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Differential approximation of min sat, max sat and related problems

Bruno Escoffier, Vangelis Th. Paschos
2007 European Journal of Operational Research  
We present differential approximation results (both positive and negative) for optimal satisfiability, optimal constraint satisfaction, and some of the most popular restrictive versions of them.  ...  As an important corollary, we exhibit an interesting structural difference between the landscapes of approximability classes in standard and differential paradigms.  ...  Proposition 3 . 3 ([6]) MAX SAT ≡ AF MIN DNF and MIN SAT ≡ AF MAX DNF.  ... 
doi:10.1016/j.ejor.2005.04.057 fatcat:gww3n54a5zf6znhapqrck2i6ou

Constant factor approximation of MAX CLIQUE [article]

Tapani Toivonen, Janne Karttunen
2019 arXiv   pre-print
A 2-approximation algorithm for MIN SAT was presented in [6]. An approximation ratio preserving reduction from MIN SAT to min vertex cover improves the approximation ratio to 2 - Θ(1/ √(n)) [10].  ...  In this paper, we show that MCP can be approximated with a constant factor in polynomial time through approximation ratio preserving reductions from MCP to MAX DNF and from MAX DNF to MIN SAT.  ...  reductions from MCP to MAX DNF and from MAX DNF to MIN SAT and even further to min vertex cover.  ... 
arXiv:1909.04396v4 fatcat:ryvhsefr2jfslh2xcb3foyo6le

A Fast Approximation Algorithm for MIN-ONE SAT

Lei Fang, Michael S. Hsiao
2008 2008 Design, Automation and Test in Europe  
In this paper, we propose a novel approximation algorithm (Re-laxSAT) for MIN-ONE SAT. RelaxSAT generates a set of constraints from the objective function to guide the search.  ...  The constraints are gradually relaxed to eliminate the conflicts with the original Boolean SAT formula until a solution is found.  ...  Conclusions and Future Works In this paper, a novel approximation algorithm for MIN-ONE SAT is proposed.  ... 
doi:10.1109/date.2008.4484921 dblp:conf/date/FangH08 fatcat:66q2w7chfzbs5d4bcwivuadtmi

Reachability Deficits in Quantum Approximate Optimization [article]

V. Akshay, H. Philathong, M.E.S. Morales, J. Biamonte
2019 arXiv   pre-print
These findings are among the first to determine strong limitations on variational quantum approximate optimization.  ...  The quantum approximate optimization algorithm (QAOA) has rapidly become a cornerstone of contemporary quantum algorithm development.  ...  Figure 2 . 2 f = E QAOA g −min(HSAT ) vs clause density for 3-SAT (Top) and 2-SAT (Bottom) for QAOA with driver Hamiltonian, Hx = (|+ +|) ⊗n .  ... 
arXiv:1906.11259v2 fatcat:plms3qmixvbjppklghiiy3zglq

An 0.828-approximation algorithm for the uncapacitated facility location problem

A.A. Ageev, M.I. Sviridenko
1999 Discrete Applied Mathematics  
PII: S 0 1 6 6 -2 1 8 X ( 9 9 ) 0 0 1 0 3 -1  ...  We suggest a polynomial-time approximation algorithm for the unconstrained version of the problem, based on the idea of randomized rounding due to Goemans and Williamson (SIAM J.  ...  A 2( √ 2 − 1)-approximation algorithm for MAX SAT * In this section we present a 2( √ 2−1)-approximation algorithm for solving MAX SAT * .  ... 
doi:10.1016/s0166-218x(99)00103-1 fatcat:dyvubpflozeczjx2nrc4bflnym

