Minimal amount of edges needed to be removed to make a graph triangle free (approximation algorithm)












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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?










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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
















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?










share|cite|improve this question









$endgroup$












  • $begingroup$
    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














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?










share|cite|improve this question









$endgroup$




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






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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


















  • $begingroup$
    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










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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.






share|cite|improve this answer









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    $begingroup$

    Try the greedy algorithm: in each step, eliminate the biggest possible number of triangles by deleting the edge contained in the most triangles.






    share|cite|improve this answer









    $endgroup$


















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      $begingroup$

      Try the greedy algorithm: in each step, eliminate the biggest possible number of triangles by deleting the edge contained in the most triangles.






      share|cite|improve this answer









      $endgroup$
















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        $begingroup$

        Try the greedy algorithm: in each step, eliminate the biggest possible number of triangles by deleting the edge contained in the most triangles.






        share|cite|improve this answer









        $endgroup$



        Try the greedy algorithm: in each step, eliminate the biggest possible number of triangles by deleting the edge contained in the most triangles.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 17 '18 at 9:04









        A. PongráczA. Pongrácz

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