Scheduling Wireless Links in the Physical Interference Model by Fractional Edge Coloring

We consider the link scheduling problem in wireless mesh networks for capacity maximization. Unlike all previous approaches, ours views capacity in terms of covering a graph's edges by matchings that are feasible in the sense of the physical interference model, thus leading to a novel fractional edge-chromatic indicator of the graph. Network capacity is then defined as a function of this indicator, whose exact computation can be formulated as a linear programming problem. Solving this problem for an extensive collection of random geometric graphs that instantiate networks in the physical interference model reveals that, depending on node density, often a network admits increased capacity by virtue of simply scheduling links based on fractional, rather than integer, edge coloring. This settles a heretofore unaddressed issue in the physical interference model.