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
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Mathieu Mari
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up vote
4
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 yesterday
Mathieu Mari
232
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
4
down vote
favorite
up vote
4
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 yesterday
Mathieu Mari
232
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 yesterday
Mathieu Mari
232
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 yesterday
Mathieu Mari
232
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 yesterday
Mathieu Mari
232
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 yesterday
Mathieu Mari
232
asked yesterday
Mathieu Mari
232
232
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.
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
6
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 yesterday
Gamow
3,62931229
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
6
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 yesterday
Gamow
3,62931229
add a comment |
up vote
6
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 yesterday
Gamow
3,62931229
add a comment |
up vote
6
down vote
accepted
up vote
6
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 yesterday
Gamow
3,62931229
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 yesterday
Gamow
3,62931229
answered yesterday
Gamow
3,62931229
answered yesterday
Gamow
3,62931229
answered yesterday
Gamow
3,62931229
3,62931229
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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