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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
Tight bounds on quantum searching
, 1996
"... We provide a tight analysis of Grover’s algorithm for quantum database searching. We give a simple closedform formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine the number of iterations necessary to achieve almost certainty of f ..."
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Cited by 124 (9 self)
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We provide a tight analysis of Grover’s algorithm for quantum database searching. We give a simple closedform formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine the number of iterations necessary to achieve almost certainty
Locally Adaptive Dimensionality Reduction for Indexing Large Time Series Databases
 In proceedings of ACM SIGMOD Conference on Management of Data
, 2002
"... Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions' involve performing dimensionality reduction on the data, then indexing the reduced d ..."
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Cited by 316 (33 self)
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distance approximation, and a nonlower bounding, but very tight Euclidean distance approximation and show how they can support fast exact searchin& and even faster approximate searching on the same index structure. We theoretically and empirically compare APCA to all the other techniques
Coalition Structure Generation with Worst Case Guarantees
, 1999
"... Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition ..."
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Cited by 270 (9 self)
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necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time
Reverse Search for Enumeration
 Discrete Applied Mathematics
, 1993
"... The reverse search technique has been recently introduced by the authors for efficient enumeration of vertices of polyhedra and arrangements. In this paper, we develop this idea in a general framework and show its broader applications to various problems in operations research, combinatorics, and ..."
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Cited by 205 (26 self)
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connected induced subgraphs of a graph, and (vi) all topological orderings of an acyclic graph. Finally we propose a new algorithm for the 01 integer programming problem which can be considered as an alternative to the branchandbound algorithm. 1 Introduction The listing of all objects that satisfy
Arbitrarily Tight Bounds On The Distribution Of Smooth Integers
 Proceedings of the Millennial Conference on Number Theory
, 2002
"... This paper presents lower bounds and upper bounds on the distribution of smooth integers; builds an algebraic framework for the bounds; shows how the bounds can be computed at extremely high speed using FFTbased powerseries exponentiation; explains how one can choose the parameters to achieve ..."
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Cited by 7 (2 self)
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This paper presents lower bounds and upper bounds on the distribution of smooth integers; builds an algebraic framework for the bounds; shows how the bounds can be computed at extremely high speed using FFTbased powerseries exponentiation; explains how one can choose the parameters to achieve
Searching for Mobile Intruders in a Polygonal Region by a Group of Mobile Searchers
 SIAM JOURNAL ON COMPUTING
"... The problem of searching for mobile intruders in a polygonal region by mobile searchers is considered. A searcher can move continuously inside a polygon holding a flashlight that emits a single ray of light whose direction can be changed continuously. The visibility of a searcher at any time instant ..."
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Cited by 156 (3 self)
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+ blog 3 rc, and ps(P ) 2 + dlog 2 ge. These upper bounds are tight or almost tight in the worst case, since we show that for any natural number s 2, there is a polygon P such that ps(P ) = log 3 (n + 1) = log 3 (2r + 3) = 1 + log 3 (2g \Gamma 1) = s.
Combinatorial Geometry
, 1995
"... Abstract. Let P be a set of n points in ~d (where d is a small fixed positive integer), and let F be a collection of subsets of ~d, each of which is defined by a constant number of bounded degree polynomial inequalities. We consider the following Frange searching problem: Given P, build a data stru ..."
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Cited by 185 (24 self)
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Abstract. Let P be a set of n points in ~d (where d is a small fixed positive integer), and let F be a collection of subsets of ~d, each of which is defined by a constant number of bounded degree polynomial inequalities. We consider the following Frange searching problem: Given P, build a data
Searching the integers
"... 1 Problem Definition Consider an ordered universe U, and a set T ⊂ U with T  = n. The goal is to preprocess T, such that the following query can be answered efficiently: given x ∈ U, report the predecessor of x, i.e. max{y ∈ T  y < x}. One can also consider the dynamic problem, where elements ..."
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as examples. The problem was considered in many computational models. In fact, most models below were initially defined to study the predecessor problem. comparison model: The problem can be solved through binary search in Θ(lg n) comparisons. There is a lot of work on adaptive bounds, which may
Results 1  10
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