Unconstrained and Constrained Fault-Tolerant Resource Allocation

First, we study the Unconstrained Fault-Tolerant Resource Allocation (UFTRA) problem (a.k.a. FTFA problem in \cite{shihongftfa}). In the problem, we are given a set of sites equipped with an unconstrained number of facilities as resources, and a set of clients with set $\mathcal{R}$ as corresponding connection requirements, where every facility belonging to the same site has an identical opening (operating) cost and every client-facility pair has a connection cost. The objective is to allocate facilities from sites to satisfy $\mathcal{R}$ at a minimum total cost. Next, we introduce the Constrained Fault-Tolerant Resource Allocation (CFTRA) problem. It differs from UFTRA in that the number of resources available at each site $i$ is limited by $R_{i}$. Both problems are practical extensions of the classical Fault-Tolerant Facility Location (FTFL) problem \cite{Jain00FTFL}. For instance, their solutions provide optimal resource allocation (w.r.t. enterprises) and leasing (w.r.t. clients) strategies for the contemporary cloud platforms. In this paper, we consider the metric version of the problems. For UFTRA with uniform $\mathcal{R}$, we present a star-greedy algorithm. The algorithm achieves the approximation ratio of 1.5186 after combining with the cost scaling and greedy augmentation techniques similar to \cite{Charikar051.7281.853,Mahdian021.52}, which significantly improves the result of \cite{shihongftfa} using a phase-greedy algorithm. We also study the capacitated extension of UFTRA and give a factor of 2.89. For CFTRA with uniform $\mathcal{R}$, we slightly modify the algorithm to achieve 1.5186-approximation. For a more general version of CFTRA, we show that it is reducible to FTFL using linear programming

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