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The Complexity of L(p, q)-Edge-Labelling
The L ( p , q )- Edge-Labelling problem is the edge variant of the well-known L ( p , q )- Labelling problem. It is equivalent to the L ( p , q )- Labelling problem itself if we restrict the input of the latter problem to line graphs. So far, the complexity of L ( p , q )- Edge-Labelling was onl...
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| Published in: | Algorithmica 2023-11, Vol.85 (11), p.3406-3429 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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| container_end_page | 3429 |
| container_issue | 11 |
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| container_title | Algorithmica |
| container_volume | 85 |
| creator | Berthe, Gaétan Martin, Barnaby Paulusma, Daniël Smith, Siani |
| description | The
L
(
p
,
q
)-
Edge-Labelling
problem is the edge variant of the well-known
L
(
p
,
q
)-
Labelling
problem. It is equivalent to the
L
(
p
,
q
)-
Labelling
problem itself if we restrict the input of the latter problem to line graphs. So far, the complexity of
L
(
p
,
q
)-
Edge-Labelling
was only partially classified in the literature. We complete this study for all
p
,
q
≥
0
by showing that whenever
(
p
,
q
)
≠
(
0
,
0
)
, the
L
(
p
,
q
)-
Edge-Labelling
problem is NP-complete. We do this by proving that for all
p
,
q
≥
0
except
p
=
q
=
0
, there is an integer
k
so that
L
(
p
,
q
)-Edge-
k
-Labelling
is NP-complete. |
| doi_str_mv | 10.1007/s00453-023-01120-4 |
| format | article |
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L
(
p
,
q
)-
Edge-Labelling
problem is the edge variant of the well-known
L
(
p
,
q
)-
Labelling
problem. It is equivalent to the
L
(
p
,
q
)-
Labelling
problem itself if we restrict the input of the latter problem to line graphs. So far, the complexity of
L
(
p
,
q
)-
Edge-Labelling
was only partially classified in the literature. We complete this study for all
p
,
q
≥
0
by showing that whenever
(
p
,
q
)
≠
(
0
,
0
)
, the
L
(
p
,
q
)-
Edge-Labelling
problem is NP-complete. We do this by proving that for all
p
,
q
≥
0
except
p
=
q
=
0
, there is an integer
k
so that
L
(
p
,
q
)-Edge-
k
-Labelling
is NP-complete.</description><identifier>ISSN: 0178-4617</identifier><identifier>EISSN: 1432-0541</identifier><identifier>DOI: 10.1007/s00453-023-01120-4</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithm Analysis and Problem Complexity ; Algorithms ; Complexity ; Computer Science ; Computer Systems Organization and Communication Networks ; Data Structures and Information Theory ; Labeling ; Mathematics of Computing ; Theory of Computation</subject><ispartof>Algorithmica, 2023-11, Vol.85 (11), p.3406-3429</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-c5631b5ef19f03a61b65907f9ae390fc1770ea5e6d6af861c3faa30c32524c8d3</cites><orcidid>0000-0002-4642-8614</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Berthe, Gaétan</creatorcontrib><creatorcontrib>Martin, Barnaby</creatorcontrib><creatorcontrib>Paulusma, Daniël</creatorcontrib><creatorcontrib>Smith, Siani</creatorcontrib><title>The Complexity of L(p, q)-Edge-Labelling</title><title>Algorithmica</title><addtitle>Algorithmica</addtitle><description>The
L
(
p
,
q
)-
Edge-Labelling
problem is the edge variant of the well-known
L
(
p
,
q
)-
Labelling
problem. It is equivalent to the
L
(
p
,
q
)-
Labelling
problem itself if we restrict the input of the latter problem to line graphs. So far, the complexity of
L
(
p
,
q
)-
Edge-Labelling
was only partially classified in the literature. We complete this study for all
p
,
q
≥
0
by showing that whenever
(
p
,
q
)
≠
(
0
,
0
)
, the
L
(
p
,
q
)-
Edge-Labelling
problem is NP-complete. We do this by proving that for all
p
,
q
≥
0
except
p
=
q
=
0
, there is an integer
k
so that
L
(
p
,
q
)-Edge-
k
-Labelling
