The Partial Visibility Representation Extension Problem
For a graph G , a function ψ is called a bar visibility representation of G when for each vertex v ∈ V ( G ) , ψ ( v ) is a horizontal line segment ( bar ) and u v ∈ E ( G ) if and only if there is an unobstructed, vertical, ε -wide line of sight between ψ ( u ) and ψ ( v ) . Graphs admitting such r...
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| Vydáno v: | Algorithmica Ročník 80; číslo 8; s. 2286 - 2323 |
|---|---|
| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.08.2018
Springer Nature B.V |
| Témata: | |
| ISSN: | 0178-4617, 1432-0541 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | For a graph
G
, a function
ψ
is called a
bar visibility representation
of
G
when for each vertex
v
∈
V
(
G
)
,
ψ
(
v
)
is a horizontal line segment (
bar
) and
u
v
∈
E
(
G
)
if and only if there is an unobstructed, vertical,
ε
-wide line of sight between
ψ
(
u
)
and
ψ
(
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
ψ
(
u
)
strictly below the bar
ψ
(
v
)
for each directed edge (
u
,
v
) of
G
. We study a generalization of the recognition problem where a function
ψ
′
defined on a subset
V
′
of
V
(
G
) is given and the question is whether there is a bar visibility representation
ψ
of
G
with
ψ
(
v
)
=
ψ
′
(
v
)
for every
v
∈
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. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0178-4617 1432-0541 |
| DOI: | 10.1007/s00453-017-0322-4 |