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AverageCase Intractability vs. WorstCase Intractability
 IN THE 23RD INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
, 1998
"... We use the assumption that all sets in NP (or other levels of the polynomialtime hierarchy) have efficient averagecase algorithms to derive collapse consequences for MA, AM, and various subclasses of P/poly. As a further consequence we show for C 2 fP(PP);PSPACEg that C is not tractable in the a ..."
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Cited by 3 (1 self)
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We use the assumption that all sets in NP (or other levels of the polynomialtime hierarchy) have efficient averagecase algorithms to derive collapse consequences for MA, AM, and various subclasses of P/poly. As a further consequence we show for C 2 fP(PP);PSPACEg that C is not tractable
Worstcase equilibria
 IN PROCEEDINGS OF THE 16TH ANNUAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
, 1999
"... In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a ver ..."
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Cited by 851 (17 self)
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In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a
On WorstCase to AverageCase Reductions for NP Problems
 IN PROCEEDINGS OF THE 44TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 2003
"... We show that if an NPcomplete problem has a nonadaptive selfcorrector with respect to a samplable distribution then coNP is contained in AM/poly and the polynomial hierarchy collapses to the third level. Feigenbaum and Fortnow show the same conclusion under the stronger assumption that an NPcompl ..."
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Cited by 61 (6 self)
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complete problem has a nonadaptive random selfreduction. Our result
WorstCase to AverageCase Reductions Revisited
"... Abstract. A fundamental goal of computational complexity (and foundations of cryptography) is to find a polynomialtime samplable distribution (e.g., the uniform distribution) and a language in NTIME(f(n)) for some polynomial function f, such that the language is hard on the average with respect to ..."
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Cited by 5 (0 self)
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to this distribution, given that NP is worstcase hard (i.e. NP ̸ = P, or NP ̸ ⊆ BPP). Currently, no such result is known even if we relax the language to be in nondeterministic subexponential time. There has been a long line of research trying to explain our failure in proving such worstcase/averagecase
On WorstCase to AverageCase Reductions for NP Problems
"... 1. Introduction WorstCase versus AverageCase Complexity A problem in distributional NP [18] is a pair (L, D)where ..."
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1. Introduction WorstCase versus AverageCase Complexity A problem in distributional NP [18] is a pair (L, D)where
WorstCase to AverageCase Reductions for Module Lattices
"... Abstract. Most latticebased cryptographic schemes are built upon the assumed hardness of the Short Integer Solution (SIS) and Learning With Errors (LWE) problems. Their efficiencies can be drastically improved by switching the hardness assumptions to the more compact RingSIS and RingLWE problems. ..."
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Cited by 7 (1 self)
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lattices (which themselves generalize arbitrary and ideal lattices). As these new problems enlarge the toolbox of the latticebased cryptographer, they could prove useful for designing new schemes. Importantly, the worstcase to averagecase reductions for the module problems are (qualitatively) sharp
Worstcase to averagecase reductions based on Gaussian measures
 SIAM J. on Computing
, 2004
"... We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost linear in the dimension of the lattice. The lattice problems we consider are the shortest vector problem, the shortest indepe ..."
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Cited by 128 (23 self)
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We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost linear in the dimension of the lattice. The lattice problems we consider are the shortest vector problem, the shortest
A WorstCase to AverageCase Connection for CVP
"... We prove a connection of the worstcase complexity and the averagecase complexity for the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP for lattices under a certain natural distribution, at least with ..."
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We prove a connection of the worstcase complexity and the averagecase complexity for the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP for lattices under a certain natural distribution, at least
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
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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is of particular interest and that do not yet fit into this theory. A major open question is whether the existence of hardonaverage problems in NP can be based on the P ̸ = NP assumption or on related worstcase assumptions. We review negative results showing that certain proof techniques cannot prove such a
Results 1  10
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1,466,507