arXiv subjects

D. Manjunath

Publications and source records attributed to D. Manjunath.

34 records · Page 2Linked to original sources

arXiv2016

On the Maximum Rate of Networked Computation in a Capacitated Network

Given a capacitated communication network $\mathcal{N}$ and a function f that needs to be computed on $\mathcal{N},$ we study the problem of generating a computation and communication schedule in $\mathcal{N}$ to maximize the rate of computation of f. Shah et. al.[IEEE Journal of Selected Areas in Communication, 2013] studied this problem when the computation schema $\mathcal{G}$ for f is a tree. We define the notion of a schedule when $\mathcal{G}$ is a general DAG and show that finding an optimal schedule is equivalent to finding the solution of a packing LP. We prove that approximating the maximum rate is MAX SNP-hard by looking at the packing LP. For this packing LP we prove that solving the separation oracle of its dual is equivalent to solving the LP. The separation oracle of the dual reduces to the problem of finding minimum cost embedding given $\mathcal{N},\mathcal{G},$ which we prove to be MAX SNP-hard even when $\mathcal{G}$ has bounded degree and bounded edge weights and $\mathcal{N}$ has just three vertices. We present a polynomial time algorithm to compute the maximum rate of function computation when $\mathcal{N}$ has two vertices by reducing the problem to a version of submodular function minimization problem. For the general $\mathcal{N}$ we study restricted class of schedules and its equivalent packing LP. We observe that for this packing LP also the separation oracle of its dual reduces to finding minimum cost embedding. A version of this minimum cost embedding problem has been studied in literature. We present a quadratic integer program for the minimum cost embedding problem and its linear programming relaxation based on earthmover metric. We also present some approximate algorithms for special classes of $\mathcal{G}.$

cs.DC↗

arXiv2015

Stability and Equilibrium Analysis of Laneless Traffic with Local Control Laws

In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis representing the direction of motion and the X-axis representing the lateral or the direction perpendicular to the direction of motion. Different influence graphs are used to model the interaction between the vehicles in these two directions. The instantaneous accelerations of each car, in both X and Y directions, are functions of the measurements from the neighbouring cars according to these influence graphs. The stability and equilibrium spacings of the car formation is analyzed for usual traffic situations such as steady flow, obstacles, lane changing and rogue drivers arbitrarily changing positions inside the formation. Conditions are derived under which the formation maintains stability and the desired intercar spacing for each of these traffic events. Simulations for some of these scenarios are included.

eess.SY↗

arXiv2015

Optimal Embedding of Functions for In-Network Computation: Complexity Analysis and Algorithms

We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The algorithm to compute the given function is described by a weighted directed acyclic graph and is called the computation graph. An embedding defines the computation communication sequence that obtains the function at the sink. Two kinds of optimal embeddings are sought, the embedding that---(1)~minimizes delay in obtaining function at sink, and (2)~minimizes cost of one instance of computation of function. This abstraction is motivated by three applications---in-network computation over sensor networks, operator placement in distributed databases, and module placement in distributed computing. We first show that obtaining minimum-delay and minimum-cost embeddings are both NP-complete problems and that cost minimization is actually MAX SNP-hard. Next, we consider specific forms of the computation graph for which polynomial time solutions are possible. When the computation graph is a tree, a polynomial time algorithm to obtain the minimum delay embedding is described. Next, for the case when the function is described by a layered graph we describe an algorithm that obtains the minimum cost embedding in polynomial time. This algorithm can also be used to obtain an approximation for delay minimization. We then consider bounded treewidth computation graphs and give an algorithm to obtain the minimum cost embedding in polynomial time.

cs.DC↗

arXiv2015

How Hard is Computing Parity with Noisy Communications?

We show a tight lower bound of $Ω(N \log\log N)$ on the number of transmissions required to compute the parity of $N$ input bits with constant error in a noisy communication network of $N$ randomly placed sensors, each having one input bit and communicating with others using local transmissions with power near the connectivity threshold. This result settles the lower bound question left open by Ying, Srikant and Dullerud (WiOpt 06), who showed how the sum of all the $N$ bits can be computed using $O(N \log\log N)$ transmissions. The same lower bound has been shown to hold for a host of other functions including majority by Dutta and Radhakrishnan (FOCS 2008). Most works on lower bounds for communication networks considered mostly the full broadcast model without using the fact that the communication in real networks is local, determined by the power of the transmitters. In fact, in full broadcast networks computing parity needs $θ(N)$ transmissions. To obtain our lower bound we employ techniques developed by Goyal, Kindler and Saks (FOCS 05), who showed lower bounds in the full broadcast model by reducing the problem to a model of noisy decision trees. However, in order to capture the limited range of transmissions in real sensor networks, we adapt their definition of noisy decision trees and allow each node of the tree access to only a limited part of the input. Our lower bound is obtained by exploiting special properties of parity computations in such noisy decision trees.