A fast approximation algorithm for MIN-ONE SAT

Lei Fang, Michael S. Hsiao
2008 Proceedings of the conference on Design, automation and test in Europe - DATE '08  
In this paper, we propose a novel approximation algorithm (Re-laxSAT) for MIN-ONE SAT. RelaxSAT generates a set of constraints from the objective function to guide the search.  ...  The constraints are gradually relaxed to eliminate the conflicts with the original Boolean SAT formula until a solution is found.  ...  Conclusions and Future Works In this paper, a novel approximation algorithm for MIN-ONE SAT is proposed.  ... 
doi:10.1145/1403375.1403636 fatcat:ose3u7lmwrgzrosymkh5wqnkjq

The Sturm-Liouville eigenvalue problem and NP-complete problems in the quantum setting with queries [article]

A. Papageorgiou, H. Wozniakowski
2005 arXiv   pre-print
We are grateful for valuable comments and suggestions how to improve the presentation of the paper from Stefan Heinrich, Marek Kwas, Klaus Meer Joseph F. Traub and Mihalis Yannakakis.  ...  Acknowledgments This research has been supported in part by the National Science Foundation, the Defense Advanced Research Projects Agency, and the Air Force Research Laboratory.  ...  Hence, Min(x) ≤ x j ≤ y ≤ Min(x) + ε and x j is an ε-approximation that solves the minimization problem MIN 2 . We now formalize the idea of this algorithm. Let (1 − δ 1 ) 3 = 1 − δ.  ... 
arXiv:quant-ph/0504194v1 fatcat:ksu42crzgzdtbpz6ue7bx6tbmq

The Sturm-Liouville Eigenvalue Problem and NP-Complete Problems in the Quantum Setting with Queries

A. Papageorgiou, H. Woźniakowski
2006 Quantum Information Processing  
These algorithms use of order ε −1/3 bit queries or log ε −1 power queries and compute an ε-approximation of the smallest eigenvalue with probability 3 4 .  ...  Here, SAT stands for the satisfiability problem, TSP for the traveling salesman problem, MIN for the minimization problem of choosing the smallest number out of N real numbers, GRO for Grover's problem  ...  We are grateful for valuable comments and suggestions how to improve the presentation of the paper from Stefan Heinrich, Marek Kwas, Klaus Meer Joseph F. Traub and Mihalis Yannakakis.  ... 
doi:10.1007/s11128-006-0043-0 fatcat:ipbcw6iq2vhotn6ij3lrrjl3se

On the Complexity of Nash Equilibrium Reoptimization

Andrea Celli, Alberto Marchesi, Nicola Gatti
2017 Conference on Uncertainty in Artificial Intelligence  
In a reoptimization problem, we are given an instance, its optimal solution, and a local modification, and we are asked to find the exact or an approximate solution to the modified instance.  ...  Reoptimization is crucial whenever an instance needs to be solved repeatedly and, at each repetition, its parameters may slightly change.  ...  Exact solution Approximate solution Max/Min social welfare NP-hard 2 / ∈ Poly-APX 3 Max/Min player utility NP-hard 2 / ∈ Poly-APX 3 Max support NP-hard / ∈ Log-APX 3 Min support NP-hard / ∈ Log-APX 4 2  ... 
dblp:conf/uai/CelliMG17 fatcat:jdm5ymlykbemhcdq7kfftwmmne

Nontrapping Arrest of Langmuir Wave Damping near the Threshold Amplitude

A. V. Ivanov, Iver H. Cairns
2006 Physical Review Letters  
Arrest of linear damping is found to be a second-order effect due to ballistic evolution of perturbations, resonant power transfer between field and particles, and organization of phase space into a positive  ...  and starts to grow approximately exponentially before undergoing irregular oscillations in amplitude [2, 3] (Fig. 1 ).  ...  A sat at which the first exponential growth phase saturates [3] : e.g., t min ∝ (A 0 − A ⋆ 0 ) −τ min and A min ∝ (A 0 − A ⋆ 0 ) β min .  ... 
doi:10.1103/physrevlett.96.175001 pmid:16712306 fatcat:nqvcerokunacjlqxmukiyyl2ca

