Recovery of disrupted airline operations using k-maximum matching in graphs

When an aircraft is approaching airport, it gets a short time interval called slot by Air Traffic Control that can use to land. If the landing of delayed for some reason, loses its and Airline Operation Controllers have assign new one. However, slots are scarce resource airports and, in order avoid waits too long, regularly modify assignment aircraft. Due system implemented exchange slots, controllers slot-assignment using only two kinds operations: either was free A, or give another B A B. The problem then be modelled as follows. Let k?1 odd integer, let G graph M matching G, i.e., set pairwise disjoint edges. k-maximum largest possible obtained from augmenting paths length at most k. This has already been studied context wireless networks, mainly because provides simple approximation maximum problem. paper polynomial-time algorithm when k?3. We prove NP-hard planar bipartite graphs with degree 3 any integer k?5.