Minimizing Regret in Billboard Advertisement under Zonal Influence Constraint

In a typical billboard advertisement technique, a number of digital billboards are owned by an influence provider, and many advertisers approach the influence provider for a specific number of views of their advertisement content on a payment basis. If the influence provider provides the demanded or more influence, then he will receive the full payment or else a partial payment. In the context of an influence provider, if he provides more or less than an advertiser's demanded influence, it is a loss for him. This is formalized as 'Regret', and naturally, in the context of the influence provider, the goal will be to allocate the billboard slots among the advertisers such that the total regret is minimized. In this paper, we study this problem as a discrete optimization problem and propose four solution approaches. The first one selects the billboard slots from the available ones in an incremental greedy manner, and we call this method the Budget Effective Greedy approach. In the second one, we introduce randomness with the first one, where we perform the marginal gain computation for a sample of randomly chosen billboard slots. The remaining two approaches are further improvements over the second one. We analyze all the algorithms to understand their time and space complexity. We implement them with real-life trajectory and billboard datasets and conduct a number of experiments. It has been observed that the randomized budget effective greedy approach takes reasonable computational time while minimizing the regret.