9782780
A paradigm for class identification problems
The following problem arises in many applications involving classification, identification, and inference. There is a set of objects X, and a particular x /spl isin/ X is chosen (unknown to us). Based on information obtained about x in a sequential manner, one wishes to decide whether x belongs to one class of objects A/sub 0/ or a different class of objects A/sub 1/. The authors study a general paradigm applicable to a broad range of problems of this type, which they refer to as problems of class identification or discernibility. They consider various types of information sequences, and various success criteria including discernibility in the limit, discernibility with a stopping criterion, uniform discernibility, and discernibility in the Cesaro sense. They consider decision rules both with and without memory. Necessary and sufficient conditions for discernibility are provided for each case in terms of separability conditions on the sets A/sub 0/ and A/sub 1/. They then show that for any sets A/sub 0/ and A/sub 1/, various types of separability can be achieved by allowing failure on appropriate sets of small measure. Applications to problems in language identification, system identification, and discrete geometry are discussed. >
15102047
Separation of random number generation and resolvability
We consider the problem of determining when a given source can be used to approximate the output due to any input to a given channel. We provide achievability and converse results for a general source and channel. For the special case of a full-rank discrete memoryless channel we give a stronger converse result than we can give for a general channel.
11400186
On probably correct classification of concepts
We consider the problem of classifying an unknown concept into one of two subclasses of concepts. Specifically, if C is a concept class and Co and Cl are two disjoint subsets of C, given an unknown c E Co U Cl we wish to decide whether c c Co or c E Cl based on a set of random examples. We consider both uniform and non-uniform probably correct classification for which the number of samples is or is not required to be independent of c, respectively. For both cases, we obtain necessary and sufficient conditions on Co and Cl that allow probably correct classification. The conditions obtained are in terms of separability and/or coverability conditions on the classes Co and Cl. Furthermore, in the non-uniform case we show that this is equivalent to classification in the limit. Several examples of the applicability of our results are also provided.
1752947
Learning decision rules for pattern classification under a family of probability measures
In this paper, uniformly consistent estimation (learnability) of decision rules for pattern classification under a family of probability measures is investigated. In particular, it is shown that uniform boundedness of the metric entropy of the class of decision rules is both necessary and sufficient for learnability under each of two conditions: (i) the family of probability measures is totally bounded, with respect to the total variation metric, and (ii) the family of probability measures contains an interior point, when equipped with the same metric. In particular, this shows that insofar as uniform consistency is concerned, when the family of distributions contains a total variation neighborhood, nothing is gained by this knowledge about the distribution. Then two sufficient conditions for learnability are presented. Specifically, it is shown that learnability with respect to each of a finite collection of families of probability measures implies learnability with respect to their union; also, learnability with respect to each of a finite number of measures implies learnability with respect to the convex hull of the corresponding families of uniformly absolutely continuous probability measures.
2125855
A deterministic approach to throughput scaling in wireless networks
We address the problem of how throughput in a wireless network scales as the number of users grows. Following the model of Gupta and Kumar, we consider n identical nodes placed in a fixed area. Pairs of transmitters and receivers wish to communicate but are subject to interference from other nodes. Throughput is measured in bit-meters per second. We provide a very elementary deterministic approach that gives achievability results in terms of three key properties of the node locations. As a special case, we obtain /spl Omega/(/spl radic/n) throughput for a general class of network configurations in a fixed area. Results for random node locations in a fixed area can also be derived as special cases of the general result by verifying the growth rate of three parameters. For example, as a simple corollary of our result we obtain a stronger (almost sure) version of the /spl radic/n//spl radic/(logn) throughput for random node locations in a fixed area obtained by Gupta and Kumar. Results for some other interesting non-independent and identically distributed (i.i.d.) node distributions are also provided.
