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 ?
reference-request complexity-classes approximation-algorithms approximation-hardness planar-graphs
asked Nov 20 at 14:12
Mathieu Mari
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up vote
6
down vote
favorite
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
asked Nov 20 at 14:12
Mathieu Mari
332
New contributor
Mathieu Mari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
6
down vote
favorite
up vote
6
down vote
favorite
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
asked Nov 20 at 14:12
Mathieu Mari
332
New contributor
Mathieu Mari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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
reference-request complexity-classes approximation-algorithms approximation-hardness planar-graphs
asked Nov 20 at 14:12
Mathieu Mari
332
New contributor
Mathieu Mari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 14:12
Mathieu Mari
332
New contributor
Mathieu Mari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 14:12
Mathieu Mari
332
New contributor
Mathieu Mari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 14:12
Mathieu Mari
332
asked Nov 20 at 14:12
Mathieu Mari
332
332
New contributor
Mathieu Mari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Mathieu Mari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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1 Answer
1
active
oldest
votes
up vote
10
down vote
accepted
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
answered Nov 20 at 15:14
Gamow
3,66931331
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
10
down vote
accepted
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
answered Nov 20 at 15:14
Gamow
3,66931331
add a comment |
up vote
10
down vote
accepted
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
answered Nov 20 at 15:14
Gamow
3,66931331
add a comment |
up vote
10
down vote
accepted
up vote
10
down vote
accepted
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
answered Nov 20 at 15:14
Gamow
3,66931331
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
answered Nov 20 at 15:14
Gamow
3,66931331
answered Nov 20 at 15:14
Gamow
3,66931331
answered Nov 20 at 15:14
Gamow
3,66931331
answered Nov 20 at 15:14
Gamow
3,66931331
3,66931331
add a comment |
add a comment |
Mathieu Mari is a new contributor. Be nice, and check out our Code of Conduct.
Mathieu Mari is a new contributor. Be nice, and check out our Code of Conduct.
Mathieu Mari is a new contributor. Be nice, and check out our Code of Conduct.
Mathieu Mari is a new contributor. Be nice, and check out our Code of Conduct.
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