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NP IS AS EASY AS DETECTING UNIQUE SOLUTIONS
, 1986
"... For every known NPcomplete problem, the number of solutions of its instances varies over a large range, from zero to exponentially many. It is therefore natural to ask if the inherent intractability of NPcomplete problems is caused by this wide variation. We give a negative answer to this questi ..."
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Cited by 233 (1 self)
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to this question using the notion of randomized polynomial time reducibility. We show that the problems of distinguishing between instances of SAT having zero or one solution, or of finding solutions to instances of SAT having a unique solution, are as hard as SAT, under randomized reductions. Several corollaries
Corrigendum to “unique solutions
 Mathematical Logic Quarterly
, 2007
"... Work in progress started during a Feodor Lynen Research ..."
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Cited by 2 (0 self)
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Work in progress started during a Feodor Lynen Research
Entrepreneurship: Unique Solutions for Unique Environments
, 2006
"... Background Paper to the Plenary Presentation to the ..."
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Cited by 2 (0 self)
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Background Paper to the Plenary Presentation to the
The Nash Bargaining Solution in Economic Modeling
 Rand Journal of Economics
, 1986
"... This article establishes the relationship between the static axiomatic theory of bargaining and the sequential strategic approach to bargaining. We consider two strategic models of alternating offers. The models differ in the source of the incentive of the bargaining parties to reach agreement: the ..."
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Cited by 563 (1 self)
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: the bargainers ' time preference and the risk of breakdown of negotiation. Each of the models has a unique perfect equilibrium. When the motivation to reach agreement is made negligible, in each model the unique perfect equilibrium outcome approaches the Nash bargaining solution, with utilities that reflect
THE UNIQUE SOLUTION OF THE INVERSE DIFFRACTION PROBLEM
, 1979
"... The problem of the determination of the values of a field on a surface from its values on a surface to which it has propagated is shown to have a unique solution if the field satisfies any linear elliptic partial differential equation. Suppose that a scalar field ~ is the solution of a linear second ..."
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Cited by 1 (0 self)
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The problem of the determination of the values of a field on a surface from its values on a surface to which it has propagated is shown to have a unique solution if the field satisfies any linear elliptic partial differential equation. Suppose that a scalar field ~ is the solution of a linear
The Probability of Unique Solutions of Sequencing by Hybridization
, 1996
"... We determine the asymptotic limiting probability as m !1 that a random string of length m over some alphabet \Sigma can be determined uniquely by its substrings of length `. This is an abstraction of a problem faced when trying to sequence DNA clones by SBH. Research done while visiting Carnegie M ..."
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Cited by 31 (1 self)
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We determine the asymptotic limiting probability as m !1 that a random string of length m over some alphabet \Sigma can be determined uniquely by its substrings of length `. This is an abstraction of a problem faced when trying to sequence DNA clones by SBH. Research done while visiting Carnegie
A note on the unique solution of linear complementarity problem
, 2016
"... Abstract: In this note, the unique solution of the linear complementarity problem (LCP) is further discussed. Using the absolute value equations, some new results are obtained to guarantee the unique solution of the LCP for any real vector. ..."
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Abstract: In this note, the unique solution of the linear complementarity problem (LCP) is further discussed. Using the absolute value equations, some new results are obtained to guarantee the unique solution of the LCP for any real vector.
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 568 (10 self)
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that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y having a representation y = Φα0 by a coefficient vector α0 ∈ R m with fewer than ρ · n nonzeros, the solution α1 of the ℓ 1 minimization problem min �x�1 subject to Φα = y is unique and equal to α0
USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
, 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
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Cited by 1399 (16 self)
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The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking
Results 1  10
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16,240