In this paper, we introduce and study the Influential Billboard Slot Selection Problem Under Zonal Influence Constraint. We propose a simple, greedy approach to solve this problem. Though this method is easy to understand and simple to implement due to the excessive number of marginal gain computations, this method is not scalable. We design a branch and bound framework with two bound estimation techniques that divide the problem into different zones and integrate the zone-specific solutions to obtain a solution for the whole. We implement both the solution methodologies with real-world billboard and trajectory datasets and several experiments have been reported. We compare the performance of the proposed solution approaches with several baseline methods. The results show that the proposed approaches lead to more effective solutions with reasonable computational overhead than the baseline methods.

This paper introduces the Context-Dependent Influential Billboard Slot Selection Problem. First, we show that the problem is NP-hard. We also show that the influence function holds the bi-monotonicity, bi-submodularity, and non-negativity properties. We propose an orthant-wise Stochastic Greedy approach to solve this problem. We show that this method leads to a constant factor approximation guarantee. Subsequently, we propose an orthant-wise Incremental and Lazy Greedy approach. We analyze the performance guarantee of this algorithm as well as time and space complexity.

In this paper, we solve the Regret Minimization problem in the context of billboard advertisement and pose it as a discrete optimization problem. We propose four efficient solution approaches for this problem and analyze them to understand their time and space complexity. We implement all the solution methodologies with real-life datasets and compare the obtained results with the existing solution approaches from the literature. We observe that the proposed solutions lead to less regret while taking less computational time.

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.

In a typical billboard advertisement technique, a number of digital billboards are owned by an influence provider, and several commercial houses 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 two solution approaches.

In this paper, we formulate the Influential Billboard Slot Selection Problem as a discrete optimization problem and show that this problem is NP-Hard and hard to approximate within a constant factor. We propose a Pruned Submodularity Graph-based solution approach to solve this problem with its detailed analysis and illustration with a problem instance.