@InProceedings{nie_646,
    title = {Size-constrained k-submodular maximization in near-linear time},
    author = {Nie, Guanyu and Zhu, Yanhui and Nadew, Yididiya Y. and Basu, Samik and Pavan, A. and Quinn, Christopher John},
    abstract = {We investigate the problems of maximizing k-submodular functions over total size constraints and over individual size constraints. k-submodularity is a generalization of submodularity beyond just picking items of a ground set, instead associating one of k types to chosen items.  For sensor selection problems, for instance, this enables modeling of which type  of sensor to put at a location, not simply whether to put a sensor or not.   We propose and analyze threshold-greedy algorithms for both types of constraints.  We prove that our proposed algorithms achieve the best known approximation ratios for both constraint types, up to a user-chosen parameter that balances computational complexity and the approximation ratio, while only using a number of function evaluations that depends linearly (up to poly-logarithmic terms) on the number of elements n, the number of types k, and the inverse of the user chosen parameter.  Other algorithms that achieve the best-known deterministic approximation ratios require a number of  function evaluations that depends linearly on the budget B, while our methods do not.  We empirically demonstrate our algorithms' performance in applications of sensor placement with k types and influence maximization with k topics.}
}

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