Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies randomized approximation algorithm for a variant of the set cover problem called {\em minimum submodular cost partial multi-cover} (SCPMC). In a \emph{partial set cover problem}, the goal is to find a minimum cost subcollection of sets covering at least a required fraction of elements. In a {\em multi-cover problem}, each element $e$ has a covering requirement $r_e$, and the goal is to find a minimum cost subcollection of sets $\mathcal S'$ which fully covers all elements, where an element $e$ is fully covered by $\mathcal S'$ if $e$ belongs to at least $r_e$ sets of $\mathcal S'$. In a \emph{minimum submodular cost set cover problem} (SCSC), the objective function is submodular and the constraint is a set cover. #R##N#The SCPMC problem studied in this paper is a combination of the above three problems. Previous work shows that such a combination enormously increases the difficulty of studies. #R##N#, assuming that the maximum covering requirement $r_{\max}=\max_e r_e$ is a constant and the objection function is nonnegative, monotone increasing, and submodular,  give the first randomized algorithm for SCPMC achieving performance ratio $O(b)$ with a high probability, where $b=\max_e\binom{f}{r_{e}}$ and $f$ is the maximum number of sets containing a common element. The algorithm is based on a novel non-linear program. Furthermore, in the case when the covering requirement $r\equiv 1$, an $O(f)$-approximation can be achieved even when monotonicity requirement is dropped off from the objective function.
['Yishuo Shi', 'Zhao Zhang', 'Ding-Zhu Du']
I am writing a research paper on a idea Randomized Approximation Algorithm for Minimum Submodular Cost Partial Multi-Cover Problem.
[{"from": "human", "value": "I am writing a research paper on a idea Randomized Approximation Algorithm for Minimum Submodular Cost Partial Multi-Cover Problem."}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies randomized approximation algorithm for a variant of the set cover problem called {\\em minimum submodular cost partial multi-cover} (SCPMC). In a \\emph{partial set cover problem}, the goal is to find a minimum cost subcollection of sets covering at least a required fraction of elements. In a {\\em multi-cover problem}, each element $e$ has a covering requirement $r_e$, and the goal is to find a minimum cost subcollection of sets $\\mathcal S'$ which fully covers all elements, where an element $e$ is fully covered by $\\mathcal S'$ if $e$ belongs to at least $r_e$ sets of $\\mathcal S'$. In a \\emph{minimum submodular cost set cover problem} (SCSC), the objective function is submodular and the constraint is a set cover. #R##N#The SCPMC problem studied in this paper is a combination of the above three problems. Previous work shows that such a combination enormously increases the difficulty of studies. #R##N#, assuming that the maximum covering requirement $r_{\\max}=\\max_e r_e$ is a constant and the objection function is nonnegative, monotone increasing, and submodular,  give the first randomized algorithm for SCPMC achieving performance ratio $O(b)$ with a high probability, where $b=\\max_e\\binom{f}{r_{e}}$ and $f$ is the maximum number of sets containing a common element. The algorithm is based on a novel non-linear program. Furthermore, in the case when the covering requirement $r\\equiv 1$, an $O(f)$-approximation can be achieved even when monotonicity requirement is dropped off from the objective function."}]