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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
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 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
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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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 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 ..."
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Cited by 3 (0 self)
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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
An Improved WorstCase to AverageCase Connection for Lattice Problems (extended abstract)
 In FOCS
, 1997
"... We improve a connection of the worstcase complexity and the averagecase complexity of some wellknown lattice problems. This fascinating connection was first discovered by Ajtai [1] in 1996. We improve the exponent of this connection from 8 to 3:5 + ffl. Department of Computer Science, State Unive ..."
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Cited by 57 (10 self)
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We improve a connection of the worstcase complexity and the averagecase complexity of some wellknown lattice problems. This fascinating connection was first discovered by Ajtai [1] in 1996. We improve the exponent of this connection from 8 to 3:5 + ffl. Department of Computer Science, State
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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of the complications in previous work. Our technical contributions are twofold. First, we show tight connections between this new parameter and existing lattice parameters. One such important connection is between this parameter and the length of the shortest set of linearly independent vectors. Second, we prove
WorstCase Vs. Algorithmic AverageCase Complexity in the PolynomialTime Hierarchy
 In Proceedings of the 10th International Workshop on Randomization and Computation, RANDOM 2006
, 2006
"... We show that for every integer k> 1, if Σk, the k’th level of the polynomialtime hierarchy, is worstcase hard for probabilistic polynomialtime algorithms, then there is a language L ∈ Σk such that for every probabilistic polynomialtime algorithm that attempts to decide it, there is a samplabl ..."
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Cited by 2 (1 self)
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We show that for every integer k> 1, if Σk, the k’th level of the polynomialtime hierarchy, is worstcase hard for probabilistic polynomialtime algorithms, then there is a language L ∈ Σk such that for every probabilistic polynomialtime algorithm that attempts to decide it, there is a
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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result. While the relation between worstcase and averagecase complexity for general NP problems remains open, there has been progress in understanding the relation between different “degrees ” of averagecase complexity. We discuss some of these “hardness amplification ” results. 1
Q : Worstcase Fair Weighted Fair Queueing
"... The Generalized Processor Sharing (GPS) discipline is proven to have two desirable properties: (a) it can provide an endtoend boundeddelay service to a session whose traffic is constrained by a leaky bucket; (b) it can ensure fair allocation of bandwidth among all backlogged sessions regardless o ..."
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Cited by 361 (11 self)
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The Generalized Processor Sharing (GPS) discipline is proven to have two desirable properties: (a) it can provide an endtoend boundeddelay service to a session whose traffic is constrained by a leaky bucket; (b) it can ensure fair allocation of bandwidth among all backlogged sessions regardless of whether or not their traffic is constrained. The former property is the basis for supporting guaranteed service traffic while the later property is important for supporting besteffort service traffic. Since GPS uses an idealized fluid model which cannot be realized in the real world, various packet approximation algorithms of GPS have been proposed. Among these, Weighted Fair Queueing (WFQ) also known as Packet Generalized Processor Sharing (PGPS) has been considered to be the best one in terms of accuracy. In particular, it has been proven that the delay bound provided by WFQ is within one packet transmission time of that provided by GPS. In this paper, we will show that, contrary to pop...
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