标题： 非齐次随机二分图的极值平面匹配 显示英文标题

标题： Extremal Planar Matchings of Inhomogenous Random Bipartite Graphs

摘要： 本文研究了非齐次随机二部图的最大匹配规模和最小权值匹配。 我们的研究动机来源于在中继网络中有效利用交叉边以全面提升网络性能。 首先我们考虑具有边长约束的伯努利平面匹配，并得到最大匹配规模的偏差估计。 接着我们将完备二部图的每条边赋以正随机权重，得到了包含指定数量边的平面匹配最小权值的界。 此外，我们还利用分割法和鞅方法得到了适当缩放与中心化的最小权值匹配的~\(L^2-\)收敛性。 显示英文摘要

摘要： In this paper we study maximum size and minimum weight planar matchings of inhomogenous random bipartite graphs. Our motivation for this study comes from efficient usage of cross edges in relay networks for overall improvement in network performance. We first consider Bernoulli planar matchings with a constraint on the edge length and obtain deviation estimates for the maximum size of a planar matching. We then equip each edge of the complete bipartite graph with a positive random weight and obtain bounds on the minimum weight of a planar matching containing a given number of edges. We also use segmentation and martingale methods to obtain~\(L^2-\)convergence of the minimum weight, appropriately scaled and centred.