Filters








125 Hits in 2.7 sec

Improved Approximation Algorithms for Max-2SAT with Cardinality Constraint [chapter]

Markus Bläser, Bodo Manthey
2002 Lecture Notes in Computer Science  
The optimization problem Max-2SAT-CC is Max-2SAT with the additional cardinality constraint that the value one may be assigned to at most K variables.  ...  We present an approximation algorithm with polynomial running time for Max-2SAT-CC. This algorithm achieves, for any > 0, approximation ratio 6+3·e 16+2·e − ≈ 0.6603.  ...  Conclusions We have presented an approximation algorithm with approximation performance 6+3·e 16+2·e − (for an arbitrary > 0) for Max-2SAT-CC, the Max-2SAT problem with the additional constraint that the  ... 
doi:10.1007/3-540-36136-7_17 fatcat:uyrx7zlecnbcpe67bnf2gevzty

On Approximation Hardness of the Minimum 2SAT-DELETION Problem [chapter]

Miroslav Chlebík, Janka Chlebíková
2004 Lecture Notes in Computer Science  
We further prove that any k-approximation algorithm for Minimum 2SAT-Deletion polynomially reduces to a (2 − 2 k+1 )-approximation algorithm for the Minimum Vertex Cover problem.  ...  One ingredient of these improvements is our proof that for the Minimum Vertex Cover problem restricted to graphs with a perfect matching its threshold on polynomial time approximability is the same as  ...  For any t > 1 2 the existence of a robust algorithm with g(ε) = O(ε t ) would significantly improve (for large d) on currently the best approximation factor (2 − 5 2d+3 ) on polynomial time approximation  ... 
doi:10.1007/978-3-540-28629-5_18 fatcat:hrxncdqginh6hdvtkdivwhb4pm

Minimum 2SAT-DELETION: Inapproximability results and relations to Minimum Vertex Cover

Miroslav Chlebík, Janka Chlebíková
2007 Discrete Applied Mathematics  
It is one of the prototypes in the approximability hierarchy of minimization problems Khanna et al. [Constraint satisfaction: the approximability of minimization problems,  ...  The MINIMUM 2SAT-DELETION problem is to delete the minimum number of clauses in a 2SAT instance to make it satisfiable.  ...  for the MIN-VC-PM problem based on approximation algorithms for the MAX-2SAT problem.  ... 
doi:10.1016/j.dam.2006.04.039 fatcat:jvnqm4pmgnfojm3bnz534g55he

Global Cardinality Constraints Make Approximating Some Max-2-CSPs Harder [article]

Per Austrin, Aleksa Stankovic
2019 arXiv   pre-print
Assuming the Unique Games Conjecture, we show that existing approximation algorithms for some Boolean Max-2-CSPs with cardinality constraints are optimal.  ...  In particular, we prove that Max-Cut with cardinality constraints is UG-hard to approximate within \approx 0.858, and that Max-2-Sat with cardinality constraints is UG-hard to approximate within \approx  ...  Acknowledgements The authors thank Johan Håstad for helpful suggestions and comments on the manuscript. We also thank anonymous reviewers for their helpful remarks.  ... 
arXiv:1907.04165v2 fatcat:zrmrqpq4xjbaxjrvaih2kvowgu

Global Cardinality Constraints Make Approximating Some Max-2-CSPs Harder

Per Austrin, Aleksa Stankovic, Michael Wagner
2019 International Workshop on Approximation Algorithms for Combinatorial Optimization  
Assuming the Unique Games Conjecture, we show that existing approximation algorithms for some Boolean Max-2-CSPs with cardinality constraints are optimal.  ...  In particular, we prove that Max-Cut with cardinality constraints is UG-hard to approximate within ≈ 0.858, and that Max-2-Sat with cardinality constraints is UG-hard to approximate within ≈ 0.929.  ...  We also thank anonymous reviewers for their helpful remarks. 24:15 Another interesting research direction would be to come up with hardness results for some other well-know Max-CSPs like Max-3-Sat, or  ... 
doi:10.4230/lipics.approx-random.2019.24 dblp:conf/approx/AustrinS19 fatcat:dgvshqkiezguhb5hodcbmftpui

A Note on Max k-Vertex Cover: Faster FPT-AS, Smaller Approximate Kernel and Improved Approximation

Pasin Manurangsi, Michael Wagner
2018 ACM-SIAM Symposium on Discrete Algorithms  
for 2SAT with cardinality constraint [52] to give an 0.92-approximation algorithm for Max k-VC in polynomial time.  ...  This improves upon the best known polynomial time approximation algorithm of Feige and Langberg [23] which yields (0.75 + δ)-approximation for some (small and unspecified) constant δ > 0.  ...  Max Bisection 2SAT from [6] .  ... 
doi:10.4230/oasics.sosa.2019.15 dblp:conf/soda/Manurangsi19 fatcat:pa6rl2rwzrdsrgepskfsxzlpba

Adding cardinality constraints to integer programs with applications to maximum satisfiability

Markus Bläser, Thomas Heynen, Bodo Manthey
2008 Information Processing Letters  
To do this, we develop a general technique for adding a cardinality constraint to certain integer programs.  ...  If each clause is restricted to have at most literals, we obtain the problem Max-SAT-CC. Sviridenko (Algorithmica, 30(3):398-405, 2001) designed a (1 − e −1 )-approximation algorithm for Max-SAT-CC.  ...  Acknowledgement We thank the anonymous referee for many helpful comments.  ... 
doi:10.1016/j.ipl.2007.08.024 fatcat:ffon2fnpcbb5jgosifshyy4tg4

