Simple algorithms for partial and simultaneous rectangular duals with given contact orientations

A rectangular dual of a graph G is contact representation by axis-aligned rectangles such that (i) no four share point and (ii) the union all rectangle. The partial extension problem for duals asks whether given can be extended to dual, is, there exists where some vertices are represented prescribed rectangles. simultaneous two (or more) graphs subgraph admit coincide on shared subgraph. Combinatorially, described regular edge labeling (REL), which determines orientations rectangle contacts. We describe linear-time algorithms when each input together with REL. Both based formulations as linear programs, yet they have geometric interpretations seen extensions classic algorithm Kant He computes graph.