Results 1  10
of
427,985
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 ..."
Abstract

Cited by 851 (17 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 245 (11 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 61 (6 self)
 Add to MetaCart
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 NPcomplete problem has a nonadaptive random selfreduction. Our result
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 ..."
Abstract
 Add to MetaCart
1. Introduction WorstCase versus AverageCase Complexity A problem in distributional NP [18] is a pair (L, D)where
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 ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
connections. While we can not do that unconditionally, we are able to show that under a mild derandomization assumption, the worstcase hardness of NP implies the averagecase hardness of NTIME(f(n)) (under the uniform distribution) where f is computable in quasipolynomial time. 1
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. ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
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 Running Times for AverageCase Algorithms
"... Abstract—Under a standard hardness assumption we exactly characterize the worstcase running time of languages that are in average polynomialtime over all polynomialtime samplable distributions. More precisely we show that if exponential time is not infinitely often in subexponential space, then t ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract—Under a standard hardness assumption we exactly characterize the worstcase running time of languages that are in average polynomialtime over all polynomialtime samplable distributions. More precisely we show that if exponential time is not infinitely often in subexponential space
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 ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
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 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 ..."
Abstract

Cited by 128 (23 self)
 Add to MetaCart
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
Query Complexity: WorstCase Quantum Versus AverageCase Classical
, 2008
"... In this note we investigate the relationship between worstcase quantum query complexity and averagecase classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean ..."
Abstract
 Add to MetaCart
In this note we investigate the relationship between worstcase quantum query complexity and averagecase classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean
Results 1  10
of
427,985