Algorithms for Optimizing the Ratio of Monotone k-Submodular Functions

We study a new optimization problem that minimizes the ratio of two monotone k-submodular functions. The has applications in sensor placement, influence maximization, and feature selection among many others where one wishes to make tradeoff between objectives, measured as functions (e.g., solution cost vs. quality). develop three greedy based algorithms for problem, with approximation ratios depend on curvatures and/or values apply our placement aims install k types sensors, while minimizing uncertainty measurements, well an maximization seeks advertise products minimize advertisement expected number influenced users. Our experimental results demonstrate effectiveness respective runtime efficiency algorithms. Finally, we discuss various extensions problems.