Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Assume that each of n voters may or may not approve each of m issues. If an agent (the lobby) may influence up to k voters, then the central question of the NP-hard LOBBYING problem is whether the lobby can choose the voters to be influenced so that as a result each issue gets a majority of approvals. This problem can be modeled as a simple matrix modification problem: Can one replace k rows of a binary n×m-matrix by k all-1 rows such that each column in the resulting matrix has a majority of 1s? Significantly extending on previous work that shod parameterized intractability (W[2]-completeness) with respect to the number k of modified rows,  study how natural parameters such as n, m, k, or the "maximum number of 1s missing for any column to have a majority of 1s" (referred to as "gap value g") govern the computational complexity of LOBBYING. Among other results,  prove that LOBBYING is fixed-parameter tractable for parameter m and provide a greedy logarithmic-factor approximation algorithm which solves LOBBYING even optimally if m ≤ 4.  also show empirically that this greedy algorithm performs ll on general instances. As a further key result,  prove that LOBBYING is LOGSNP-complete for constant values g ≥ 1, thus providing a first natural complete problem from voting for this complexity class of limited nondeterminism.
['Robert Bredereck', 'Jiehua Chen', 'Sepp Hartung', 'Stefan Kratsch', 'Rolf Niedermeier', 'Ondřej Suchý', 'Gerhard J. Woeginger']
I am writing a research paper on a idea A multivariate complexity analysis of lobbying in multiple referenda
[{"from": "human", "value": "I am writing a research paper on a idea A multivariate complexity analysis of lobbying in multiple referenda"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Assume that each of n voters may or may not approve each of m issues. If an agent (the lobby) may influence up to k voters, then the central question of the NP-hard LOBBYING problem is whether the lobby can choose the voters to be influenced so that as a result each issue gets a majority of approvals. This problem can be modeled as a simple matrix modification problem: Can one replace k rows of a binary n\u00d7m-matrix by k all-1 rows such that each column in the resulting matrix has a majority of 1s? Significantly extending on previous work that shod parameterized intractability (W[2]-completeness) with respect to the number k of modified rows,  study how natural parameters such as n, m, k, or the \"maximum number of 1s missing for any column to have a majority of 1s\" (referred to as \"gap value g\") govern the computational complexity of LOBBYING. Among other results,  prove that LOBBYING is fixed-parameter tractable for parameter m and provide a greedy logarithmic-factor approximation algorithm which solves LOBBYING even optimally if m \u2264 4.  also show empirically that this greedy algorithm performs ll on general instances. As a further key result,  prove that LOBBYING is LOGSNP-complete for constant values g \u2265 1, thus providing a first natural complete problem from voting for this complexity class of limited nondeterminism."}]