In a cost sharing problem on a weighted undirected graph, all other nodes want to connect to the source node for some service. Each edge has a cost denoted by a weight and all the connected nodes should share the total cost for the connectivity. The goal of the existing solutions (e.g. folk solution and cycle-complete solution) is to design cost sharing rules with nice properties, e.g. budget balance and cost monotonicity. However, they did not consider the cases that each non-source node has a budget which is the maximum it can pay for its cost share and may cut its adjacent edges to reduce its cost share. In this paper, we design two cost sharing mechanisms taking into account the nodes' budgets and incentivizing all nodes to report all their adjacent edges so that we can minimize the total cost for the connectivity.

翻译：在加权无向图上的成本分摊问题中，所有非源节点希望连接到源节点以获取某种服务。每条边具有一个以权重表示的成本，所有连接的节点需共同承担连接总成本。现有解决方案（如folk解和cycle-complete解）的目标是设计具有良好性质的成本分摊规则，例如预算平衡性和成本单调性。然而，这些方案未考虑每个非源节点具有预算（即其可支付成本份额的上限），且节点可能切断其相邻边以降低自身成本份额的情况。本文设计了两种成本分摊机制，该机制考虑了节点的预算限制，并激励所有节点如实报告其所有相邻边，从而最小化连接总成本。