Yi Zhou, Parikshit Ram, et al.
ICLR 2023
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.
Yi Zhou, Parikshit Ram, et al.
ICLR 2023
Alan J. Hoffman
J. Comb. Theory Ser. A
Peter Wendt
Electronic Imaging: Advanced Devices and Systems 1990
Elizabeth A. Sholler, Frederick M. Meyer, et al.
SPIE AeroSense 1997