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245
Capacity bounds via duality with applications to multipleantenna systems on flatfading channels
 IEEE Trans. Inform. Theory
, 2003
"... A general technique is proposed for the derivation of upper bounds on channel capacity. The technique is based on a dual expression for channel capacity where the maximization (of mutual information) over distributions on the channel input alphabet is replaced with a minimization (of average relativ ..."
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Cited by 101 (36 self)
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A general technique is proposed for the derivation of upper bounds on channel capacity. The technique is based on a dual expression for channel capacity where the maximization (of mutual information) over distributions on the channel input alphabet is replaced with a minimization (of average relative entropy) over distributions on the channel output alphabet. Every choice of an output distribution — even if not the channel image of some input distribution — leads to an upper bound on mutual information. The proposed approach is used in order to study multiantenna flat fading channels with memory where the realization of the fading process is unknown at the transmitter and unknown (or only partially known) at the receiver. It is demonstrated that, for high signaltonoise ratio (SNR), the capacity of such channels typically grows only doublelogarithmically in the SNR. This is in stark contrast to the case with perfect receiver side information where capacity grows logarithmically in the SNR. To better understand this phenomenon
An extended localized algorithm for connected dominating set formation in ad hoc wireless networks
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 2004
"... 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 sy ..."
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Cited by 101 (14 self)
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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 dominatingsetbased 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 dominatingsetbased 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.
The Power of Two Random Choices: A Survey of Techniques and Results
 in Handbook of Randomized Computing
, 2000
"... 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 ..."
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Cited by 98 (2 self)
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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.,...
The Concept of Comonotonicity in Actuarial Science and Finance: Applications
 Mathematics & Economics
, 2002
"... In an insurance c o text,o ne isoB interested in thedistributio functio o a sum o rando variables. Such a sum appears when coBBthe aggregate claimso f an insurance po rtfo o ver a certain reference perio d. Italso appears when coBdisco ted payments related to a single po licyo a poBat di#erent futur ..."
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Cited by 82 (38 self)
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In an insurance c o text,o ne isoB interested in thedistributio functio o a sum o rando variables. Such a sum appears when coBBthe aggregate claimso f an insurance po rtfo o ver a certain reference perio d. Italso appears when coBdisco ted payments related to a single po licyo a poBat di#erent future po ints in time. Theassumptio o mutual independence between the coB oB ts o the sum is very co venient fro a coB po int o view, butsoB no a realistico ne. In The Concept of Comonotonicity in Actuarial Science and Finance: Theory, we determined appro ximatio fo sumso f rando variables, when thedistributio o f the coB oB ts are kno wn, but thesto chastic dependence structure between them isunkno wn oto o cumberso to wo rk with. Practical applicatio o f thistheo will becoBin this paper. o. papers are to a large extent ano verviewo recent research resultsos tained by theautho butalso newtheoBand practical results are presented. 1
CDMA Codeword Optimization: interference avoidance and convergence via class warfare
 IEEE Transactions on Information Theory
, 2001
"... 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 starti ..."
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Cited by 51 (16 self)
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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...
Semantics of ranking queries for probabilistic data and expected ranks
 In Proc. of ICDE’09
, 2009
"... 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 traditi ..."
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Cited by 42 (1 self)
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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 topk 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 topk over deterministic data. Specifically, we define a number of fundamental properties, including exactk, containment, uniquerank, valueinvariance, 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 wellfounded 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 attributelevel and tuplelevel 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 topk has been found. Finally, a comprehensive experimental study confirms the effectiveness of our approach. I.
Improving Service by Informing Customers about Anticipated Delays
 Management Science
, 1999
"... This paper studies alternative ways to manage a multiserver system such as a telephone call center. Three alternatives can be described succinctly by: (i) blocking, (ii) reneging and (iii) balking. The first alternative – blocking – is to have no provision for waiting. The second alternative is to ..."
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Cited by 38 (9 self)
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This paper studies alternative ways to manage a multiserver system such as a telephone call center. Three alternatives can be described succinctly by: (i) blocking, (ii) reneging and (iii) balking. 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 information 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 firstcome firstserved 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). Birthanddeath process models are proposed 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 servicetime 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 servicetime distributions.
Probabilistic data exchange
 In Proc. ICDT
, 2010
"... 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 ..."
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Cited by 28 (5 self)
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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.
The Theory of Assortative Matching Based on Costly Signals
 REVIEW OF ECONOMIC STUDIES
, 2009
"... We study twosided markets with a finite numbers of agents on each side, and with twosided incomplete information. Agents are matched assortatively on the basis of costly signals. Asymmetries in signaling activity between the two sides of the market can be explained either by asymmetries in size or ..."
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Cited by 27 (1 self)
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We study twosided markets with a finite numbers of agents on each side, and with twosided incomplete information. Agents are matched assortatively on the basis of costly signals. Asymmetries in signaling activity between the two sides of the market can be explained either by asymmetries in size or in heterogeneity. Our main results identify general conditions under which the potential increase in expected output due to assortative matching (relative to random matching) is o¤set by the costs of signaling. Finally, we look at the limit model with a continuum of agents, and point out differences and similarities to the finite version. Technically, the paper is based on the elegant theory about stochastic order relations among differences of order statistics, pioneered by R. Barlow and F. Proschan (1966) in the framework of reliability theory.
Expected Utility Theory without the Completeness Axiom,”Journal of Economic Theory, Volume 115, Issue 1
, 2004
"... 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 mul ..."
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Cited by 27 (5 self)
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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 multiutility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a welldefined sense.