Year: 2012
Type: preprint
Abstract: We show that the left/right relation on the set of s-t-paths of a plane graph induces a so-called submodular lattice. If the embedding of the graph is s-t-planar, this lattice is even consecutive. This implies that Ford and Fulkerson's uppermost path algorithm for maximum flow in such graphs is indeed a special case of a two-phase greedy algorithm on lattice polyhedra. We also show that the properties submodularity and consecutivity cannot be achieved simultaneously by any partial order on the paths if the graph is planar but not s-t-planar, thus providing a characterization of this class of graphs.
Source: arXiv (Cornell University)
Authors: Matuschke, Jannik, Peis, Britta
Institution: Technische Universität Berlin
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2404526054