Saikat Ray

Arbitrary Throughput Versus Complexity Tradeoffs in Wireless Networks Using Graph Partitioning

Several policies have recently been proposed for attaining the maximum throughput region, or a guaranteed fraction thereof, through dynamic link scheduling. Among these policies, the ones that attain the maximum throughput region require a computation time which is linear in the network size, and the ones that require constant or logarithmic computation time attain only certain fractions of the maximum throughput region. In contrast, in this paper we propose policies that can attain any desirable fraction of the maximum throughput region using a computation time that is largely independent of the network size. First, using a combination of graph partitioning techniques and Lyapunov arguments, we propose a simple policy for tree topologies under the primary interference model that requires each link to exchange only 1 bit information with its adjacent links and approximates the maximum throughput region using a computation time that depends only on the maximum degree of nodes and the approximation factor. Then we develop a framework for attaining arbitrary close approximations for the maximum throughput region in arbitrary networks, and use this framework to obtain any desired tradeoff between throughput guarantees and computation times for a large class of networks and interference models. Specifically, given any epsiv > 0, the maximum throughput region can be approximated in these networks within a factor of 1-epsiv using a computation time that depends only on the maximum node degree and epsiv .

Statistical location detection with sensor networks

The paper develops a systematic framework for designing a stochastic location detection system with associated performance guarantees using a wireless sensor network. To detect the location of a mobile sensor, the system relies on RF-characteristics of the signal transmitted by the mobile sensor, as it is received by stationary sensors (clusterheads). Location detection is posed as a hypothesis testing problem over a discretized space. Large deviations results enable the characterization of the probability of error leading to a placement problem that maximizes an information-theoretic distance (Chernoff distance) among all pairs of probability distributions of observations conditional on the sensor locations. The placement problem is shown to be NP-hard and is formulated as a linear integer programming problem; yet, large instances can be solved efficiently by leveraging special-purpose algorithms from the theory of discrete facility location. The resultant optimal placement is shown to provide asymptotic guarantees on the probability of error in location detection under quite general conditions by minimizing an upper bound of the error-exponent. Numerical results show that the proposed framework is computationally feasible and the resultant clusterhead placement performs near-optimal even with a small number of observation samples in a simulation environment.

Always acyclic distributed path computation

Distributed routing algorithms may give rise to transient loops during path recomputation, which can pose significant stability problems in high-speed networks. We present a new algorithm, Distributed Path Computation with Intermediate Variables (DIV), which can be combined with any distributed routing algorithm to guarantee that the directed graph induced by the routing decisions remains acyclic at all times. The key contribution of DIV, besides its ability to operate with any routing algorithm, is an update mechanism using simple message exchanges between neighboring nodes that guarantees loop-freedom at all times. DIV provably outperforms existing loop-prevention algorithms in several key metrics such as frequency of synchronous updates and the ability to maintain paths during transitions. Simulation results quantifying these gains in the context of shortest path routing are presented. In addition, DIVs universal applicability is illustrated by studying its use with a routing that operates according to a nonshortest path objective. Specifically, the routing seeks robustness against failures by maximizing the number of next-hops available at each node for each destination.

Distributed path computation without transient loops: an intermediate variables approach

Paths with loops, even transient ones, pose significant stability problems in networks. As a result, much effort has been devoted over the past thirty years to designing distributed algorithms capable of avoiding loops. We present a new algorithm, Distributed Path Computation with Intermediate Variables (DIV), that guarantees that no loops, transient or steady-state, can ever form. DIVs novelty is in that it is not restricted to shortest paths, can easily handle arbitrary sequences of changes and updates, and provably outperforms earlier approaches in several key metrics. In addition, when used with distance-vector style path computation algorithms, DIV also prevents counting-to-infinity; hence further improving convergence. The paper introduces DIV and its key properties. Simulation quantifying its performance gains are also presented.

Optimizing location detection services in wireless sensor networks

We propose a systematic framework for placing a given number of clusterheads in a hierarchical wireless sensor network to facilitate location detection service. The problem of location detection is posed as a hypothesis testing problem over a discretized space. Then, the clusterheads are placed in locations that maximize the worst case Chernoff distance between the conditional densities over all location pairs. Linear integer programming is used to determine the optimal placement. The resultant placement provides an asymptotic guarantee on the probability of error in location detection under quite general conditions. We obtain numerical results on the scalability of our proposed mathematical programming, and quantify the performance of the location detection system with the resultant clusterhead placement by simulation. Numerical and simulation results show that our proposed framework is computationally feasible and the resultant clusterhead placement performs near-optimum even with a small number of observation samples.

Optimal On-demand Mobile Sensor Allocation

In many practical applications of sensor networks, the level of sensor coverage needed at different locations varies with time. Pre-computation of sensor deployment in such cases is inadequate; on-the-fly redistribution of nodes in the network, as the system evolves, becomes necessary. Reallocation of sensors consumes resources (e.g., energy). Thus it is desirable to do so while minimizing a global metric of cost. The contribution of this paper is a distributed sensor reallocation algorithm superior to existing algorithms that computes the set of sensor movement that satisfies the demand of sensors at each part of the network, if it is at all feasible, while optimizing a given metric of interest, such as the total distance traveled. In general such discrete problems are NP-hard. However, the proposed algorithm is polynomial-time computable as it exploits a special structure of the problem. We numerically establish its superiority over previous algorithms.

SAMPLER: An Optimal MAC Algorithm for Wireless Instrumentation Systems

Wireless devices provide flexible solutions for industrial instrumentation applications, such as quality control of manufacture of jet engines. In this context, the dominant issues are providing high-throughput, and reliability in the sense of not losing samples due to buffer overflow at the wireless devices. A random medium access control (MAC) scheme, such as the IEEE 802.15.4, is unlikely to perform well along those metrics. CSMA/CA, the foundation of IEEE 802.15.4, is inefficient at the high-throughput regime. The polling mode of IEEE 802.15.4, on the other hand, ignores the buffer constraints, thereby increasing the risk of buffer overflow. In this paper, we propose SAMPLER, a scheduled MAC protocol that is optimal, in the sense of minimizing sample losses while maximizing throughput, in the typical scenario where a sophisticated access point forms a star topology with the wireless sensors. We describe SAMPLER, its properties and demonstrate its superior performance compared to random-access MAC through simulations.

Polynomial-Time Optimal Distributed Algorithm for Dynamic Allocation of Discrete Resources

Today a growing number of applications that operate in dynamic environments use distributed systems. Often, one or more constrained resources need to be allocated across such systems. In addition, for a number of important applications, the resources to be allocated are discrete quantities and the demand profile is intrinsically location and time dependent (thus pre-computating the resource allocation problem off-line is inadequate). We model such systems using graphs - vertices representing the sites and edges capturing locality - where each vertex is associated with the a pair of (integer) numbers representing the current and the required level of a resource. We seek on-the-fly reallocation of resources that satisfy the demand at each node, if it is feasible to do so, while minimizing a given metric of interest, such as the total distance traveled, maximum disruption time, etc. Due to integrality constraints, one expects such a problem to be NP-hard. However, we show that the matrix representing constraints of the problem satisfies the Total Unimodularity property and hence the problem is solvable in polynomial time. We propose a distributed algorithm that employs only local communications. We characterize the proposed algorithm and by numerical performance evaluation, show that it significantly outperforms known heuristic algorithms.