A Note on Max k-Vertex Cover: Faster FPT-AS, Smaller Approximate Kernel and Improved Approximation [article]

Pasin Manurangsi
2018 arXiv   pre-print
for 2SAT with cardinality constraint [SODA'12] to give an 0.92-approximation for Max k-VC in polynomial time.  ...  This improves upon Feige and Langberg's algorithm [J. Algorithms'01] which yields (0.75 + δ)-approximation for some (unspecified) constant δ > 0.  ...  Most importantly, they show that, for Max 2SAT with cardinality constraint, if the cardinality constraint is x 1 + · · · + x n = n/2 (i.e. k = n/2), then an 0.94-approximation can be achieved in polynomial  ... 
arXiv:1810.03792v1 fatcat:7bhcloorlvdejbv7vt56bdvrc4

Sticky Brownian Rounding and its Applications to Constraint Satisfaction Problems

Sepehr Abbasi-Zadeh, Nikhil Bansal, Guru Guruganesh, Aleksandar Nikolov, Roy Schwartz, Mohit Singh
2022 ACM Transactions on Algorithms  
Focusing on constraint satisfaction problems, we apply our method to several classical problems, including Max-Cut , Max-2SAT , and Max-DiCut , and derive new algorithms that are competitive with the best  ...  To illustrate the versatility and general applicability of our approach, we give new approximation algorithms for the Max-Cut problem with side constraints that crucially utilizes measure concentration  ...  ACKNOWLEDGEMENTS The authors are grateful to Assaf Naor and Ronen Eldan for sharing their manuscript with us.  ... 
doi:10.1145/3459096 fatcat:dzaold5vz5hvvj7mtdmu7r7fse

Page 4249 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
Summary: “We propose a 0.935-approximation algorithm for MAX 2SAT and a 0.863-approximation algorithm for MAX DI- CUT.  ...  for MAX 2SAT and MAX DICUT.  ... 

Solving Max-SAT as Weighted CSP [chapter]

Simon de Givry, Javier Larrosa, Pedro Meseguer, Thomas Schiex
2003 Lecture Notes in Computer Science  
For the last ten years, a significant amount of work in the constraint community has been devoted to the improvement of complete methods for solving soft constraints networks.  ...  We then solve Max-SAT instances using state-of-the-art algorithms for weighted Max-CSP, dedicated Max-SAT solvers and the state-of-the-art MIP solver CPLEX.  ...  Acknowledgements We would like to thank Michel Correge and Michel Lemaître for letting us use CPLEX, for hosting the associated heavy benchmarking and associated nuisances.  ... 
doi:10.1007/978-3-540-45193-8_25 fatcat:3bexqko4yvbpfdiexayiquqdqq

Sticky Brownian Rounding and its Applications to Constraint Satisfaction Problems [article]

Sepehr Abbasi-Zadeh, Nikhil Bansal, Guru Guruganesh, Aleksandar Nikolov, Roy Schwartz, Mohit Singh
2019 arXiv   pre-print
Focusing on constraint satisfaction problems, we apply our method to several classical problems, including Max-Cut, Max-2SAT, and MaxDiCut, and derive new algorithms that are competitive with the best  ...  To illustrate the versatility and general applicability of our approach, we give new approximation algorithms for the Max-Cut problem with side constraints that crucially utilizes measure concentration  ...  The authors are grateful to Assaf Naor and Ronen Eldan for sharing their manuscript with us.  ... 
arXiv:1812.07769v2 fatcat:klegjafsxjhsnd5shzkwrg4wcm

Restricted LCS [chapter]

Zvi Gotthilf, Danny Hermelin, Gad M. Landau, Moshe Lewenstein
2010 Lecture Notes in Computer Science  
In the last part of this paper we present two approximation algorithms for the hard variants of the problem.  ...  Afterwards, we present a dynamic programming solution for RLCS and we show that this algorithm implies that RLCS is in FPT when parameterized by the total length of the restriction strings.  ...  Improved dynamic programming algorithms were proposed in [4, 7] . In [9] , fast approximation algorithms were designed for this basic CLCS variant.  ... 
doi:10.1007/978-3-642-16321-0_26 fatcat:5mmnmjh3ljgazl5bdepeuxghua

Approximation algorithms for grooming in optical network design

Spyridon Antonakopoulos, Lisa Zhang
2011 Theoretical Computer Science  
We show how to approximate both objectives up to small constant factors in this case, while similarly improving the approximation and hardness of the interchange distance problem as well.  ...  On the other extreme of generality, for arbitrary network topologies and traffic demands that request arbitrary amounts of bandwidth, we show a logarithmic approximation for cost minimization and a 2-approximation  ...  Improved grooming with general costs in line and tree topologies In this section we focus on improving the approximation ratios for grooming with general costs.  ... 
doi:10.1016/j.tcs.2011.03.034 fatcat:ew2m4rza5rbetdbstrkyffiwzu

Semidefinite Programming and Integer Programming [chapter]

Monique Laurent, Franz Rendl
2005 Handbooks in Operations Research and Management Science  
We thank a referee for his careful reading and his suggestions that helped improve the presentation of this chapter.  ...  This improved MAX 2SAT algorithm leads to a slightly improved 0.7554-approximation algorithm for general MAX SAT.  ...  A refinement of this algorithm is given in [94] with an improved performance ratio 0.7584. The improved Feige-Goemans 0.931-approximation algorithm for MAX 2SAT.  ... 
doi:10.1016/s0927-0507(05)12008-8 fatcat:ez23hvr5znfolnppcugzpevgpu
« Previous Showing results 1 — 15 out of 125 results