近年來已經有很多解決天際線問題的方法被提出。從市場的觀點來看，支配的概念有助於選擇具競爭力的產品。廠商可能會想要在一筆有限的預算下更新一些不具競爭力的產品，並獲得最多的潛在客戶數。在這篇論文中我們嘗試解決一個新的問題在於這些不具競爭力的產品之中更新他們成為不被現存產品所支配並得到最大的潛在客戶數。給了兩組資料集A和P以及一個有限的預算M，而A中為不具競爭力的產品集合，P中為具有競爭力的產品集合；我們將從P中挑選出一些產品能夠更新成為不被A中產品所支配的產品並且更新後的產品能得到最大的潛在客戶數。我們提出了近似的演算法建置在一個能夠群集相似的點有趣的資料結構以及能夠排除更新花費較大的產品上。我們在實驗部分做三組不同分布的造資料集以及一組實際資料集。實驗結果顯示近似的方法能夠比基本的算法更有效率且在也有不錯的精確度。

Recently, many approaches on solving the skyline problems have been proposed. From the perspective of marketing, the domination concept is conducive to choose the competitive products. A product provider may want to know which uncompetitive products can be upgraded to gain much more potential customers under a limited budget. In this paper, we make the first attempt to address a new problem on upgrading uncompetitive products to maximize the number of potential customers, which returns a set of products that are not dominated by any existing products and maximize the number of potential customers. Given two data sets A and P, the former represents a set of competitive products while the latter represents a set of uncompetitive products waiting for being upgraded, and a limited budget of M, we return some products in P that are upgraded to avoid being dominated by any products in A under the condition of M and these products can maximize the number of potential customers. We propose an approximate algorithm based on an interesting index structure to group together the similar products and prune the other products that may cost too much. A series of experiments on a real dataset and three synthetic datasets are performed. The experiment results show that the approximate method is more efficient than a basic method and also has a good accurate rate.

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