6063474
PAC learning with generalized samples and an application to stochastic geometry
In this paper, we introduce an extension of the standard PAC learning model which allows the use of generalized samples. We view a generalized sample as a pair consisting of a functional on the concept class together with the value obtained by the functional operating on the unknown concept. It appears that this model can be applied to a number of problems in signal processing and geometric reconstruction to provide sample size bounds under a PAC criterion. We consider a specific application of the model to a problem of curve reconstruction, and discuss some connections with a result from stochastic geometry.
6871855
The complexity of adding failsafe fault-tolerance
In this paper, we focus our attention on the problem of automating the addition of 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. And, in the presence of faults, it satisfies its safety specification. We present a somewhat unexpected result that, in general, the problem of adding failsafe fault-tolerance in distributed programs is NP-hard. Towards this end, we reduce the 3-SAT problem to the problem of adding failsafe fault-tolerance. We also identify a class of specifications, monotonic specifications and a class of programs, monotonic programs. Given a (positive) monotonic specification and a (negative) monotonic program, we show that failsafe fault-tolerance can be added in polynomial time. We note that the monotonicity restrictions are met for commonly encountered problems such as Byzantine agreement, distributed consensus, and atomic commitment. Finally, we argue that the restrictions on the specifications and programs are necessary to add failsafe fault-tolerance in polynomial time; we prove that if only one of these conditions is satisfied, the addition of failsafe fault-tolerance is still NP-hard.
14751317
Reducing the cost of the critical path in secure multicast for dynamic groups
In this paper we focus on the problem of secure multicast in dynamic groups. In this problem, a group of users communicate using a shared key. Due to the dynamic nature of these groups, to preserve secrecy, it is necessary to change the group key whenever the group membership changes. While the group key, is being changed, the group communication needs to be interrupted until the rekeying is complete. This interruption is especially necessary if the rekeying is done because a user has left (or is removed). We split the rekeying cost into two parts: the cost of the critical path-where each user receives the new group key, and the cost of the non-critical path-where each user receives any other keys that it needs to obtain. We present two algorithms that show the trade off between the cost of the critical path and the cost of the non-critical path. We also compare our algorithms to previous algorithms and show that our algorithms reduce the cost of the critical path while keeping the total cost manageable.
33040079
Resettable vector clocks
Vector clocks (VC) are an inherent component of a rich class of distributed applications. In this paper, we first consider the problem of realistic implementation-more specifically, bounded-space and fault-tolerant-of applications that use vector clocks (VC). To this end, we generalize the notion of VC to resettable vector clocks (RVC), and provide a realistic implementation of RVC. Further, we identify an interface contract under which our RVC implementation can be substituted for VC in client applications, without affecting the client's correctness. This interface contract is designed for phase-based applications that provide certain communication guarantees. Based on such substitution and the use of the interface contract, we show how to transform the client so that it is itself realistically implemented. We illustrate our method in the context of Ricart-Agrawala's mutual exclusion program and Garg-Chase's predicate detection program.
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.
8636414
A Case Study on Prototyping Power Management Protocols for Sensor Networks
Power management is an important problem in battery powered sensor networks as the sensors are required to operate for a long time (usually, several weeks to several months). One of the challenges in developing power management protocols for sensor networks is prototyping. Specifically, existing programming platforms for sensor networks (e.g., nesC/TinyOS) use an event-driven programming model and, hence, require the designers to be responsible for stack management, buffer management, flow control, etc. Therefore, the designers simplify prototyping their solutions either by implementing their own discrete event simulators or by modeling them in specialized simulators. To enable the designers to prototype power management protocols in target platform (e.g., nesC/TinyOS), in this paper, we use ProSe, a programming tool for sensor networks. ProSe enables the designers to specify their programs in simple abstract models while hiding low-level challenges of sensor networks and programming-level challenges. As a case study, in this paper, we specify a power management protocol with ProSe, automatically generate the corresponding nesC/TinyOS code, and evaluate its performance. Based on the performance results, we expect that ProSe enables the designers to rapidly prototype, quickly deploy, and easily evaluate their protocols.