The Partial Visibility Representation Extension Problem

Steven Chaplick*, Grzegorz Guspiel, Grzegorz Gutowski, Tomasz Krawczyk, Giuseppe Liotta

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


For a graph G, a function psi is called a bar visibility representation of G when for each vertex v is an element of V (G), psi(v) is a horizontal line segment (bar) and uv is an element of E(G) iff there is an unobstructed, vertical, e-wide line of sight between psi(u) and psi(v). Graphs admitting such representations are well understood (via simple characterizations) and recognizable in linear time. For a directed graph G, a bar visibility representation. of G, additionally, for each directed edge (u, v) of G, puts the bar.(u) strictly below the bar.(v). We study a generalization of the recognition problem where a function psi' defined on a subset V' of V (G) is given and the question is whether there is a bar visibility representation psi of G with psi vertical bar V' = psi'. We show that for undirected graphs this problem together with closely related problems are NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time.
Original languageEnglish
Title of host publicationGraph Drawing and Network Visualization. GD 2016
EditorsY. Hu, M. Nöllenburg
Publication statusPublished - 2016
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science

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