cs.DC↗

arXiv2013

A Stochastic Kaczmarz Algorithm for Network Tomography

We develop a stochastic approximation version of the classical Kaczmarz algorithm that is incremental in nature and takes as input noisy real time data. Our analysis shows that with probability one it mimics the behavior of the original scheme: starting from the same initial point, our algorithm and the corresponding deterministic Kaczmarz algorithm converge to precisely the same point. The motivation for this work comes from network tomography where network parameters are to be estimated based upon end-to-end measurements. Numerical examples via Matlab based simulations demonstrate the efficacy of the algorithm.

math.OC↗

arXiv2013

On Connectivity Thresholds in the Intersection of Random Key Graphs on Random Geometric Graphs

In a random key graph (RKG) of $n$ nodes each node is randomly assigned a key ring of $K_n$ cryptographic keys from a pool of $P_n$ keys. Two nodes can communicate directly if they have at least one common key in their key rings. We assume that the $n$ nodes are distributed uniformly in $[0,1]^2.$ In addition to the common key requirement, we require two nodes to also be within $r_n$ of each other to be able to have a direct edge. Thus we have a random graph in which the RKG is superposed on the familiar random geometric graph (RGG). For such a random graph, we obtain tight bounds on the relation between $K_n,$ $P_n$ and $r_n$ for the graph to be asymptotically almost surely connected.

cs.IT↗

arXiv2012

On the Separability of Targets Using Binary Proximity Sensors

We consider the problem where a network of sensors has to detect the presence of targets at any of $n$ possible locations in a finite region. All such locations may not be occupied by a target. The data from sensors is fused to determine the set of locations that have targets. We term this the separability problem. In this paper, we address the separability of an asymptotically large number of static target locations by using binary proximity sensors. Two models for target locations are considered: (i) when target locations lie on a uniformly spaced grid; and, (ii) when target locations are i.i.d. uniformly distributed in the area. Sensor locations are i.i.d uniformly distributed in the same finite region, independent of target locations. We derive conditions on the sensing radius and the number of sensors required to achieve separability. Order-optimal scaling laws, on the number of sensors as a function of the number of target locations, for two types of separability requirements are derived. The robustness or security aspects of the above problem is also addressed. It is shown that in the presence of adversarial sensors, which toggle their sensed reading and inject binary noise, the scaling laws for separability remain unaffected.

cs.IT↗

arXiv2012

In-Network Estimation of Frequency Moments

We consider the problem of estimating functions of distributed data using a distributed algorithm over a network. The extant literature on computing functions in distributed networks such as wired and wireless sensor networks and peer-to-peer networks deals with computing linear functions of the distributed data when the alphabet size of the data values is small, O(1). We describe a distributed randomized algorithm to estimate a class of non-linear functions of the distributed data which is over a large alphabet. We consider three types of networks: point-to-point networks with gossip based communication, random planar networks in the connectivity regime and random planar networks in the percolating regime both of which use the slotted Aloha communication protocol. For each network type, we estimate the scaled $k$-th frequency moments, for $k \geq 2$. Specifically, for every $k \geq 2,$ we give a distributed randomized algorithm that computes, with probability $(1-δ),$ an $ε$-approximation of the scaled $k$-th frequency moment, $F_k/N^k$, using time $O(M^{1-\frac{1}{k-1}} T)$ and $O(M^{1-\frac{1}{k-1}} \log N \log (δ^{-1})/ε^2)$ bits of transmission per communication step. Here, $N$ is the number of nodes in the network, $T$ is the information spreading time and $M=o(N)$ is the alphabet size.

cs.NI↗

arXiv2010

Network Flows for Functions

We consider in-network computation of an arbitrary function over an arbitrary communication network. A network with capacity constraints on the links is given. Some nodes in the network generate data, e.g., like sensor nodes in a sensor network. An arbitrary function of this distributed data is to be obtained at a terminal node. The structure of the function is described by a given computation schema, which in turn is represented by a directed tree. We design computing and communicating schemes to obtain the function at the terminal at the maximum rate. For this, we formulate linear programs to determine network flows that maximize the computation rate. We then develop fast combinatorial primal-dual algorithm to obtain $ε$-approximate solutions to these linear programs. We then briefly describe extensions of our techniques to the cases of multiple terminals wanting different functions, multiple computation schemas for a function, computation with a given desired precision, and to networks with energy constraints at nodes.

