A Simpler Self-reduction Algorithm for Matroid Path-width
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F18%3A00101457" target="_blank" >RIV/00216224:14330/18:00101457 - isvavai.cz</a>
Result on the web
<a href="http://arxiv.org/abs/1605.09520" target="_blank" >http://arxiv.org/abs/1605.09520</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/17M1120129" target="_blank" >10.1137/17M1120129</a>
Alternative languages
Result language
angličtina
Original language name
A Simpler Self-reduction Algorithm for Matroid Path-width
Original language description
The path-width of matroids naturally generalizes the better known parameter of path-width for graphs and is NP-hard by a reduction from the graph case. While the term matroid path-width was formally introduced in [J. Geelen, B. Gerards, and G. Whittle, J. Combin. Theory Ser. B, 96 (2006), pp. 405-425] in pure matroid theory, it was soon recognized in [N. Kashyap, SIAM J. Discrete Math., 22 (2008), pp. 256-272] that it is the same concept as the long-studied so-called trellis complexity in coding theory, later named trellis-width, and hence it is an interesting notion also from the algorithmic perspective. It follows from a result of Hlineny [P. Hlieny, J. Combin. Theory Ser. B, 96 (2006), pp. 325-351] that the decision problem-whether a given matroid over a finite field has path-width at most t-is fixed-parameter tractable (FPT) in t, but this result does not give any clue about constructing a path-decomposition. The first constructive and rather complicated FPT algorithm for path-width of matroids over a finite field was given in [J. Jeong, E. J. Kim, and S. Oum, in Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2016, pp. 1695-1704]. Here we propose a simpler "self-reduction" FPT algorithm for a path-decomposition. Precisely, we design an efficient routine that constructs an optimal pathdecomposition of a matroid by calling any subroutine for testing whether the path-width of a matroid is at most t (such as the aforementioned decision algorithm for matroid path-width).
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA17-00837S" target="_blank" >GA17-00837S: Structural properties, parameterized tractability and hardness in combinatorial problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Discrete Mathematics
ISSN
0895-4801
e-ISSN
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Volume of the periodical
32
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
1425-1440
UT code for WoS article
000436975900037
EID of the result in the Scopus database
2-s2.0-85049597399