams. Each source forwards each of its streams to one or more nodes in the second stage that are called reflectors. A reflector can split an incoming stream into multiple identical outgoing streams, which are then sent on to nodes in the third and final stage that act as sinks and are located in edge networks near end-users. As the packets in a stream travel from one stage to the next, some of them may be lost. A sink combines the packets from multiple instances of the same stream (by reordering packets and discarding duplicates) to form a single instance of the stream with minimal loss. Our primary contribution is an algorithm that constructs an overlay network that provably satisfies capacity and reliability constraints to within a constant factor of optimal, and minimizes cost to within a logarithmic factor of optimal. Further in the common case where only the transmission costs are minimized, we show that our algorithm produces a solution that has cost within a factor of 2 of optimal. We also implement our algorithm and evaluate it on realistic traces derived from Akamai's live streaming network. Our empirical results show that our algorithm can be used to efficiently construct large-scale overlay networks in practice with near-optimal cost

Robust Algorithms for TSP and Steiner Tree

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.Comment: 39 pages. An extended abstract of this paper appeared in the Proceedings of the 47th International Colloquium on Automata, Languages, and Programming (ICALP), 202

Universal Algorithms for Clustering Problems

This paper presents universal algorithms for clustering problems, including the widely studied $k$-median, $k$-means, and $k$-center objectives. The input is a metric space containing all potential client locations. The algorithm must select $k$ cluster centers such that they are a good solution for any subset of clients that actually realize. Specifically, we aim for low regret, 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 solution $SOL$ for a clustering problem is said to be an $(\alpha, \beta)$-approximation if for all subsets of clients $C'$, it satisfies $SOL(C') \leq \alpha \cdot OPT(C') + \beta \cdot MR$, where $OPT(C')$ is the cost of the optimal solution for clients $C'$ and $MR$ is the minimum regret achievable by any solution. Our main results are universal algorithms for the standard clustering objectives of $k$-median, $k$-means, and $k$-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 $\ell_p$-objectives and the setting where some subset of the clients are fixed. We also give hardness results showing that $(\alpha, \beta)$-approximation is NP-hard if $\alpha$ or $\beta$ 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.Comment: Appeared in ICALP 2021, Track A. Fixed mismatch between paper title and arXiv titl

Symmetric Interdiction for Matching Problems

Motivated by denial-of-service network attacks, we introduce the symmetric interdiction model, where both the interdictor and the optimizer are subject to the same constraints of the underlying optimization problem. We give a general framework that relates optimization to symmetric interdiction for a broad class of optimization problems. We then study the symmetric matching interdiction problem - with applications in traffic engineering - in more detail. This problem can be simply stated as follows: find a matching whose removal minimizes the size of the maximum matching in the remaining graph. We show that this problem is APX-hard, and obtain a 3/2-approximation algorithm that improves on the approximation guarantee provided by the general framework

Curator: Efficient Indexing for Multi-Tenant Vector Databases

Vector databases have emerged as key enablers for bridging intelligent applications with unstructured data, providing generic search and management support for embedding vectors extracted from the raw unstructured data. As multiple data users can share the same database infrastructure, multi-tenancy support for vector databases is increasingly desirable. This hinges on an efficient filtered search operation, i.e., only querying the vectors accessible to a particular tenant. Multi-tenancy in vector databases is currently achieved by building either a single, shared index among all tenants, or a per-tenant index. The former optimizes for memory efficiency at the expense of search performance, while the latter does the opposite. Instead, this paper presents Curator, an in-memory vector index design tailored for multi-tenant queries that simultaneously achieves the two conflicting goals, low memory overhead and high performance for queries, vector insertion, and deletion. Curator indexes each tenant's vectors with a tenant-specific clustering tree and encodes these trees compactly as sub-trees of a shared clustering tree. Each tenant's clustering tree adapts dynamically to its unique vector distribution, while maintaining a low per-tenant memory footprint. Our evaluation, based on two widely used data sets, confirms that Curator delivers search performance on par with per-tenant indexing, while maintaining memory consumption at the same level as metadata filtering on a single, shared index

