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TIGHT BOUNDS FOR BLIND SEARCH ON THE INTEGERS
, 2008
"... We analyze a simple random process in which a token is moved in the interval A = {0,..., n}: Fix a probability distribution µ over {1,..., n}. Initially, the token is placed in a random position in A. In round t, a random value d is chosen according to µ. If the token is in position a ≥ d, then it ..."
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Cited by 3 (1 self)
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, then it is moved to position a − d. Otherwise it stays put. Let T be the number of rounds until the token reaches position 0. We show tight bounds for the expectation of T for the optimal distribution µ. More precisely, we show that minµ{Eµ(T)} = Θ ` (log n) 2 ´. For the proof, a novel potential function argument
Tight Bounds for Blind Search on the Integers and the Reals
, 2010
"... We analyse a simple random process in which a token is moved in the interval A = {0,..., n}. Fix a probability distribution µ over D = {1,...,n}. Initially, the token is placed in a random position in A. In round t, a random step size d is chosen according to µ. If the token is in position x � d, ..."
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, then it is moved to position x − d. Otherwise it stays put. Let TX be the number of rounds until the token reaches position 0. We show tight bounds for the expectation Eµ(TX) of TX for varying distributions µ. More precisely, we show that minµ{Eµ(TX)} =Θ ( (log n) 2). The same bounds are proved for the analogous
The Omega Test: a fast and practical integer programming algorithm for dependence analysis
 Communications of the ACM
, 1992
"... The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method ..."
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Cited by 521 (15 self)
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The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method of last resort for si:8 ti ns that cannot be deci:A by si[976 methods. We present evi[77B that suggests thiwi sdomi s wrong, and that the Omega testi s competi ti ve wi th approxi mate algori thms usedi n practi ce and sui table for usei n producti on compi lers. Experi ments suggest that, for almost all programs, the average ti me requi red by the Omega test to determi ne the di recti on vectors for an array pai ri s less than 500 secs on a 12 MIPS workstati on. The Omega testi based on an extensi n of Four i0Motzki var i ble eli937 ti n (aliB: r programmiA method) toi nteger programmi ng, and has worstcase exponenti al ti me complexi ty. However, we show that for manysiB7 ti ns i whi h ...
Blind Signal Separation: Statistical Principles
, 2003
"... Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mut ..."
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Cited by 522 (4 self)
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Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption
A Fast Quantum Mechanical Algorithm for Database Search
 ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1996
"... Imagine a phone directory containing N names arranged in completely random order. In order to find someone's phone number with a probability of , any classical algorithm (whether deterministic or probabilistic)
will need to look at a minimum of names. Quantum mechanical systems can be in a supe ..."
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Cited by 1126 (10 self)
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Imagine a phone directory containing N names arranged in completely random order. In order to find someone's phone number with a probability of , any classical algorithm (whether deterministic or probabilistic)
will need to look at a minimum of names. Quantum mechanical systems can be in a superposition of states and simultaneously examine multiple names. By properly adjusting the phases of various operations, successful computations reinforce each other while others interfere randomly. As a result, the desired phone number can be obtained in only steps. The algorithm is within a small constant factor of the fastest possible quantum mechanical algorithm.
A Limited Memory Algorithm for Bound Constrained Optimization
 SIAM Journal on Scientific Computing
, 1994
"... An algorithm for solving large nonlinear optimization problems with simple bounds is described. ..."
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Cited by 557 (9 self)
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An algorithm for solving large nonlinear optimization problems with simple bounds is described.
Mtree: An Efficient Access Method for Similarity Search in Metric Spaces
, 1997
"... A new access meth d, called Mtree, is proposed to organize and search large data sets from a generic "metric space", i.e. whE4 object proximity is only defined by a distance function satisfyingth positivity, symmetry, and triangle inequality postulates. We detail algorith[ for insertion o ..."
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Cited by 652 (38 self)
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A new access meth d, called Mtree, is proposed to organize and search large data sets from a generic "metric space", i.e. whE4 object proximity is only defined by a distance function satisfyingth positivity, symmetry, and triangle inequality postulates. We detail algorith[ for insertion
Suffix arrays: A new method for online string searches
, 1991
"... A new and conceptually simple data structure, called a suffix array, for online string searches is introduced in this paper. Constructing and querying suffix arrays is reduced to a sort and search paradigm that employs novel algorithms. The main advantage of suffix arrays over suffix trees is that ..."
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Cited by 827 (0 self)
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A new and conceptually simple data structure, called a suffix array, for online string searches is introduced in this paper. Constructing and querying suffix arrays is reduced to a sort and search paradigm that employs novel algorithms. The main advantage of suffix arrays over suffix trees
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