Figure 7
Example of network graph and matchings under the 
-hop interference model, in which the greedy algorithm achieves no greater than 
of the optimal performance (
and 
). The subset 
are the edges inside the cycles. (Solid black edges in (a).) An instance of maximal matching for 
is shown in (c). Active edges are marked in red. By circulating the active edges in (c), we can obtain similar maximal matchings. Assume that 
consists of those maximal matching with an identical weight. Similarly we can construct 
from maximal matchings like (d). Note that both 
and 
serve all edges in 
for the same amount of time, but a maximal matching of 
has 
times more active edges than a maximal matching of 
. Hence, it can be shown that 
for all 
. To make sure that the schedule of (d) is maximal, we color vertices interfered by the active edge in the upper wheel in black, and vertices interfered by the active edge in the lower wheel in gray.Topology; horizontal edgesTopology; a part of vertical edgesA maximal matching of 
A maximal matching of 