Path auction is held in a graph, where each edge stands for a commodity and the weight of this edge represents the prime cost. Bidders own some edges and make bids for their edges. The auctioneer needs to purchase a sequence of edges to form a path between two specific vertices. Path auction can be considered as a kind of combinatorial reverse auctions. Core-selecting mechanism is a prevalent mechanism for combinatorial auction. However, pricing in core-selecting combinatorial auction is computationally expensive, one important reason is the exponential core constraints. The same is true of path auction. To solve this computation problem, we simplify the constraint set and get the optimal set with only polynomial constraints in this paper. Based on our constraint set, we put forward two fast core pricing algorithms for the computation of bidder-Pareto-optimal core outcome. Among all the algorithms, our new algorithms have remarkable runtime performance. Finally, we validate our algorithms on real-world datasets and obtain excellent results.

中文翻译：

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路径拍卖的快速核心定价算法

路径拍卖以图形表示，其中每个边代表商品，该边的权重代表主要成本。投标人拥有一些优势，并为自己的优势出价。拍卖师需要购买一系列边缘，以形成两个特定顶点之间的路径。路径拍卖可以视为一种组合反向拍卖。核心选择机制是组合拍卖的一种普遍机制。然而，核心选择组合拍卖的定价在计算上是昂贵的，一个重要原因是指数核心约束。路径拍卖也是如此。为了解决该计算问题，本文简化了约束集，仅使用多项式约束获得了最优集。根据我们的约束集，我们提出了两种快速核心定价算法，用于计算投标人-帕累托最优核心结果。在所有算法中，我们的新算法具有出色的运行时性能。最后，我们在现实世界的数据集上验证我们的算法，并获得出色的结果。