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32
Mining Generalized Association Rules
, 1995
"... We introduce the problem of mining generalized association rules. Given a large database of transactions, where each transaction consists of a set of items, and a taxonomy (isa hierarchy) on the items, we find associations between items at any level of the taxonomy. For example, given a taxonomy th ..."
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Cited by 447 (7 self)
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We introduce the problem of mining generalized association rules. Given a large database of transactions, where each transaction consists of a set of items, and a taxonomy (isa hierarchy) on the items, we find associations between items at any level of the taxonomy. For example, given a taxonomy that says that jackets isa outerwear isa clothes, we may infer a rule that "people who buy outerwear tend to buy shoes". This rule may hold even if rules that "people who buy jackets tend to buy shoes", and "people who buy clothes tend to buy shoes" do not hold. An obvious solution to the problem is to add all ancestors of each item in a transaction to the transaction, and then run any of the algorithms for mining association rules on these "extended transactions ". However, this "Basic" algorithm is not very fast; we present two algorithms, Cumulate and EstMerge, which run 2 to 5 times faster than Basic (and more than 100 times faster on one reallife dataset). We also present a new interes...
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 99 (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.,...
Parallel Randomized Load Balancing
 In Symposium on Theory of Computing. ACM
, 1995
"... It is well known that after placing n balls independently and uniformly at random into n bins, the fullest bin holds \Theta(log n= log log n) balls with high probability. Recently, Azar et al. analyzed the following: randomly choose d bins for each ball, and then sequentially place each ball in the ..."
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Cited by 56 (8 self)
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It is well known that after placing n balls independently and uniformly at random into n bins, the fullest bin holds \Theta(log n= log log n) balls with high probability. Recently, Azar et al. analyzed the following: randomly choose d bins for each ball, and then sequentially place each ball in the least full of its chosen bins [2]. They show that the fullest bin contains only log log n= log d + \Theta(1) balls with high probability. We explore extensions of this result to parallel and distributed settings. Our results focus on the tradeoff between the amount of communication and the final load. Given r rounds of communication, we provide lower bounds on the maximum load of \Omega\Gamma r p log n= log log n) for a wide class of strategies. Our results extend to the case where the number of rounds is allowed to grow with n. We then demonstrate parallelizations of the sequential strategy presented in Azar et al. that achieve loads within a constant factor of the lower bound for two ...
Evolutionary Algorithms  How to Cope With Plateaus of Constant Fitness and When to Reject Strings of The Same Fitness
, 2000
"... The most simple evolutionary algorithm, the socalled (1+1)EA accepts a child if its fitness is at least as large (in the case of maximization) as the fitness of its parent. The variant (1 + 1) # EA only accepts a child if its fitness is strictly larger than the fitness of its parent. Here two funct ..."
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Cited by 47 (14 self)
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The most simple evolutionary algorithm, the socalled (1+1)EA accepts a child if its fitness is at least as large (in the case of maximization) as the fitness of its parent. The variant (1 + 1) # EA only accepts a child if its fitness is strictly larger than the fitness of its parent. Here two functions related to the class of long path functions are presented such that the (1 + 1)EA maximizes one of it in polynomial time and needs exponential time for the other while the (1+1) # EA has the opposite behavior. These results prove that small changes of an evolutionary algorithm may change its behavior significantly. Since the (1 + 1)EA and the (1 + 1) # EA di#er only on plateaus of constant fitness, the results also show how evolutionary algorithms behave on such plateaus. The (1 + 1)EA can pass a path of constant fitness and polynomial length in polynomial time. Finally, for these functions it is shown that local performance measures like the quality gain and the progress rate do not de...
On learning monotone DNF under product distributions
 In Proceedings of the Fourteenth Annual Conference on Computational Learning Theory
, 2001
"... We show that the class of monotone 2 O( √ log n)term DNF formulae can be PAC learned in polynomial time under the uniform distribution from random examples only. This is an exponential improvement over the best previous polynomialtime algorithms in this model, which could learn monotone o(log 2 n) ..."
