  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.
