Minimal amount of edges needed to be removed to make a graph triangle free (approximation algorithm)
0
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Given a graph G = (V,E) there is a minimal number of edges - k - that need to be removed to make G triangle free. I'm trying to find an approximation algorithm (that is as efficient as possible) that finds a set of edges to remove to make G triangle free that is no larger than 3k.
Can someone help me?
graph-theory
asked Aug 17 '18 at 8:24
DanDan
31
$endgroup$
|
show 1 more comment
0
$begingroup$
Given a graph G = (V,E) there is a minimal number of edges - k - that need to be removed to make G triangle free. I'm trying to find an approximation algorithm (that is as efficient as possible) that finds a set of edges to remove to make G triangle free that is no larger than 3k.
Can someone help me?
graph-theory
asked Aug 17 '18 at 8:24
DanDan
31
$endgroup$
$begingroup$
Could you show us your efforts? Did you try the greedy algorithm, for example?
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:31
$begingroup$
By greedy algorithm I assume you mean looping through all possible triangles on the graph and removing edges from them as they come. But that won't work. for example you can have a single edge that is part of n-2 triangles (where n is the numbers of vertices) but instead of removing that edge the algorithm will remove n-2 other edges.
$endgroup$
– Dan
Aug 17 '18 at 8:37
$begingroup$
No, my greedy approach would be to compute the number of triangles containing the edge $e$ for all $ein E$. Then pick the edge that is contained in the biggest number of triangles. Remove it. Iterate. Not sure this works, just asking if you tried it.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:39
$begingroup$
So "greedy" is meant in the sense that in each step we eliminate as many triangles as possible.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:45
$begingroup$
yes, that seems to work, thanks
$endgroup$
– Dan
Aug 17 '18 at 8:59
|
show 1 more comment
0
0
0
$begingroup$
Given a graph G = (V,E) there is a minimal number of edges - k - that need to be removed to make G triangle free. I'm trying to find an approximation algorithm (that is as efficient as possible) that finds a set of edges to remove to make G triangle free that is no larger than 3k.
Can someone help me?
graph-theory
asked Aug 17 '18 at 8:24
DanDan
31
$endgroup$
Given a graph G = (V,E) there is a minimal number of edges - k - that need to be removed to make G triangle free. I'm trying to find an approximation algorithm (that is as efficient as possible) that finds a set of edges to remove to make G triangle free that is no larger than 3k.
Can someone help me?
graph-theory
graph-theory
asked Aug 17 '18 at 8:24
DanDan
31
asked Aug 17 '18 at 8:24
DanDan
31
asked Aug 17 '18 at 8:24
DanDan
31
asked Aug 17 '18 at 8:24
DanDan
31
asked Aug 17 '18 at 8:24
DanDan
31
31
$begingroup$
Could you show us your efforts? Did you try the greedy algorithm, for example?
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:31
$begingroup$
By greedy algorithm I assume you mean looping through all possible triangles on the graph and removing edges from them as they come. But that won't work. for example you can have a single edge that is part of n-2 triangles (where n is the numbers of vertices) but instead of removing that edge the algorithm will remove n-2 other edges.
$endgroup$
– Dan
Aug 17 '18 at 8:37
$begingroup$
No, my greedy approach would be to compute the number of triangles containing the edge $e$ for all $ein E$. Then pick the edge that is contained in the biggest number of triangles. Remove it. Iterate. Not sure this works, just asking if you tried it.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:39
$begingroup$
So "greedy" is meant in the sense that in each step we eliminate as many triangles as possible.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:45
$begingroup$
yes, that seems to work, thanks
$endgroup$
– Dan
Aug 17 '18 at 8:59
|
show 1 more comment
$begingroup$
Could you show us your efforts? Did you try the greedy algorithm, for example?
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:31
$begingroup$
By greedy algorithm I assume you mean looping through all possible triangles on the graph and removing edges from them as they come. But that won't work. for example you can have a single edge that is part of n-2 triangles (where n is the numbers of vertices) but instead of removing that edge the algorithm will remove n-2 other edges.
$endgroup$
– Dan
Aug 17 '18 at 8:37
$begingroup$
No, my greedy approach would be to compute the number of triangles containing the edge $e$ for all $ein E$. Then pick the edge that is contained in the biggest number of triangles. Remove it. Iterate. Not sure this works, just asking if you tried it.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:39
$begingroup$
So "greedy" is meant in the sense that in each step we eliminate as many triangles as possible.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:45
$begingroup$
yes, that seems to work, thanks
$endgroup$
– Dan
Aug 17 '18 at 8:59
$begingroup$
Could you show us your efforts? Did you try the greedy algorithm, for example?
