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 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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 uv∈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. 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. |
| Author | Gutowski, Grzegorz Guśpiel, Grzegorz Chaplick, Steven Krawczyk, Tomasz Liotta, Giuseppe |
| Author_xml | – sequence: 1 givenname: Steven orcidid: 0000-0003-3501-4608 surname: Chaplick fullname: Chaplick, Steven organization: Lehrstuhl für Informatik I, Universität Würzburg – sequence: 2 givenname: Grzegorz orcidid: 0000-0002-3303-8107 surname: Guśpiel fullname: Guśpiel, Grzegorz organization: Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University – sequence: 3 givenname: Grzegorz orcidid: 0000-0003-3313-1237 surname: Gutowski fullname: Gutowski, Grzegorz email: gutowski@tcs.uj.edu.pl organization: Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University – sequence: 4 givenname: Tomasz surname: Krawczyk fullname: Krawczyk, Tomasz organization: Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University – sequence: 5 givenname: Giuseppe surname: Liotta fullname: Liotta, Giuseppe organization: Universitá degli Studi di Perugia |
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| CitedBy_id | crossref_primary_10_1016_j_comgeo_2020_101668 crossref_primary_10_1016_j_comgeo_2019_101592 crossref_primary_10_1007_s00454_022_00394_9 crossref_primary_10_1016_j_dam_2025_07_009 crossref_primary_10_1016_j_tcs_2022_03_031 |
| Cites_doi | 10.1142/S0129054106004261 10.1016/S0304-3975(95)00257-X 10.1007/BF02122694 10.1016/j.tcs.2012.02.010 10.1016/S0020-0190(97)00048-3 10.1142/S0218195912500045 10.1016/0166-218X(92)90018-6 10.1016/0020-0190(95)00020-D 10.1007/s00454-010-9310-z 10.1007/s00454-016-9831-1 10.1007/978-3-540-77974-2 10.1145/2543581.2543589 10.1137/S0895480198343455 10.1007/BF02187850 10.7155/jgaa.00260 10.1007/BF02187705 10.1145/2629341 10.1016/0012-365X(93)90340-Y 10.1002/net.3230020103 10.1016/0012-365X(83)90128-0 10.1016/0022-0000(89)90034-2 10.1007/BF01108622 10.1137/S0097539794280736 10.1145/2738054 10.1137/S0097539794277123 10.1016/0304-3975(88)90123-5 10.1002/net.3230140202 10.1017/S0963548300001139 10.1016/j.tcs.2015.02.007 10.1016/0012-365X(91)90069-E 10.1016/0012-365X(87)90190-7 10.1007/978-3-319-12340-0_12 10.1007/978-3-642-33090-2_58 10.1007/s00453-016-0186-z 10.1145/800017.800517 10.1145/323233.323253 10.1145/62212.62254 10.1007/s00453-016-0133-z 10.1007/978-3-319-50106-2_21 10.1007/978-3-319-03841-4_12 10.1007/3-540-44541-2_8 |
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| Keywords | Bar visibility SPQR-trees St-ordering Partial representation extension Planar graphs NP-completeness |
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| Snippet | 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... 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 uv∈E(G) if... |
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| SubjectTerms | Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Graph theory Graphical representations Graphs Mathematics of Computing Set theory Theory of Computation Visibility |
| Title | The Partial Visibility Representation Extension Problem |
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