Retracting Graphs to Cycles

We initiate the algorithmic study of retracting a graph into a cycle in the graph, which seeks a mapping of the graph vertices to the cycle vertices so as to minimize the maximum stretch of any edge, subject to the constraint that the restriction of the mapping to the cycle is the identity map. This problem has its roots in the rich theory of retraction of topological spaces, and has strong ties to well-studied metric embedding problems such as minimum bandwidth and 0-extension. Our first result is an O(min{k, sqrt{n}})-approximation for retracting any graph on n nodes to a cycle with k nodes. We also show a surprising connection to Sperner\u27s Lemma that rules out the possibility of improving this result using certain natural convex relaxations of the problem. Nevertheless, if the problem is restricted to planar graphs, we show that we can overcome these integrality gaps by giving an optimal combinatorial algorithm, which is the technical centerpiece of the paper. Building on our planar graph algorithm, we also obtain a constant-factor approximation algorithm for retraction of points in the Euclidean plane to a uniform cycle

Reliable Client Accounting for Hybrid Content-Distribution Networks

Content distribution networks (CDNs) have started to adopt hybrid designs, which employ both dedicated edge servers and resources contributed by clients. Hybrid designs combine many of the advantages of infrastructurebased and peer-to-peer systems, but they also present new challenges. This paper identifies reliable client accounting as one such challenge. Operators of hybrid CDNs are accountable to their customers (i.e., content providers) for the CDN’s performance. Therefore, they need to offer reliable quality of service and a detailed account of content served. Service quality and accurate accounting, however, depend in part on interactions among untrusted clients. Using the Akamai NetSession client network in a case study, we demonstrate that a small number of malicious clients used in a clever attack could cause significant accounting inaccuracies. We present a method for providing reliable accounting of client interactions in hybrid CDNs. The proposed method leverages the unique characteristics of hybrid systems to limit the loss of accounting accuracy and service quality caused by faulty or compromised clients. We also describe RCA, a system that applies this method to a commercial hybrid content-distribution network. Using trace-driven simulations, we show that RCA can detect and mitigate a variety of attacks, at the expense of a moderate increase in logging overhead

cISP: A Speed-of-Light Internet Service Provider

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 cost-effective wide-area networks that move data over paths very close to great-circle paths, at speeds very close to the speed of light in vacuum. Our cISP design augments the Internet's fiber with free-space wireless connectivity. cISP addresses the fundamental challenge of simultaneously providing low latency and scalable bandwidth, while accounting for numerous practical factors ranging from transmission tower availability to packet queuing. We show that instantiations of cISP across the contiguous 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, we estimate that the economic value from such networks would substantially exceed their expense

Understanding the Role of Registrars in DNSSEC Deployment

The Domain Name System (DNS) provides a scalable, flexible name resolution service. Unfortunately, its unauthenticated architecture has become the basis for many security attacks. To address this, DNS Security Extensions (DNSSEC) were introduced in 1997. DNSSEC’s deployment requires support from the top-level domain (TLD) registries and registrars, as well as participation by the organization that serves as the DNS operator. Unfortunately, DNSSEC has seen poor deployment thus far: despite being proposed nearly two decades ago, only 1% of .com, .net, and .org domains are properly signed. In this paper, we investigate the underlying reasons why DNSSEC adoption has been remarkably slow. We focus on registrars, as most TLD registries already support DNSSEC and registrars often serve as DNS operators for their customers. Our study uses large-scale, longitudinal DNS measurements to study DNSSEC adoption, coupled with experiences collected by trying to deploy DNSSEC on domains we purchased from leading domain name registrars and resellers. Overall, we find that a select few registrars are responsible for the (small) DNSSEC deployment today, and that many leading registrars do not support DNSSEC at all, or require customers to take cumbersome steps to deploy DNSSEC. Further frustrating deployment, many of the mechanisms for conveying DNSSEC information to registrars are error-prone or present security vulnerabilities. Finally, we find that using DNSSEC with third-party DNS operators such as Cloudflare requires the domain owner to take a number of steps that 40% of domain owners do not complete. Having identified several operational challenges for full DNSSEC deployment, we make recommendations to improve adoption