Constrained shortest paths for QoS routing and path protection in communication networks.

The CSDP (k) problem requires the selection of a set of k > 1 link-disjoint paths with minimum total cost and with total delay bounded by a given upper bound. This problem arises in the context of provisioning paths in a network that could be used to provide resilience to link failures. Again we studied the LP relaxation of the ILP formulation of the problem from the primal perspective and proposed an approximation algorithm.We have studied certain combinatorial optimization problems that arise in the context of two important problems in computer communication networks: end-to-end Quality of Service (QoS) and fault tolerance. These problems can be modeled as constrained shortest path(s) selection problems on networks with each of their links associated with additive weights representing the cost, delay etc.The problems considered above assume that the network status is known and accurate. However, in real networks, this assumption is not realistic. So we considered the QoS route selection problem under inaccurate state information. Here the goal is to find a path with the highest probability that satisfies a given delay upper bound. We proposed a pseudo-polynomial time approximation algorithm, a fully polynomial time approximation scheme, and a strongly polynomial time heuristic for this problem.Finally we studied the constrained shortest path problem with multiple additive constraints. Using the LARAC algorithm as a building block and combining ideas from mathematical programming, we proposed a new approximation algorithm.First we studied the QoS single route selection problem, i.e., the constrained shortest path (CSP) problem. The goal of the CSP problem is to identify a minimum cost route which incurs a delay less than a specified bound. It can be formulated as an integer linear programming (ILP) problem which is computationally intractable. The LARAC algorithm reported in the literature is based on the dual of the linear programming relaxation of the ILP formulation and gives an approximate solution. We proposed two new approximation algorithms solving the dual problem. Next, we studied the CSP problem using the primal simplex method and exploiting certain structural properties of networks. This led to a novel approximation algorithm

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

Lower Bounds for Structuring Unreliable Radio Networks

In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks---a generalization of the standard graph-based model that now includes unreliable links controlled by an adversary. We begin by proving that a natural geographic constraint on the network topology is required to solve these problems efficiently (i.e., in time polylogarthmic in the network size). We then prove the importance of the assumption that nodes are provided advance knowledge of their reliable neighbors (i.e, neighbors connected by reliable links). Combined, these results answer an open question by proving that the efficient MIS and CDS algorithms from [Censor-Hillel, PODC 2011] are optimal with respect to their dual graph model assumptions. They also provide insight into what properties of an unreliable network enable efficient local computation.Comment: An extended abstract of this work appears in the 2014 proceedings of the International Symposium on Distributed Computing (DISC

Algorithms and literate programs for weighted low-rank approximation with missing data

Linear models identification from data with missing values is posed as a weighted low-rank approximation problem with weights related to the missing values equal to zero. Alternating projections and variable projections methods for solving the resulting problem are outlined and implemented in a literate programming style, using Matlab/Octave's scripting language. The methods are evaluated on synthetic data and real data from the MovieLens data sets

Generating Representative ISP Technologies From First-Principles

Understanding and modeling the factors that underlie the growth and evolution of network topologies are basic questions that impact capacity planning, forecasting, and protocol research. Early topology generation work focused on generating network-wide connectivity maps, either at the AS-level or the router-level, typically with an eye towards reproducing abstract properties of observed topologies. But recently, advocates of an alternative "first-principles" approach question the feasibility of realizing representative topologies with simple generative models that do not explicitly incorporate real-world constraints, such as the relative costs of router configurations, into the model. Our work synthesizes these two lines by designing a topology generation mechanism that incorporates first-principles constraints. Our goal is more modest than that of constructing an Internet-wide topology: we aim to generate representative topologies for single ISPs. However, our methods also go well beyond previous work, as we annotate these topologies with representative capacity and latency information. Taking only demand for network services over a given region as input, we propose a natural cost model for building and interconnecting PoPs and formulate the resulting optimization problem faced by an ISP. We devise hill-climbing heuristics for this problem and demonstrate that the solutions we obtain are quantitatively similar to those in measured router-level ISP topologies, with respect to both topological properties and fault-tolerance