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.

翻译：在典型的公告板广告技术中，影响力提供商拥有若干数字广告牌，而众多广告商基于付费方式向其寻求特定次数的广告内容曝光。若影响力提供商提供达到或超过需求的曝光量，则可获得全额付款，否则仅能获得部分付款。对影响力提供商而言，无论提供超过还是低于广告商需求的曝光量，都将造成损失。这种损失被形式化定义为"遗憾"。自然地，从影响力提供商角度出发，目标是在广告商之间分配广告时段，使总遗憾最小化。本文将该问题作为离散优化问题进行研究，并提出四种求解方案。第一种方案采用增量贪心方式从可用广告牌中挑选时段，我们称之为预算有效贪心法。第二种方案引入随机性，通过对随机选取的广告牌样本计算边际增益。剩余两种方案则是对第二种方案的进一步改进。我们分析了所有算法的时间与空间复杂度，并基于真实轨迹与公告板数据集进行了实验验证。实验结果表明，随机化预算有效贪心法在最小化遗憾的同时，计算时间合理。