is NP-complete.</description><subject>Algorithm Analysis and Problem Complexity</subject><subject>Algorithms</subject><subject>Complexity</subject><subject>Computer Science</subject><subject>Computer Systems Organization and Communication Networks</subject><subject>Data Structures and Information Theory</subject><subject>Labeling</subject><subject>Mathematics of Computing</subject><subject>Theory of Computation</subject><issn>0178-4617</issn><issn>1432-0541</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KAzEUhYMoWKsv4KrgxoLRe_M7WUqpPzDgpq5Dmia1ZdqZJlOwb-Oz-GSOjuDOxeVszncufIRcItwigL7LAEJyCqw7RAZUHJEBCs4oSIHHZACoCyoU6lNylvMaAJk2akDGs7cwmtSbpgrvq_YwquOovG5uPj92YzpdLAMt3TxU1Wq7PCcn0VU5XPzmkLw-TGeTJ1q-PD5P7kvqmYaWeqk4zmWIaCJwp3CupAEdjQvcQPSoNQQng1ooFwuFnkfnOHjOJBO-WPAhuep3m1Tv9iG3dl3v07Z7aVlRCGVMAbxrsb7lU51zCtE2abVx6WAR7LcS2yuxnRL7o8SKDuI9lLvydhnS3_Q_1BfMNGGm</recordid><startdate>20231101</startdate><enddate>20231101</enddate><creator>Berthe, Gaétan</creator><creator>Martin, Barnaby</creator><creator>Paulusma, Daniël</creator><creator>Smith, Siani</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-4642-8614</orcidid></search><sort><creationdate>20231101</creationdate><title>The Complexity of L(p, q)-Edge-Labelling</title><author>Berthe, Gaétan ; Martin, Barnaby ; Paulusma, Daniël ; Smith, Siani</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-c5631b5ef19f03a61b65907f9ae390fc1770ea5e6d6af861c3faa30c32524c8d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algorithm Analysis and Problem Complexity</topic><topic>Algorithms</topic><topic>Complexity</topic><topic>Computer Science</topic><topic>Computer Systems Organization and Communication Networks</topic><topic>Data Structures and Information Theory</topic><topic>Labeling</topic><topic>Mathematics of Computing</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Berthe, Gaétan</creatorcontrib><creatorcontrib>Martin, Barnaby</creatorcontrib><creatorcontrib>Paulusma, Daniël</creatorcontrib><creatorcontrib>Smith, Siani</creatorcontrib><collection>CrossRef</collection><jtitle>Algorithmica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Berthe, Gaétan</au><au>Martin, Barnaby</au><au>Paulusma, Daniël</au><au>Smith, Siani</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Complexity of L(p, q)-Edge-Labelling</atitle><jtitle>Algorithmica</jtitle><stitle>Algorithmica</stitle><date>2023-11-01</date><risdate>2023</risdate><volume>85</volume><issue>11</issue><spage>3406</spage><epage>3429</epage><pages>3406-3429</pages><issn>0178-4617</issn><eissn>1432-0541</eissn><abstract>The
L
(
p
,
q
)-
Edge-Labelling
problem is the edge variant of the well-known
L
(
p
,
q
)-
Labelling
problem. It is equivalent to the
L
(
p
,
q
)-
Labelling
problem itself if we restrict the input of the latter problem to line graphs. So far, the complexity of
L
(
p
,
q
)-
Edge-Labelling
was only partially classified in the literature. We complete this study for all
p
,
q
≥
0
by showing that whenever
(
p
,
q
)
≠
(
0
,
0
)
, the
L
(
p
,
q
)-
Edge-Labelling
problem is NP-complete. We do this by proving that for all
p
,
q
≥
0
except
p
=
q
=
0
, there is an integer
k
so that
L
(
p
,
q
)-Edge-
k
-Labelling
is NP-complete.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00453-023-01120-4</doi><tpages>24</tpages><orcidid>https://orcid.org/0000-0002-4642-8614</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0178-4617 |
| ispartof | Algorithmica, 2023-11, Vol.85 (11), p.3406-3429 |
| issn | 0178-4617 1432-0541 |
| language | eng |
| recordid | cdi_proquest_journals_2884699803 |
| source | Springer Nature |
| subjects | Algorithm Analysis and Problem Complexity Algorithms Complexity Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Labeling Mathematics of Computing Theory of Computation |
| title | The Complexity of L(p, q)-Edge-Labelling |
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