Does Max Planar 3-SAT admit a PTAS?












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Suppose we are given a formula $phi$ of 3-SAT, with variables $x_1,dots, x_n$ and clauses $C_1,dots, C_m$. Consider the graph $G_phi$ where there is one node for each clause $C_i$, for each positive literal $x_i$ and for each negative literal $overline{x_i}$. A literal is adjacent to a clause if and only if this clause contains the literal. $phi$ is a planar instance If $G_phi$ is planar.



Max planar 3-SAT is defined as the restriction of Max 3-SAT to planar instances.



This problem is known to be NP-hard. Is this problem also APX-Hard or there exists a known PTAS for this problem ?










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    6














    Suppose we are given a formula $phi$ of 3-SAT, with variables $x_1,dots, x_n$ and clauses $C_1,dots, C_m$. Consider the graph $G_phi$ where there is one node for each clause $C_i$, for each positive literal $x_i$ and for each negative literal $overline{x_i}$. A literal is adjacent to a clause if and only if this clause contains the literal. $phi$ is a planar instance If $G_phi$ is planar.



    Max planar 3-SAT is defined as the restriction of Max 3-SAT to planar instances.



    This problem is known to be NP-hard. Is this problem also APX-Hard or there exists a known PTAS for this problem ?










    share|cite|improve this question

























      6












      6








      6







      Suppose we are given a formula $phi$ of 3-SAT, with variables $x_1,dots, x_n$ and clauses $C_1,dots, C_m$. Consider the graph $G_phi$ where there is one node for each clause $C_i$, for each positive literal $x_i$ and for each negative literal $overline{x_i}$. A literal is adjacent to a clause if and only if this clause contains the literal. $phi$ is a planar instance If $G_phi$ is planar.



      Max planar 3-SAT is defined as the restriction of Max 3-SAT to planar instances.



      This problem is known to be NP-hard. Is this problem also APX-Hard or there exists a known PTAS for this problem ?










      share|cite|improve this question













      Suppose we are given a formula $phi$ of 3-SAT, with variables $x_1,dots, x_n$ and clauses $C_1,dots, C_m$. Consider the graph $G_phi$ where there is one node for each clause $C_i$, for each positive literal $x_i$ and for each negative literal $overline{x_i}$. A literal is adjacent to a clause if and only if this clause contains the literal. $phi$ is a planar instance If $G_phi$ is planar.



      Max planar 3-SAT is defined as the restriction of Max 3-SAT to planar instances.



      This problem is known to be NP-hard. Is this problem also APX-Hard or there exists a known PTAS for this problem ?







      reference-request complexity-classes approximation-algorithms approximation-hardness planar-graphs






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      asked Nov 20 at 14:12









      Mathieu Mari

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          Yes, a PTAS for Max-Planar-3-SAT can be constructed by using Brenda Baker's approach.

          This has been observed, for instance, in Theorem 17 in




          Pierluigi Crescenzi and LucaTrevisan:

          "Max NP-completeness made easy"

          Theoretical Computer Science 28, (1999), Pages 65-79







          share|cite|improve this answer





















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            1 Answer
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            1 Answer
            1






            active

            oldest

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            active

            oldest

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            active

            oldest

            votes









            10














            Yes, a PTAS for Max-Planar-3-SAT can be constructed by using Brenda Baker's approach.

            This has been observed, for instance, in Theorem 17 in




            Pierluigi Crescenzi and LucaTrevisan:

            "Max NP-completeness made easy"

            Theoretical Computer Science 28, (1999), Pages 65-79







            share|cite|improve this answer


























              10














              Yes, a PTAS for Max-Planar-3-SAT can be constructed by using Brenda Baker's approach.

              This has been observed, for instance, in Theorem 17 in




              Pierluigi Crescenzi and LucaTrevisan:

              "Max NP-completeness made easy"

              Theoretical Computer Science 28, (1999), Pages 65-79







              share|cite|improve this answer
























                10












                10








                10






                Yes, a PTAS for Max-Planar-3-SAT can be constructed by using Brenda Baker's approach.

                This has been observed, for instance, in Theorem 17 in




                Pierluigi Crescenzi and LucaTrevisan:

                "Max NP-completeness made easy"

                Theoretical Computer Science 28, (1999), Pages 65-79







                share|cite|improve this answer












                Yes, a PTAS for Max-Planar-3-SAT can be constructed by using Brenda Baker's approach.

                This has been observed, for instance, in Theorem 17 in




                Pierluigi Crescenzi and LucaTrevisan:

                "Max NP-completeness made easy"

                Theoretical Computer Science 28, (1999), Pages 65-79








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                share|cite|improve this answer



                share|cite|improve this answer










                answered Nov 20 at 15:14









                Gamow

                3,90931532




                3,90931532






























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