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:31
$begingroup$
Could you show us your efforts? Did you try the greedy algorithm, for example?
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:31
$begingroup$
By greedy algorithm I assume you mean looping through all possible triangles on the graph and removing edges from them as they come. But that won't work. for example you can have a single edge that is part of n-2 triangles (where n is the numbers of vertices) but instead of removing that edge the algorithm will remove n-2 other edges.
$endgroup$
– Dan
Aug 17 '18 at 8:37
$begingroup$
By greedy algorithm I assume you mean looping through all possible triangles on the graph and removing edges from them as they come. But that won't work. for example you can have a single edge that is part of n-2 triangles (where n is the numbers of vertices) but instead of removing that edge the algorithm will remove n-2 other edges.
$endgroup$
– Dan
Aug 17 '18 at 8:37
$begingroup$
No, my greedy approach would be to compute the number of triangles containing the edge $e$ for all $ein E$. Then pick the edge that is contained in the biggest number of triangles. Remove it. Iterate. Not sure this works, just asking if you tried it.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:39
$begingroup$
No, my greedy approach would be to compute the number of triangles containing the edge $e$ for all $ein E$. Then pick the edge that is contained in the biggest number of triangles. Remove it. Iterate. Not sure this works, just asking if you tried it.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:39
$begingroup$
So "greedy" is meant in the sense that in each step we eliminate as many triangles as possible.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:45
$begingroup$
So "greedy" is meant in the sense that in each step we eliminate as many triangles as possible.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:45
$begingroup$
yes, that seems to work, thanks
$endgroup$
– Dan
Aug 17 '18 at 8:59
$begingroup$
yes, that seems to work, thanks
$endgroup$
– Dan
Aug 17 '18 at 8:59
|
show 1 more comment
1 Answer
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Try the greedy algorithm: in each step, eliminate the biggest possible number of triangles by deleting the edge contained in the most triangles.
answered Aug 17 '18 at 9:04
A. PongráczA. Pongrácz
6,0431929
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Try the greedy algorithm: in each step, eliminate the biggest possible number of triangles by deleting the edge contained in the most triangles.
answered Aug 17 '18 at 9:04
A. PongráczA. Pongrácz
6,0431929
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add a comment |
0
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Try the greedy algorithm: in each step, eliminate the biggest possible number of triangles by deleting the edge contained in the most triangles.
answered Aug 17 '18 at 9:04
A. PongráczA. Pongrácz
6,0431929
$endgroup$
add a comment |
0
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Try the greedy algorithm: in each step, eliminate the biggest possible number of triangles by deleting the edge contained in the most triangles.
answered Aug 17 '18 at 9:04
A. PongráczA. Pongrácz
6,0431929
$endgroup$
Try the greedy algorithm: in each step, eliminate the biggest possible number of triangles by deleting the edge contained in the most triangles.
answered Aug 17 '18 at 9:04
A. PongráczA. Pongrácz
6,0431929
answered Aug 17 '18 at 9:04
A. PongráczA. Pongrácz
6,0431929
answered Aug 17 '18 at 9:04
A. PongráczA. Pongrácz
6,0431929
answered Aug 17 '18 at 9:04
A. PongráczA. Pongrácz
6,0431929
6,0431929
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$begingroup$
Could you show us your efforts? Did you try the greedy algorithm, for example?
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:31
$begingroup$
By greedy algorithm I assume you mean looping through all possible triangles on the graph and removing edges from them as they come. But that won't work. for example you can have a single edge that is part of n-2 triangles (where n is the numbers of vertices) but instead of removing that edge the algorithm will remove n-2 other edges.
$endgroup$
– Dan
Aug 17 '18 at 8:37
$begingroup$
No, my greedy approach would be to compute the number of triangles containing the edge $e$ for all $ein E$. Then pick the edge that is contained in the biggest number of triangles. Remove it. Iterate. Not sure this works, just asking if you tried it.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:39
$begingroup$
So "greedy" is meant in the sense that in each step we eliminate as many triangles as possible.
$endgroup$
– A. Pongrácz
Aug 17 '18 at 8:45
$begingroup$
yes, that seems to work, thanks
$endgroup$
– Dan
Aug 17 '18 at 8:59