W.C. Tang, H. Rosen, et al.
SPIE Optics, Electro-Optics, and Laser Applications in Science and Engineering 1991
We characterize 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 et al. (Discrete Appl. Math. 10 (1985) 117-124). The algorithmic characterization gives an efficient way to identify such matrices. Hoffman and Tucker (J. Combin. Theory Ser. A 47 (1988) 6-5). 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. © 2001 Elsevier Science B.V.
W.C. Tang, H. Rosen, et al.
SPIE Optics, Electro-Optics, and Laser Applications in Science and Engineering 1991
R.B. Morris, Y. Tsuji, et al.
International Journal for Numerical Methods in Engineering
Salvatore Certo, Anh Pham, et al.
Quantum Machine Intelligence
I.K. Pour, D.J. Krajnovich, et al.
SPIE Optical Materials for High Average Power Lasers 1992