TY - JOUR

T1 - The Partial Visibility Representation Extension Problem

AU - Chaplick, Steven

AU - Guspiel, Grzegorz

AU - Gutowski, Grzegorz

AU - Krawczyk, Tomasz

AU - Liotta, Giuseppe

N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2018

Y1 - 2018

N2 - 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) if and only if there is an unobstructed, vertical, epsilon-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, puts the bar psi (u) strictly below the bar psi (v) for each directed edge (u, v) of G. 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. of G with psi(v) = psi' (v) for every v is an element of V'. We show that for undirected graphs this problem, and other closely related problems, is NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time.

AB - 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) if and only if there is an unobstructed, vertical, epsilon-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, puts the bar psi (u) strictly below the bar psi (v) for each directed edge (u, v) of G. 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. of G with psi(v) = psi' (v) for every v is an element of V'. We show that for undirected graphs this problem, and other closely related problems, is NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time.

U2 - 10.1007/S00453-017-0322-4

DO - 10.1007/S00453-017-0322-4

M3 - Article

SN - 0178-4617

VL - 80

SP - 2286

EP - 2323

JO - Algorithmica

JF - Algorithmica

IS - 8

ER -