While Bitcoin heavily dominates the cryptocurrency markets, its use in micropayments is still a challenge due to long transaction confirmation times and high fees. Recently, the concept of off-chain transactions is introduced that led to the idea of establishing a payment channel network called Lightning Network (LN), which utilizes multi-hop payments. Off-chain links provide the ability to make instant payments without a need to writing to Blockchain. However, LN's design still favors fees, and it is creating hub nodes or relays that defeat the purpose of Blockchain. In addition, it is still not reliable, as not all transactions are guaranteed to be delivered to their destinations. These issues hinder its wide adoption by retailers. To address this issue, in this paper, we argue that the retailers could create a private payment channel network among them to serve their business needs, just like the concept of private Blockchains. The goal is to build a pure peer-to-peer topology that will prevent the formation of hub nodes while also eliminating the need for any relays to increase the robustness of the payments. Assuming off-chain links as edges and retailers as nodes, we formulate the problem as a multi-flow commodity problem where transactions represent the commodities from various sources to destinations. As the multi-flow commodity problem is NP-Complete, we propose a heuristic approach that utilizes Dijkstra's shortest path algorithm for payments in a dynamic way by updating the edge weights when new paths need to be found. The order of transactions is randomized to provide fairness among the retailers. We further extend this approach to guarantee the privacy of payments by forcing all the payments to travel at least three hops. We utilized k-shortest path algorithm to choose from k options that will meet our criterion. The evaluations indicate that the proposed heuristic comes close to an optimal solution while providing scalability and guaranteeing user privacy.

尽管比特币在加密货币市场上占据着主导地位，但由于交易确认时间长和手续费高，其在小额支付中的使用仍然是一个挑战。最近，引入了脱链交易的概念，这导致了建立名为Lightning Network（LN）的支付渠道网络的想法，该网络利用了多跳支付。链外链接提供了即时付款的功能，而无需写入区块链。但是，LN的设计仍然偏向于收费，并且它正在创建枢纽节点或中继，这违背了区块链的目的。另外，它仍然不可靠，因为不能保证所有交易都可以传递到目的地。这些问题阻碍了零售商的广泛采用。为了解决这个问题，在本文中，我们认为，零售商可以在其中建立一个专用支付渠道网络来满足其业务需求，就像专用区块链的概念一样。目标是建立一个纯对等拓扑，该拓扑将防止集线器节点的形成，同时也无需任何中继来提高支付的健壮性。假设脱链链接为边，零售商为节点，我们将该问题表述为多流程商品问题，其中交易代表从各种来源到目的地的商品。由于多流商品问题是NP完全问题，因此我们提出了一种启发式方法，该方法采用Dijkstra最短路径算法以动态方式通过在需要找到新路径时更新边权重来动态地进行支付。交易顺序是随机的，以提供零售商之间的公平性。我们进一步通过强制所有付款至少经过三跳来扩展此方法，以确保付款的私密性。我们利用k-最短路径算法，可以从符合我们标准的k个选项中进行选择。评估表明，所提出的启发式算法在提供可伸缩性并保证用户隐私的同时，已接近最佳解决方案。