کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
427016 | 686422 | 2013 | 8 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A new bound for 3-satisfiable MaxSat and its algorithmic application A new bound for 3-satisfiable MaxSat and its algorithmic application](/preview/png/427016.png)
Let F be a CNF formula with n variables and m clauses. F is 3-satisfiable if for any 3 clauses in F , there is a truth assignment which satisfies all of them. Lieberherr and Specker (1982) and, later, Yannakakis (1994) proved that in each 3-satisfiable CNF formula at least 23 of its clauses can be satisfied by a truth assignment. We improve this result by showing that every 3-satisfiable CNF formula F contains a subset of variables U, such that some truth assignment τ will satisfy at least 23m+13mU+ρn′ clauses, where m is the number of clauses of F , mUmU is the number of clauses of F containing a variable from U , n′n′ is the total number of variables in clauses not containing a variable in U, and ρ is a positive absolute constant. Both U and τ can be found in polynomial time.We use our result to show that the following parameterized problem is fixed-parameter tractable and, moreover, has a kernel with a linear number of variables. In 3-S-MaxSat-AE, we are given a 3-satisfiable CNF formula F with m clauses and asked to determine whether there is an assignment which satisfies at least 23m+k clauses, where k is the parameter.
Journal: Information and Computation - Volume 231, October 2013, Pages 117–124