The Edge Versus Path Incidence Matrix of Series Parallel Graphs and Greedy Packing

We characterise the edge versus path incidence matrix of a series parallel graph. One characterization is algorithmic while the second is structural. The structural characterization implies that the greedy algorithm solves the max flow problem in series parallel graphs, as shown by [Bein, Brucker and Tamir, 1985]. The algorithmic characterization gives an efficient way to identify such matrices. [Hoffman and Tucker, 1988] proved that a packing problem defined by a (0,1) matrix in which no column contains another column can be solved optimally using a greedy algorithm with any permutation on the variables if and only if the (0,1) matrix is the edge versus path incidence matrix of a series parallel graph. Thus, our algorithm can be applied to check whether such a packing problem is solvable greedily.