Results 1  10
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35
On MemoryBound Functions for Fighting Spam
 In Crypto
, 2002
"... In 1992, Dwork and Naor proposed that email messages be accompanied by easytocheck proofs of computational effort in order to discourage junk email, now known as spam. They proposed specific CPUbound functions for this purpose. Burrows suggested that, since memory access speeds vary across ma ..."
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Cited by 82 (2 self)
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In 1992, Dwork and Naor proposed that email messages be accompanied by easytocheck proofs of computational effort in order to discourage junk email, now known as spam. They proposed specific CPUbound functions for this purpose. Burrows suggested that, since memory access speeds vary across machines much less than do CPU speeds, memorybound functions may behave more equitably than CPUbound functions; this approach was first explored by Abadi, Burrows, Manasse, and Wobber [8].
Lower bounds for high dimensional nearest neighbor search and related problems
, 1999
"... In spite of extensive and continuing research, for various geometric search problems (such as nearest neighbor search), the best algorithms known have performance that degrades exponentially in the dimension. This phenomenon is sometimes called the curse of dimensionality. Recent results [38, 37, 40 ..."
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Cited by 47 (2 self)
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In spite of extensive and continuing research, for various geometric search problems (such as nearest neighbor search), the best algorithms known have performance that degrades exponentially in the dimension. This phenomenon is sometimes called the curse of dimensionality. Recent results [38, 37, 40] show that in some sense it is possible to avoid the curse of dimensionality for the approximate nearest neighbor search problem. But must the exact nearest neighbor search problem suffer this curse? We provide some evidence in support of the curse. Specifically we investigate the exact nearest neighbor search problem and the related problem of exact partial match within the asymmetric communication model first used by Miltersen [43] to study data structure problems. We derive nontrivial asymptotic lower bounds for the exact problem that stand in contrast to known algorithms for approximate nearest neighbor search. 1
SuperLinear TimeSpace Tradeoff Lower Bounds for Randomized Computation
, 2000
"... We prove the first timespace lower bound tradeoffs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are an extension of those used by Ajtai [Ajt99a, ..."
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Cited by 33 (0 self)
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We prove the first timespace lower bound tradeoffs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are an extension of those used by Ajtai [Ajt99a, Ajt99b] in his timespace tradeoffs for deterministic RAM algorithms computing element distinctness and for Boolean branching programs computing a natural quadratic form. Ajtai's bounds were of the following form...
Cell probe complexity  a survey
 In 19th Conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 1999. Advances in Data Structures Workshop
"... The cell probe model is a general, combinatorial model of data structures. We give a survey of known results about the cell probe complexity of static and dynamic data structure problems, with an emphasis on techniques for proving lower bounds. 1 ..."
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Cited by 29 (0 self)
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The cell probe model is a general, combinatorial model of data structures. We give a survey of known results about the cell probe complexity of static and dynamic data structure problems, with an emphasis on techniques for proving lower bounds. 1
TimeSpace Tradeoff Lower Bounds for Randomized Computation of Decision Problems
 In Proc. of 41st FOCS
, 2000
"... We prove the first timespace lower bound tradeoffs for randomized computation of decision problems. ..."
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Cited by 28 (2 self)
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We prove the first timespace lower bound tradeoffs for randomized computation of decision problems.
TimeSpace Lower Bounds for Satisfiability
 JACM
, 2005
"... We establish the first polynomial timespace lower bounds for satisfiability on general models of computation. We show that for any constant c less than the golden ratio there exists a positive constant d such that no deterministic randomaccess Turing machine can solve satisfiability in time n c an ..."
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Cited by 25 (7 self)
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We establish the first polynomial timespace lower bounds for satisfiability on general models of computation. We show that for any constant c less than the golden ratio there exists a positive constant d such that no deterministic randomaccess Turing machine can solve satisfiability in time n c and space n d, where d approaches 1 when c does. On conondeterministic instead of deterministic machines, we prove the same for any constant c less than √ 2. Our lower bounds apply to nondeterministic linear time and almost all natural NPcomplete problems known. In fact, they even apply to the class of languages that can be solved on a nondeterministic machine in linear time and space n 1/c. Our proofs follow the paradigm of indirect diagonalization. We also use that paradigm to prove timespace lower bounds for languages higher up in the polynomialtime hierarchy.