Solving minones-2-sat as Fast as vertex cover [chapter]

Neeldhara Misra, N. S. Narayanaswamy, Venkatesh Raman, Bal Sri Shankar
2010 Lecture Notes in Computer Science  
The problem of finding a satisfying assignment for a 2-SAT formula that minimizes the number of variables that are set to 1 (min ones 2-sat) is NP-complete.  ...  In this paper, we present a polynomial-time reduction from min ones 2-sat to vertex cover without increasing the parameter and ensuring that the number of vertices in the reduced instance is equal to the  ...  While chitting set has a k O(c) kernel [AK07], a polynomial sized kernel is unlikely for min ones c-sat even for c = 3, as a special case of min ones 3-sat (not-1-in-3 SAT) is unlikely to have a polynomial  ... 
doi:10.1007/978-3-642-15155-2_48 fatcat:n2gni3uyynhpdm5bccghhrgtl4

Approximating MAX SAT by moderately exponential and parameterized algorithms

Bruno Escoffier, Vangelis Th. Paschos, Emeric Tourniaire
2014 Theoretical Computer Science  
We study approximation of the max sat problem by moderately exponential algorithms.  ...  We develop several approximation techniques that can be applied to max sat in order to get approximation ratios arbitrarily close to 1.  ...  Let us only note that several subproblems of max sat and min sat are among the first complete problems for many approximability classes [1, 16] .  ... 
doi:10.1016/j.tcs.2014.10.039 fatcat:p4spt2lilzgb3kgxqwzbws3ncm

Approximability of Economic Equilibrium for Housing Markets with Duplicate Houses [chapter]

Katarína Cechlárová, Eva Jelínková
2011 Lecture Notes in Computer Science  
In this paper we give a 2-approximation algorithm for sat(M) in the case of trichotomic preferences.  ...  On the other hand, we prove that sat(M) is hard to approximate within a factor smaller than 21/19, even if each house type is used for at most two houses.  ...  Halldórsson and Vít Jelínek for helpful suggestions.  ... 
doi:10.1007/978-3-642-25870-1_10 fatcat:yztny4gtxrh3patni73dtnhv6y

The complexity of a minimum reload cost diameter problem

Giulia Galbiati
2008 Discrete Applied Mathematics  
within any constant α < 2 if the reload costs are unrestricted, and cannot be approximated within any constant β < 5/3 if the reload costs satisfy the triangle inequality.  ...  We consider the minimum diameter spanning tree problem under the reload cost model which has been introduced by Wirth and Steffan [H.-C. Wirth, J.  ...  Theorem 2. On graphs of maximum degree 4, MIN-DIAM is not approximable within any factor α < 2 and ∆-MIN-DIAM is not approximable within any factor β < 5/3, unless P = NP. Proof.  ... 
doi:10.1016/j.dam.2008.02.013 fatcat:556ahxr3brhk3f7z3ypa4bdaaq

Rapid diagnosis of pulmonary tuberculosis and detection of drug resistance by combined simultaneous amplification testing and reverse dot blot

Yiwen Chen, Lahong Zhang, Liquan Hong, Xian Luo, Juping Chen, Leiming Tang, Jiahuan Chen, Xia Liu, Zhaojun Chen
2017 Journal of Clinical Pathology  
The sensitivity and specificity of SAT for diagnosing PTB were 66.7% and 100%, respectively, while those for culture were 53.9% and 84.2%, respectively.  ...  Conclusions The combination of SAT and RDB is promising for rapidly detecting PTB and monitoring drug resistance in clinical laboratories.  ...  Acknowledgements We thank Dr Qiang Ke and Dr Chengsong Cai for technical assistance and helpful discussions.  ... 
doi:10.1136/jclinpath-2017-204714 pmid:29138284 pmcid:PMC5969349 fatcat:vuxxtlnoojcrhpm3gqjjuxmgrm
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