cs.NI↗

arXiv2010

Load Balancing via Random Local Search in Closed and Open systems

In this paper, we analyze the performance of random load resampling and migration strategies in parallel server systems. Clients initially attach to an arbitrary server, but may switch server independently at random instants of time in an attempt to improve their service rate. This approach to load balancing contrasts with traditional approaches where clients make smart server selections upon arrival (e.g., Join-the-Shortest-Queue policy and variants thereof). Load resampling is particularly relevant in scenarios where clients cannot predict the load of a server before being actually attached to it. An important example is in wireless spectrum sharing where clients try to share a set of frequency bands in a distributed manner.

cs.NI↗

arXiv2009

Estimating Network Link Characteristics using Packet-Pair Dispersion: A Discrete Time Queueing Theoretic View

Packet-dispersion based measurement tools insert pairs of probe packets with a known separation into the network for transmission over a unicast path or a multicast tree. Samples of the separation between the probe pairs at the destination(s) are observed. Heuristic techniques are then used by these tools to estimate the path characteristics from the observations. In this paper we present a queueing theoretic setting for packet-dispersion based probing. Analogous to network tomography, we develop techniques to estimate the parameters of the arrival process to the individual links from the samples of the output separations, i.e., from the end-to-end measurements. The links are modeled as independent discrete time queues with i.i.d. arrivals. We first obtain an algorithm to obtain the (joint) distribution of the separation between the probes at the destination(s) for a given distribution of the spacing at the input. The parameter estimates of the arrival process are obtained as the minimizer of a cost function between the empirical and calculated distributions. We also carry out extensive simulations and numerical experiments to study the performance of the estimation algorithm under the fairly `harsh' conditions of non stationarity of the arrival process. We find that the estimations work fairly well for two queues in series and for multicast.

cs.NI↗

arXiv2008

Limit laws for k-coverage of paths by a Markov-Poisson-Boolean model

Let P := {X_i,i >= 1} be a stationary Poisson point process in R^d, {C_i,i >= 1} be a sequence of i.i.d. random sets in R^d, and {Y_i^t; t \geq 0, i >= 1} be i.i.d. {0,1}-valued continuous time stationary Markov chains. We define the Markov-Poisson-Boolean model C_t := {Y_i^t(X_i + C_i), i >= 1}. C_t represents the coverage process at time t. We first obtain limit laws for k-coverage of an area at an arbitrary instant. We then obtain the limit laws for the k-coverage seen by a particle as it moves along a one-dimensional path.

math.PR↗

arXiv2008

On Distributed Function Computation in Structure-Free Random Networks

We consider in-network computation of MAX in a structure-free random multihop wireless network. Nodes do not know their relative or absolute locations and use the Aloha MAC protocol. For one-shot computation, we describe a protocol in which the MAX value becomes available at the origin in $O(\sqrt{n/\log n})$ slots with high probability. This is within a constant factor of that required by the best coordinated protocol. A minimal structure (knowledge of hop-distance from the sink) is imposed on the network and with this structure, we describe a protocol for pipelined computation of MAX that achieves a rate of $Ω(1/(\log^2 n)).$

cs.IT↗

arXiv2007

On Distributed Computation in Noisy Random Planar Networks

We consider distributed computation of functions of distributed data in random planar networks with noisy wireless links. We present a new algorithm for computation of the maximum value which is order optimal in the number of transmissions and computation time.We also adapt the histogram computation algorithm of Ying et al to make the histogram computation time optimal.

cs.IT↗

arXiv2006

A Combined LIFO-Priority Scheme for Overload Control of E-commerce Web Servers

E-commerce Web-servers often face overload conditions during which revenue-generating requests may be dropped or abandoned due to an increase in the browsing requests. In this paper we present a simple, yet effective, mechanism for overload control of E-commerce Web-servers. We develop an E-commerce workload model that separates the browsing requests from revenue-generating transaction requests. During overload, we apply LIFO discipline in the browsing queues and use a dynamic priority model to service them. The transaction queues are given absolute priority over the browsing queues. This is called the LIFO-Pri scheduling discipline. Experimental results show that LIFO-Pri dramatically improves the overall Web-server throughput while also increasing the completion rate of revenue-generating requests. The Web-server was able to operate at nearly 60% of its maximum capacity even when offered load was 1.5 times its capacity. Further, when compared to a single queue FIFO system, there was a seven-fold increase in the number of completed revenue-generating requests during overload.

cs.PF↗

arXiv2006

On the topological Properties of the One Dimensional Exponential Random Geometric Graph

In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph.

math.PR↗