2979288
Transformations for write-all-with-collision model,
Dependable properties such as self-stabilization are crucial requirements in sensor networks. One way to achieve these properties is to utilize the vast literature on distributed systems where such self-stabilizing algorithms have been designed. Since these existing algorithms are designed in read/write model (or variations thereof), they cannot be directly applied in sensor networks. For this reason, we consider a new atomicity model, write all with collision (WAC), that captures the computations of sensor networks and focus on transformations from read/write model to WAC model and vice versa. We show that the transformation from WAC model to read/write model is stabilization preserving, and the transformation from read/write model to WAC model is stabilization preserving for timed systems. In the transformation from read/write model to WAC model, if the system is untimed (asynchronous) and processes are deterministic then under reasonable assumptions, we show that (1) the resulting program in WAC model can allow at most one process to execute, and (2) the resulting program in WAC model cannot be stabilizing.
11497337
Secret instantiation in ad-hoc networks
Abstract In this paper, we focus our attention on the problem of assigning initial secrets to users in ad-hoc network (respectively, sensors in a sensor network) so that they can use those secrets to ensure authentication and privacy during their communication. The goal of this assignment is to ensure that any two users can communicate securely with each other even though each user maintains only a small number of secrets. With this motivation, we present a protocol that maintains O ( n ) secrets per user where n is the number of users in the system. We show that our secret distribution protocol suffices for privacy and authentication as well as secure multihop communication between two users. Furthermore, we show that the number of secrets maintained in this protocol is within a constant factor of the optimal. For the case where user capability prevents them from maintaining the necessary secrets, we propose two probabilistic protocols that maintain O(log n) secrets and where the probability of security compromise between two users is inversely proportional to the number of secrets they maintain. Thus, our protocols provide a continuum where the level of privacy and authentication depends upon user requirements and capabilities.
12287966
Complexity issues in automated synthesis of failsafe fault-tolerance
We focus on the problem of synthesizing failsafe fault-tolerance where fault-tolerance is added to an existing (fault-intolerant) program. A failsafe fault-tolerant program satisfies its specification (including safety and liveness) in the absence of faults. However, in the presence of faults, it satisfies its safety specification. We present a somewhat unexpected result that, in general, the problem of synthesizing failsafe fault-tolerant distributed programs from their fault-intolerant version is NP-complete in the state space of the program. We also identify a class of specifications, monotonic specifications, and a class of programs, monotonic programs, for which the synthesis of failsafe fault-tolerance can be done in polynomial time (in program state space). As an illustration, we show that the monotonicity restrictions are met for commonly encountered problems, such as Byzantine agreement, distributed consensus, and atomic commitment. Furthermore, we evaluate the role of these restrictions in the complexity of synthesizing failsafe fault-tolerance. Specifically, we prove that if only one of these conditions is satisfied, the synthesis of failsafe fault-tolerance is still NP-complete. Finally, we demonstrate the application of monotonicity property in enhancing the fault-tolerance of (distributed) nonmasking fault-tolerant programs to masking.
52887342
Low-cost fault-tolerance in barrier synchronizations
We show how fault-tolerance can be effectively added to several types of faults in program computations that use barrier synchronization. We divide the faults that occur in practice into two classes, detectable and undetectable, and design a fully distributed program that tolerates the faults in both classes. Our program guarantees that every barrier is executed correctly even if detectable faults occur, and that eventually every barrier is executed correctly even if undetectable faults occur. Via analytical as well as simulation results we show that the cost of adding fault-tolerance is low, in part by comparing the times required by our program with that required by the corresponding fault-intolerant counterpart.
37856387
Collision-Free Communication in Sensor Networks
In this paper, we provide a stabilizing solution for collision-free diffusion in sensor networks. Such diffusions are often necessary in sensor networks when information from one sensor needs to be communicated to other sensors that satisfy certain geographic properties. Our solution deals with several difficulties, e.g., unidirectional links, unreliable links, long links, failed sensors, and sensors that are sleeping in order to save energy, that occur in sensor networks. It also ensures that there are no collisions during the diffusion and that the time required for the diffusion is O(D) where D is the diameter of the network. Moreover, while the solution can be applied to an arbitrary topology, it is more suitable for a commonly occurring topology, a two-dimensional grid. 
 
We show how our solution for collision-free diffusion can be used for time-division multiplexing (TDM) in sensor networks. TDM ensures that the message communication (other than the messages sent by diffusion) among sensors is also collision-free. While collision-free diffusion and time-division multiplexing are interdependent, we show how both these properties can be achieved simultaneously. Our algorithms are stabilizing fault-tolerant, i.e., collision-free diffusion and time-division multiplexing are restored even if the system reaches an arbitrary state where the sensors are corrupted or improperly initialized.
6279302
A line in the sand: a wireless sensor network for target detection, classification, and tracking
Intrusion detection is a surveillance problem of practical import that is well suited to wireless sensor networks. In this paper, we study the application of sensor networks to the intrusion detection problem and the related problems of classifying and tracking targets. Our approach is based on a dense, distributed, wireless network of multi-modal resource-poor sensors combined into loosely coherent sensor arrays that perform in situ detection, estimation, compression, and exfiltration. We ground our study in the context of a security scenario called "A Line in the Sand" and accordingly define the target, system, environment, and fault models. Based on the performance requirements of the scenario and the sensing, communication, energy, and computation ability of the sensor network, we explore the design space of sensors, signal processing algorithms, communications, networking, and middleware services. We introduce the influence field, which can be estimated from a network of binary sensors, as the basis for a novel classifier. A contribution of our work is that we do not assume a reliable network; on the contrary, we quantitatively analyze the effects of network unreliability on application performance. Our work includes multiple experimental deployments of over 90 sensor nodes at MacDill Air Force Base in Tampa, FL, as well as other field experiments of comparable scale. Based on these experiences, we identify a set of key lessons and articulate a few of the challenges facing extreme scaling to tens or hundreds of thousands of sensor nodes.
