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605,818
On the AverageCase Hardness of CVP
 In FOCS
, 2001
"... We prove a connection of the worstcase complexity to the averagecase complexity based on the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP, with a nontrivial success probability, for lattices under a c ..."
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Cited by 4 (0 self)
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We prove a connection of the worstcase complexity to the averagecase complexity based on the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP, with a nontrivial success probability, for lattices under a
Averagecase Hardness
"... Traditionally, lattices were used as tools in cryptanalysis, that is, as tools in breaking cryptographic schemes. We have seen an example of such an application in a previous lecture. In 1996, Ajtai made a surprising discovery: lattices can be used to construct cryptographic schemes [1]. His seminal ..."
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are based on some averagecase assumptions. For example, in cryptographic constructions based on factoring, the assumption is that it is hard to factor numbers chosen from a certain distribution. But how should we choose this distribution? Obviously, we should not use numbers with small factors (such
AverageCase Complexity
 in Foundations and Trends in Theoretical Computer Science Volume 2, Issue 1
, 2006
"... We survey the averagecase complexity of problems in NP. We discuss various notions of goodonaverage algorithms, and present completeness results due to Impagliazzo and Levin. Such completeness results establish the fact that if a certain specific (but somewhat artificial) NP problem is easyonav ..."
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Cited by 25 (0 self)
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with respect to the uniform distribution, then all problems in NP are easyonaverage with respect to all samplable distributions. Applying the theory to natural distributional problems remain an outstanding open question. We review some natural distributional problems whose averagecase complexity
Junta distributions and the averagecase complexity of manipulating elections
 In AAMAS
, 2006
"... Encouraging voters to truthfully reveal their preferences in an election has long been an important issue. Recently, computational complexity has been suggested as a means of precluding strategic behavior. Previous studies have shown that some voting protocols are hard to manipulate, but used N Pha ..."
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Cited by 110 (24 self)
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as the complexity measure. Such a worstcase analysis may be an insufficient guarantee of resistance to manipulation. Indeed, we demonstrate that N Phard manipulations may be tractable in the averagecase. For this purpose, we augment the existing theory of averagecase complexity with some new concepts
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 681 (1 self)
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It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard
The averagecase complexity of Shellsort
 LECTURE NOTES IN COMPUTER SCIENCE 1644
, 1999
"... We prove a general lower bound on the averagecase complexity of Shellsort: the average number of datamovements (and comparisons) made by a ppass Shellsort for 1 1+ any incremental sequence is Ω(pn p) for all p ≤ log n. Using similar arguments, we analyze the averagecase complexity of several oth ..."
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Cited by 6 (2 self)
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We prove a general lower bound on the averagecase complexity of Shellsort: the average number of datamovements (and comparisons) made by a ppass Shellsort for 1 1+ any incremental sequence is Ω(pn p) for all p ≤ log n. Using similar arguments, we analyze the averagecase complexity of several
WorstCase Optimal and AverageCase Efficient Geometric AdHoc Routing
, 2003
"... In this paper we present GOAFR, a new geometric adhoc routing algorithm combining greedy and face routing. We evaluate this algorithm by both rigorous analysis and comprehensive simulation. GOAFR is the first adhoc algorithm to be both asymptotically optimal and averagecase e#cient. For our simul ..."
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Cited by 245 (11 self)
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In this paper we present GOAFR, a new geometric adhoc routing algorithm combining greedy and face routing. We evaluate this algorithm by both rigorous analysis and comprehensive simulation. GOAFR is the first adhoc algorithm to be both asymptotically optimal and averagecase e#cient. For our
DISTRIBUTED SYSTEMS
, 1985
"... Growth of distributed systems has attained unstoppable momentum. If we better understood how to think about, analyze, and design distributed systems, we could direct their implementation with more confidence. ..."
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Cited by 755 (1 self)
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Growth of distributed systems has attained unstoppable momentum. If we better understood how to think about, analyze, and design distributed systems, we could direct their implementation with more confidence.
Powerlaw distributions in empirical data
 ISSN 00361445. doi: 10.1137/ 070710111. URL http://dx.doi.org/10.1137/070710111
, 2009
"... Powerlaw distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and manmade phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the t ..."
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Cited by 589 (7 self)
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demonstrate these methods by applying them to twentyfour realworld data sets from a range of different disciplines. Each of the data sets has been conjectured previously to follow a powerlaw distribution. In some cases we find these conjectures to be consistent with the data while in others the power law
Results 1  10
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605,818