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On the Theory of Average Case Complexity
 Journal of Computer and System Sciences
, 1997
"... This paper takes the next step in developing the theory of average case complexity initiated by Leonid A Levin. Previous works [Levin 84, Gurevich 87, Venkatesan and Levin 88] have focused on the existence of complete problems. We widen the scope to other basic questions in computational complexity. ..."
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Cited by 121 (6 self)
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This paper takes the next step in developing the theory of average case complexity initiated by Leonid A Levin. Previous works [Levin 84, Gurevich 87, Venkatesan and Levin 88] have focused on the existence of complete problems. We widen the scope to other basic questions in computational complexity
Average Case Completeness
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1991
"... We explain and advance Levin's theory of average case completeness. In particular, we exhibit examples of problems complete in the average case and prove a limitation on the power of deterministic reductions. ..."
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Cited by 75 (2 self)
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We explain and advance Levin's theory of average case completeness. In particular, we exhibit examples of problems complete in the average case and prove a limitation on the power of deterministic reductions.
Average Case Complexity ∗
"... Abstract. We attempt to motivate, justify and survey the average case reduction theory. 1. ..."
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Abstract. We attempt to motivate, justify and survey the average case reduction theory. 1.
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 238 (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
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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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 easyonaverage
AverageCase Complexity of Shellsort
, 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 any incremental sequence is Ω(pn 1+1/p) for every p. The proof method is an incompressibility argument based on Kolmogorov complexity. U ..."
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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 any incremental sequence is Ω(pn 1+1/p) for every p. The proof method is an incompressibility argument based on Kolmogorov complexity
Average Case Complexity, Revisited
"... Abstract. More than two decades elapsed since Levin set forth a theory of averagecase complexity. In this survey we present the basic aspects of this theory as well as some of the main results regarding it. The current presentation deviates from our old “Notes on Levin’s Theory of AverageCase Comp ..."
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Abstract. More than two decades elapsed since Levin set forth a theory of averagecase complexity. In this survey we present the basic aspects of this theory as well as some of the main results regarding it. The current presentation deviates from our old “Notes on Levin’s Theory of AverageCase
A publickey cryptosystem with worstcase/averagecase equivalence
, 1997
"... Abstract We present a probabilistic public key cryptosystem which is secure unless the worst case of the following lattice problem can be solved in polynomial time: "Find the shortest nonzero vector in an n dimensional lattice L where the shortest vector v is unique in the sense that any ot ..."
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Cited by 246 (5 self)
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Abstract We present a probabilistic public key cryptosystem which is secure unless the worst case of the following lattice problem can be solved in polynomial time: "Find the shortest nonzero vector in an n dimensional lattice L where the shortest vector v is unique in the sense that any
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
On Averagecase Complexity of Ray
"... A theoretical framework for analyzing averagecase time and storage complexity of ray tracing acceleration techniques is introduced by means of homogeneous spatial Poisson point processes. Then, as a demonstrative example of its application, the expected query time of the widely known technique u ..."
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A theoretical framework for analyzing averagecase time and storage complexity of ray tracing acceleration techniques is introduced by means of homogeneous spatial Poisson point processes. Then, as a demonstrative example of its application, the expected query time of the widely known technique
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