Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the ighted t-Uniform Sparsest Cut (ighted t-USC) and other related problems. In an instance of the ighted t-USC problem, a parameter t and an undirected graph G = ( V , E ) with edge-ights w : E ź R ź 0 and vertex-ights ź : V ź R + are given. The goal is to find a vertex set S ź V with | S | ź t while minimizing w ( S , V \ S ) / ź ( S ) , where w ( S , V \ S ) is the total ight of the edges with exactly one endpoint in S and ź ( S ) = ź v ź S ź ( v ) . For this problem,  present a ( O ( log ź t ) , 1 + ź ) factor bicriteria approximation algorithm. Our algorithm outperforms the current best algorithm when t = n o ( 1 ) .  also present better approximation algorithms for ighted ź-Unbalanced Cut and Min-Max k-Partitioning problems. An O(log t) bicriteria approximation algorithm for the ighted t-USC problem.The first approximation algorithm with approximation factor independent of n.For t = n o ( 1 ) the algorithm gives the best approximation factor.The algorithm is deterministic and requires solving a LP instead of a SDP.Approx algorithms for ighted k-Unbalanced Cut and Min-Max k-Partitioning problems.
['Mohammad Khairul Hasan', 'Kyung-Yong Chwa']
I am writing a research paper on a idea Approximation algorithms for the Weighted t-Uniform Sparsest Cut and some other graph partitioning problems
[{"from": "human", "value": "I am writing a research paper on a idea Approximation algorithms for the Weighted t-Uniform Sparsest Cut and some other graph partitioning problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the ighted t-Uniform Sparsest Cut (ighted t-USC) and other related problems. In an instance of the ighted t-USC problem, a parameter t and an undirected graph G = ( V , E ) with edge-ights w : E \u017a R \u017a 0 and vertex-ights \u017a : V \u017a R + are given. The goal is to find a vertex set S \u017a V with | S | \u017a t while minimizing w ( S , V \\ S ) / \u017a ( S ) , where w ( S , V \\ S ) is the total ight of the edges with exactly one endpoint in S and \u017a ( S ) = \u017a v \u017a S \u017a ( v ) . For this problem,  present a ( O ( log \u017a t ) , 1 + \u017a ) factor bicriteria approximation algorithm. Our algorithm outperforms the current best algorithm when t = n o ( 1 ) .  also present better approximation algorithms for ighted \u017a-Unbalanced Cut and Min-Max k-Partitioning problems. An O(log t) bicriteria approximation algorithm for the ighted t-USC problem.The first approximation algorithm with approximation factor independent of n.For t = n o ( 1 ) the algorithm gives the best approximation factor.The algorithm is deterministic and requires solving a LP instead of a SDP.Approx algorithms for ighted k-Unbalanced Cut and Min-Max k-Partitioning problems."}]