TimeSpace Tradeoffs, Multiparty Communication Complexity, and NearestNeighbor Problems
 In 34th Symp. on Theory of Computing (STOC’02
, 2002
"... We extend recent techniques for timespace tradeoff lower bounds using multiparty communication complexity ideas. Using these arguments, for inputs from large domains we prove larger tradeoff lower bounds than previously known for general branching programs, yielding time lower bounds of the form T ..."
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Cited by 19 (1 self)
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We extend recent techniques for timespace tradeoff lower bounds using multiparty communication complexity ideas. Using these arguments, for inputs from large domains we prove larger tradeoff lower bounds than previously known for general branching programs, yielding time lower bounds of the form T = n) when space S = n , up from T = n log n) for the best previous results. We also prove the first unrestricted separation of the power of general and oblivious branching programs by proving that 1GAP , which is trivial on general branching programs, has a timespace tradeoff of the form T = (n=S)) on oblivious Finally, using timespace tradeoffs for branching programs, we improve the lower bounds on query time of data structures for nearest neighbor problems in d dimensions from d= log n), proved in the cellprobe model [8, 5], to d) or log d= log log d) or even d log d) (depending on the metric space involved) in slightly less general but more reasonable data structure models.
TimeSpace Tradeoffs in the Counting Hierarchy
, 2001
"... We extend the lower bound techniques of [14], to the unboundederror probabilistic model. A key step in the argument is a generalization of Nepomnjasci's theorem from the Boolean setting to the arithmetic setting. This generalization is made possible, due to the recent discovery of logspaceuniform ..."
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Cited by 19 (4 self)
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We extend the lower bound techniques of [14], to the unboundederror probabilistic model. A key step in the argument is a generalization of Nepomnjasci's theorem from the Boolean setting to the arithmetic setting. This generalization is made possible, due to the recent discovery of logspaceuniform TC 0 circuits for iterated multiplication [9]. Here is an
On the number of zeropatterns of a sequence of polynomials
 Journal of the AMS
, 2002
"... Let f =(f1,...,fm) be a sequence of polynomials of degree ≤ d in n variables (m ≥ n) overafieldF. The zeropattern of f at u ∈ F n is the set of those i (1 ≤ i ≤ m) forwhichfi(u) =0. LetZF (f) denote the number of zeropatterns of f as u ranges over F n.WeprovethatZF (f) ≤ �n � � m j=0 j for d =1a ..."
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Cited by 15 (0 self)
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Let f =(f1,...,fm) be a sequence of polynomials of degree ≤ d in n variables (m ≥ n) overafieldF. The zeropattern of f at u ∈ F n is the set of those i (1 ≤ i ≤ m) forwhichfi(u) =0. LetZF (f) denote the number of zeropatterns of f as u ranges over F n.WeprovethatZF (f) ≤ �n � � m j=0 j for d =1and md
Amplifying lower bounds by means of selfreducibility
 In IEEE Conference on Computational Complexity
, 2008
"... We observe that many important computational problems in NC 1 share a simple selfreducibility property. We then show that, for any problem A having this selfreducibility property, A has polynomial size TC 0 circuits if and only if it has TC 0 circuits of size n 1+ɛ for every ɛ>0 (counting the numb ..."
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Cited by 13 (4 self)
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We observe that many important computational problems in NC 1 share a simple selfreducibility property. We then show that, for any problem A having this selfreducibility property, A has polynomial size TC 0 circuits if and only if it has TC 0 circuits of size n 1+ɛ for every ɛ>0 (counting the number of wires in a circuit as the size of the circuit). As an example of what this observation yields, consider the Boolean Formula Evaluation problem (BFE), which is complete for NC 1 and has the selfreducibility property. It follows from a lower bound of Impagliazzo, Paturi, and Saks, that BFE requires depth d TC 0 circuits of size n 1+ɛd. If one were able to improve this lower bound to show that there is some constant ɛ>0 such that every TC 0 circuit family recognizing BFE has size n 1+ɛ, then it would follow that TC 0 ̸ = NC 1. We show that proving lower bounds of the form n 1+ɛ is not ruled out by the Natural Proof framework of Razborov and Rudich and hence there is currently no known barrier for separating classes such as ACC 0,TC 0 and NC 1 via existing “natural ” approaches to proving circuit lower bounds. We also show that problems with small uniform constantdepth circuits have algorithms that simultaneously have small space and time bounds. We then make use of known timespace tradeoff lower bounds to show that SAT requires uniform depth d TC 0 and AC 0 [6] circuits of size n 1+c for some constant c depending on d. 1