ITo motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately log n= log log n with high probability. Now suppose instead that the balls are placed sequentially, and each ball is placed in the least loaded of d 2 bins chosen independently and uniformly at random. Azar, Broder, Karlin, and Upfal showed that in this case, the maximum load is log log n= log d + (1) with high probability [ABKU99]. The important implication of this result is that even a small amount of choice can lead to drastically different results in load balancing. Indeed, having just two random choices (i.e.,...

Efficient routing among a set of mobile hosts is one of the most important functions in ad hoc wireless networks. Routing based on a connected dominating set is a promising approach, where the search space for a route is reduced to the hosts in the set. A set is dominating if all the hosts in the system are either in the set or neighbors of hosts in the set. The efficiency of dominating-setbased routing mainly depends on the overhead introduced in the formation of the dominating set and the size of the dominating set. In this paper, we first review a localized formation of a connected dominating set called marking process and dominating-set-based routing. Then, we propose a dominant pruning rule to reduce the size of the dominating set. This dominant pruning rule (called Rule k) is a generalization of two existing rules (called Rule 1 and Rule 2, respectively). We prove that the vertex set derived by applying Rule k is still a connected dominating set. Rule k is more effective in reducing the dominating set derived from the marking process than the combination of Rules 1 and 2 and, surprisingly, in a restricted implementation with local neighborhood information, Rule k has the same communication complexity and less computation complexity. Simulation results confirm that Rule k outperforms Rules 1 and 2, especially in networks with relatively high vertex degree and high percentage of unidirectional links. We also prove that an upper bound exists on the average size of the dominating set derived from Rule k in its restricted implementation.

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Interference avoidance has been shown to reduce total square correlation (TSC) for given ensembles of user signature waveforms (codewords) in a synchronous CDMA system. In all experiments we have conducted, sequential application of interference avoidance produces an optimal codeword set when starting from randomly chosen initial codewords. Here we provide the rst formal proof of convergence to optimal codeword ensembles for greedy interference avoidance algorithms augmented by a technique called \class warfare" whereby users which reside in more heavily loaded areas of the signal space purposely interfere with (attack) the reception of users in less crowded areas. Coordination of deliberate interference by a complete class of aggrieved user is also sometimes necessary. Such \attacks" and subsequent codeword adjustment by attacked users are shown to strictly decrease TSC. Along the way we also show, using linear algebra and a variant of stochastic ordering, equivalence between minimiz...

This paper studies alternative ways to manage a multi-server system such as a telephone call center. Three alternatives can be described succinctly by: (i) blocking, (ii) reneging and (iii) balk-ing. The first alternative – blocking – is to have no provision for waiting. The second alternative is to allow waiting, but neither inform customers about anticipated delays nor provide state infor-mation to allow arriving customers to predict delays. The second alternative tends to yield higher server utilizations. The first alternative tends to reduce to the second, without the first-come first-served service discipline, when customers can easily retry, as with automatic redialers in telephone access. The third alternative is to both allow waiting and inform customers about anticipated delays. The third alternative tends to cause balking when all servers are busy (abandonment upon arrival) instead of reneging (abandonment after waiting). Birth-and-death process models are pro-posed to describe the performance with each alternative. Algorithms are developed to compute the conditional distributions of the time to receive service and the time to renege given each outcome. Algorithms are also developed to help the service provider predict customer waiting times before beginning service, given estimated service-time distributions and the elapsed service times of the customers in service. Better predictions may be obtained by classifying customers and thereby obtaining better estimates of their service-time distributions.

Abstract — When dealing with massive quantities of data, topk queries are a powerful technique for returning only the k most relevant tuples for inspection, based on a scoring function. The problem of efficiently answering such ranking queries has been studied and analyzed extensively within traditional database settings. The importance of the top-k is perhaps even greater in probabilistic databases, where a relation can encode exponentially many possible worlds. There have been several recent attempts to propose definitions and algorithms for ranking queries over probabilistic data. However, these all lack many of the intuitive properties of a top-k over deterministic data. Specifically, we define a number of fundamental properties, including exact-k, containment, unique-rank, value-invariance, and stability, which are all satisfied by ranking queries on certain data. We argue that all these conditions should also be fulfilled by any reasonable definition for ranking uncertain data. Unfortunately, none of the existing definitions is able to achieve this. To remedy this shortcoming, this work proposes an intuitive new approach of expected rank. This uses the well-founded notion of the expected rank of each tuple across all possible worlds as the basis of the ranking. We are able to prove that, in contrast to all existing approaches, the expected rank satisfies all the required properties for a ranking query. We provide efficient solutions to compute this ranking across the major models of uncertain data, such as attribute-level and tuple-level uncertainty. For an uncertain relation of N tuples, the processing cost is O(N log N)—no worse than simply sorting the relation. In settings where there is a high cost for generating each tuple in turn, we provide pruning techniques based on probabilistic tail bounds that can terminate the search early and guarantee that the top-k has been found. Finally, a comprehensive experimental study confirms the effectiveness of our approach. I.

The work reported here lays the foundations of data exchange in the presence of probabilistic data. This requires rethinking the very basic concepts of traditional data exchange, such as solution, universal solution, and the certain answers of target queries. We develop a framework for data exchange over probabilistic databases, and make a case for its coherence and robustness. This framework applies to arbitrary schema mappings, and finite or countably infinite probability spaces on the source and target instances. After establishing this framework and formulating the key concepts, we study the application of the framework to a concrete and practical setting where probabilistic databases are compactly encoded by means of annotations formulated over random Boolean variables. In this setting, we study the problems of testing for the existence of solutions and universal solutions, materializing such solutions, and evaluating target queries (for unions of conjunctive queries) in both the exact sense and the approximate sense. For each of the problems, we carry out a complexity analysis based on properties of the annotation, in various classes of dependencies. Finally, we show that the framework and results easily and completely generalize to allow not only the data, but also the schema mapping itself to be probabilistic.

In most practical cases, it is impossible to find an explicit expression for the distribution function of the present value of a sequence of cashflows that are discounted using a stochastic return process. In this article, the authors

We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteriesby meansof a set of von Neumann–Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a welldefined sense.

We investigate in this work the asymptotic behavior of isotropic diffusions in random environment that are small perturbations of Brownian motion. When the space dimension is three or more, we prove an invariance principle as well as transience. Our methods also apply to questions of homogenization in random media.