Homology localization through the looking-glass of parameterized complexity theory

Homology localization means finding a cycle of lowest weight that represents a homology class in a simplicial complex. It is an NP-complete problem, which this paper addresses using parameterized complexity theory. We prove that to find even a constant factor approximation to this problem is W[1]-ha...

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Vydáno v:Journal of applied and computational topology Ročník 9; číslo 2
Hlavní autoři: Blaser, Nello, Vågset, Erlend Raa
Médium: Journal Article
Jazyk:angličtina
Vydáno: 01.06.2025
ISSN:2367-1726, 2367-1734
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Abstract Homology localization means finding a cycle of lowest weight that represents a homology class in a simplicial complex. It is an NP-complete problem, which this paper addresses using parameterized complexity theory. We prove that to find even a constant factor approximation to this problem is W[1]-hard when solution size is used as a parameter. We have also designed and implemented two new algorithms that are fixed parameter tractable when parameterized by the treewidth of graphs associated to the simplicial complex. The running time of both algorithms matches the lower bounds we obtain from the exponential time hypothesis. We analysed the performance of the two algorithms experimentally and found that one algorithm is significantly faster than the other.
AbstractList Homology localization means finding a cycle of lowest weight that represents a homology class in a simplicial complex. It is an NP-complete problem, which this paper addresses using parameterized complexity theory. We prove that to find even a constant factor approximation to this problem is W[1]-hard when solution size is used as a parameter. We have also designed and implemented two new algorithms that are fixed parameter tractable when parameterized by the treewidth of graphs associated to the simplicial complex. The running time of both algorithms matches the lower bounds we obtain from the exponential time hypothesis. We analysed the performance of the two algorithms experimentally and found that one algorithm is significantly faster than the other.
ArticleNumber 16
Author Vågset, Erlend Raa
Blaser, Nello
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Cites_doi 10.1007/978-3-642-31155-0_17
10.1137/130947374
10.1007/s00454-010-9322-8
10.1007/978-3-319-21275-3
10.1090/S0273-0979-09-01249-X
10.1137/1.9781611973082.61
10.1109/ICIP.2016.7533141
10.1145/1080810.1080819
10.1137/S0097539793251219
10.1090/dimacs/049/04
10.1007/978-3-319-59050-9_7
10.1142/S0219467801000037
10.4230/LIPIcs.IPEC.2017.30
10.1017/9781316671665
10.1145/1542362.1542426
10.24963/ijcai.2019/182
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References 212_CR20
Hans L Bodlaender (212_CR2) 1996; 25
212_CR10
HL Bodlaender (212_CR3) 2016; 45
212_CR12
O Busaryev (212_CR5) 2012
212_CR13
212_CR14
212_CR15
G Carlsson (212_CR6) 2009; 46
RG Downey (212_CR11) 2012
212_CR1
212_CR4
212_CR16
212_CR17
212_CR18
212_CR19
212_CR7
C Chen (212_CR8) 2011; 45
212_CR9
References_xml – start-page: 189
  volume-title: Algorithm Theory – SWAT 2012
  year: 2012
  ident: 212_CR5
  doi: 10.1007/978-3-642-31155-0_17
– ident: 212_CR15
– volume: 45
  start-page: 317
  issue: 2
  year: 2016
  ident: 212_CR3
  publication-title: SIAM J. Comput.
  doi: 10.1137/130947374
– volume-title: Parameterized Complexity
  year: 2012
  ident: 212_CR11
– ident: 212_CR4
– ident: 212_CR1
– volume: 45
  start-page: 425
  issue: 3
  year: 2011
  ident: 212_CR8
  publication-title: Discrete & Computational Geometry
  doi: 10.1007/s00454-010-9322-8
– ident: 212_CR9
  doi: 10.1007/978-3-319-21275-3
– volume: 46
  start-page: 255
  issue: 2
  year: 2009
  ident: 212_CR6
  publication-title: Bull. Amer. Math. Soc. (N.S.)
  doi: 10.1090/S0273-0979-09-01249-X
– ident: 212_CR16
  doi: 10.1137/1.9781611973082.61
– ident: 212_CR18
  doi: 10.1109/ICIP.2016.7533141
– ident: 212_CR13
  doi: 10.1145/1080810.1080819
– volume: 25
  start-page: 1305
  issue: 6
  year: 1996
  ident: 212_CR2
  publication-title: SIAM J. Comput.
  doi: 10.1137/S0097539793251219
– ident: 212_CR12
  doi: 10.1090/dimacs/049/04
– ident: 212_CR19
  doi: 10.1007/978-3-319-59050-9_7
– ident: 212_CR14
  doi: 10.1142/S0219467801000037
– ident: 212_CR10
  doi: 10.4230/LIPIcs.IPEC.2017.30
– ident: 212_CR17
  doi: 10.1017/9781316671665
– ident: 212_CR7
  doi: 10.1145/1542362.1542426
– ident: 212_CR20
  doi: 10.24963/ijcai.2019/182
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