14885154
On-line learning of functions of bounded variation under various sampling schemes
We consider the problem of learning of an arbitrary function selected from the non-smooth class of functions that are of bounded variation. Bounds on the prediction errors resulting from sequential type algorithms are achieved for various scenarios. It is shown that for any algorithm there exists a sequence of samples and a function that results in a unit error at each step. If the samples are i.i.d. uniform then there exists an algorithm such that for any function of bounded variation the expected error is less than O(log n/n). Furthermore, for any algorithm there exists a function such that the expected error is greater than 0(1/n). We then introduce a mixed sampling setting in which an adversary can choose points but the actual samples are drawn uniformly from a 6 neighborhood of his selection. We show that there exists an algorithm such that for any function of bounded variation and for any sequence of adversarychosen points the expected cumulative error is less than 0(+ log n). Finally, results are derived for the uniform sampling case with noisy observations. We show that the order of growth of the expected error with noise sequences in Z1 remains unaltered. However, for i.i.d. zero mean and finite variance noise there exists an algorithm with expected error less than 0(1/n*), and for i.i.d. Gaussian noise any algorithm has expected error of at least o(l/@). Permission to copy without fee all or part of this material is granted provided that the copies ars not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying IS by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. ACM COLT ’93 171931CA, USA @ 1993 Acfvf 0.89791-61 ~-5/93 /o(307/0439... $1 .50
2812660
Local Versus Non-local Computation of Length of Digitized Curves
We consider the problem of computing the length of a curve from digitized versions of the curve using parallel computation. Our aim is to study the inherent parallel computational complexity of this problem as a function of the digitization level. Precise formulations for the digitization, the parallel computation, and notions of local and nonlocal computations are given. We show that length cannot be computed locally from digitizations on rectangular tessellations. However, for a random tessellation and appropriate deterministic ones, we show that the length of straight line segments can be computed locally.
1329510
Noise Conditions for Prespecified Convergence Rates of Stochastic Approximation Algorithms
We develop deterministic necessary and sufficient conditions on individual noise sequences of a stochastic approximation algorithm for the error of the iterates to converge at a given rate. Specifically, suppose {/spl rho//sub n/} is a given positive sequence converging monotonically to zero. Consider a stochastic approximation algorithm x/sub n+1/=x/sub n/-a/sub n/(A/sub n/x/sub n/-b/sub n/)+a/sub n/e/sub n/, where {x/sub n/} is the iterate sequence, {a/sub n/} is the step size sequence, {e/sub n/} is the noise sequence, and x* is the desired zero of the function f(x)=Ax-b. Then, under appropriate assumptions, we show that x/sub n/-x*=o(/spl rho//sub n/) if and only if the sequence {e/sub n/} satisfies one of five equivalent conditions. These conditions are based on well-known formulas for noise sequences: Kushner and Clark's (1978) condition, Chen's (see Proc. IFAC World Congr., p.375-80, 1996) condition, Kulkarni and Horn's (see IEEE Trails Automat. Contr., vol.41, p.419-24, 1996) condition, a decomposition condition, and a weighted averaging condition. Our necessary and sufficient condition on {e/sub n/} to achieve a convergence rate of {/spl rho//sub n/} is basically that the sequence {e/sub n///spl rho//sub n/} satisfies any one of the above five well-known conditions. We provide examples to illustrate our result. In particular, we easily recover the familiar result that if a/sub n/=a/n and {e/sub n/} is a martingale difference process with bounded variance, then x/sub n/-x*=o(n/sup -1/2/(log(n))/sup /spl beta//) for any /spl beta/>1/2.
13800701
A metric entropy bound is not sufficient for learnability
The authors prove by means of a counterexample that it is not sufficient, for probably approximately correct (PAC) learning under a class of distributions, to have a uniform bound on the metric entropy of the class of concepts to be learned. This settles a conjecture of Benedek and Itai (1991). >
7606261
Rates of convergence of nearest neighbor estimation under arbitrary sampling
Rates of convergence for nearest neighbor estimation are established in a general framework in terms of metric covering numbers of the underlying space. The first result is to find explicit finite sample upper bounds for the classical independent and identically distributed (i.i.d.) random sampling problem in a separable metric space setting. The convergence rate is a function of the covering numbers of the support of the distribution. For example, for bounded subsets of R/sup r/, the convergence rate is O(1/n/sup 2/r/). The main result is to extend the problem to allow samples drawn from a completely arbitrary random process in a separable metric space and to examine the performance in terms of the individual sample sequences. The authors show that for every sequence of samples the asymptotic time-average of nearest neighbor risks equals twice the time-average of the conditional Bayes risks of the sequence. Finite sample upper bounds under arbitrary sampling are again obtained in terms of the covering numbers of the underlying space. In particular, for bounded subsets of R/sup r/ the convergence rate of the time-averaged risk is O(1/n/sup 2/r/). The authors then establish a consistency result for k/sub n/-nearest neighbor estimation under arbitrary sampling and prove a convergence rate matching established rates for i.i.d. sampling. Finally, they show how their arbitrary sampling results lead to some classical i.i.d. sampling results and in fact extend them to stationary sampling. The framework and results are quite general while the proof techniques are surprisingly elementary. >