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Cited by 32 (15 self)
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We show that the class of monotone 2 O( √ log n)term DNF formulae can be PAC learned in polynomial time under the uniform distribution from random examples only. This is an exponential improvement over the best previous polynomialtime algorithms in this model, which could learn monotone o(log 2 n)term DNF. We also show that various classes of small constantdepth circuits which compute monotone functions are PAC learnable in polynomial time under the uniform distribution. All of our results extend to learning under any constantbounded product distribution.
Optimization with Randomized Search Heuristics  The (A)NFL Theorem, Realistic Scenarios, and Difficult Functions
 THEORETICAL COMPUTER SCIENCE
, 1997
"... The No Free Lunch (NFL) theorem due to Wolpert and Macready (1997) has led to controversial discussions on the usefulness of randomized search heuristics, in particular, evolutionary algorithms. Here a short and simple proof of the NFL theorem is given to show its elementary character. Moreover, the ..."
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Cited by 31 (1 self)
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The No Free Lunch (NFL) theorem due to Wolpert and Macready (1997) has led to controversial discussions on the usefulness of randomized search heuristics, in particular, evolutionary algorithms. Here a short and simple proof of the NFL theorem is given to show its elementary character. Moreover, the proof method leads to a generalization of the NFL theorem. Afterwards, realistic complexity theoretical based scenarios for black box optimization are presented and it is argued why NFL theorems are not possible in such situations. However, an Almost No Free Lunch (ANFL) theorem shows that for each function which can be optimized efficiently by a search heuristic there can be constructed many related functions where the same heuristic is bad. As a consequence, search heuristics use some idea how to look for good points and can be successful only for functions "giving the right hints". The consequences of these theoretical considerations for some wellknown classes of functions are discussed.
Randomized Robot Navigation Algorithms
, 1996
"... We consider the problem faced by a mobile robot that has to reach a given target by traveling through an unmapped region in the plane containing oriented rectangular obstacles. We assume the robot has no prior knowledge about the positions or sizes of the obstacles, and acquires such knowledge only ..."
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Cited by 30 (0 self)
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We consider the problem faced by a mobile robot that has to reach a given target by traveling through an unmapped region in the plane containing oriented rectangular obstacles. We assume the robot has no prior knowledge about the positions or sizes of the obstacles, and acquires such knowledge only when obstacles are encountered. Our goal is to minimize the distance the robot must travel, using the competitive ratio as our measure. We give a new randomized algorithm...
Dynamic Parameter Control in Simple Evolutionary Algorithms
, 2000
"... Evolutionary algorithms are general, randomized search heuristics that are influenced by many parameters. Though evolutionary algorithms are assumed to be robust, it is wellknown that choosing the parameters appropriately is crucial for success and efficiency of the search. It has been shown in man ..."
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Cited by 20 (7 self)
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Evolutionary algorithms are general, randomized search heuristics that are influenced by many parameters. Though evolutionary algorithms are assumed to be robust, it is wellknown that choosing the parameters appropriately is crucial for success and efficiency of the search. It has been shown in many experiments, that nonstatic parameter settings can be by far superior to static ones but theoretical verifications are hard to find. We investigate a very simple evolutionary algorithm and rigorously prove that employing dynamic parameter control can greatly speedup optimization.
On the choice of the mutation probability for the (1+1) EA
 PROC. OF PPSN VI (PARALLEL PROBLEM SOLVING FROM NATURE), LNCS
, 2000
"... When evolutionary algorithms are used for function optimization, they perform a heuristic search that is influenced by many parameters. Here, the choice of the mutation probability is investigated. It is shown for a nontrivial example function that the most recommended choice for the mutation prob ..."
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Cited by 17 (12 self)
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When evolutionary algorithms are used for function optimization, they perform a heuristic search that is influenced by many parameters. Here, the choice of the mutation probability is investigated. It is shown for a nontrivial example function that the most recommended choice for the mutation probability 1/n is by far not optimal, i. e., it leads to a superpolynomial running time while another choice of the mutation probability leads to a search algorithm with expected polynomial running time. Furthermore, a simple evolutionary algorithm with an extremely simple dynamic mutation probability scheme is suggested to overcome the difficulty of finding a proper setting for the mutation probability.