Parameterised and Fine-Grained Subgraph Counting, Modulo 2
Given a class of graphs H , the problem ⊕ Sub ( H ) is defined as follows. The input is a graph H ∈ H together with an arbitrary graph G . The problem is to compute, modulo 2, the number of subgraphs of G that are isomorphic to H . The goal of this research is to determine for which classes H the pr...
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| Veröffentlicht in: | Algorithmica Jg. 86; H. 4; S. 944 - 1005 |
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01.04.2024
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| Abstract | Given a class of graphs
H
, the problem
⊕
Sub
(
H
)
is defined as follows. The input is a graph
H
∈
H
together with an arbitrary graph
G
. The problem is to compute, modulo 2, the number of subgraphs of
G
that are isomorphic to
H
. The goal of this research is to determine for which classes
H
the problem
⊕
Sub
(
H
)
is fixed-parameter tractable (FPT), i.e., solvable in time
f
(
|
H
|
)
·
|
G
|
O
(
1
)
. Curticapean, Dell, and Husfeldt (ESA 2021) conjectured that
⊕
Sub
(
H
)
is FPT if and only if the class of allowed patterns
H
is
matching splittable
, which means that for some fixed
B
, every
H
∈
H
can be turned into a matching (a graph in which every vertex has degree at most 1) by removing at most
B
vertices. Assuming the randomised Exponential Time Hypothesis, we prove their conjecture for (I) all hereditary pattern classes
H
, and (II) all tree pattern classes, i.e., all classes
H
such that every
H
∈
H
is a tree. We also establish almost tight fine-grained upper and lower bounds for the case of hereditary patterns (I). |
|---|---|
| AbstractList | Given a class of graphs
$${\mathcal {H}}$$
H
, the problem
$$\oplus \text {{Sub}}({\mathcal {H}})$$
⊕
Sub
(
H
)
is defined as follows. The input is a graph
$$H\in {\mathcal {H}}$$
H
∈
H
together with an arbitrary graph
G
. The problem is to compute, modulo 2, the number of subgraphs of
G
that are isomorphic to
H
. The goal of this research is to determine for which classes
$${\mathcal {H}}$$
H
the problem
$$\oplus \text {{Sub}}({\mathcal {H}})$$
⊕
Sub
(
H
)
is fixed-parameter tractable (FPT), i.e., solvable in time
$$f(|H|)\cdot |G|^{O(1)}$$
f
(
|
H
|
)
·
|
G
|
O
(
1
)
. Curticapean, Dell, and Husfeldt (ESA 2021) conjectured that
$$\oplus \text {{Sub}}({\mathcal {H}})$$
⊕
Sub
(
H
)
is FPT if and only if the class of allowed patterns
$${\mathcal {H}}$$
H
is
matching splittable
, which means that for some fixed
B
, every
$$H \in {\mathcal {H}}$$
H
∈
H
can be turned into a matching (a graph in which every vertex has degree at most 1) by removing at most
B
vertices. Assuming the randomised Exponential Time Hypothesis, we prove their conjecture for (I) all hereditary pattern classes
$${\mathcal {H}}$$
H
, and (II) all tree pattern classes, i.e., all classes
$${\mathcal {H}}$$
H
such that every
$$H\in {\mathcal {H}}$$
H
∈
H
is a tree. We also establish almost tight fine-grained upper and lower bounds for the case of hereditary patterns (I). Given a class of graphs H , the problem ⊕ Sub ( H ) is defined as follows. The input is a graph H ∈ H together with an arbitrary graph G . The problem is to compute, modulo 2, the number of subgraphs of G that are isomorphic to H . The goal of this research is to determine for which classes H the problem ⊕ Sub ( H ) is fixed-parameter tractable (FPT), i.e., solvable in time f ( | H | ) · | G | O ( 1 ) . Curticapean, Dell, and Husfeldt (ESA 2021) conjectured that ⊕ Sub ( H ) is FPT if and only if the class of allowed patterns H is matching splittable , which means that for some fixed B , every H ∈ H can be turned into a matching (a graph in which every vertex has degree at most 1) by removing at most B vertices. Assuming the randomised Exponential Time Hypothesis, we prove their conjecture for (I) all hereditary pattern classes H , and (II) all tree pattern classes, i.e., all classes H such that every H ∈ H is a tree. We also establish almost tight fine-grained upper and lower bounds for the case of hereditary patterns (I). Given a class of graphs H, the problem ⊕Sub(H) is defined as follows. The input is a graph H∈H together with an arbitrary graph G. The problem is to compute, modulo 2, the number of subgraphs of G that are isomorphic to H. The goal of this research is to determine for which classes H the problem ⊕Sub(H) is fixed-parameter tractable (FPT), i.e., solvable in time f(|H|)·|G|O(1). Curticapean, Dell, and Husfeldt (ESA 2021) conjectured that ⊕Sub(H) is FPT if and only if the class of allowed patterns H is matching splittable, which means that for some fixed B, every H∈H can be turned into a matching (a graph in which every vertex has degree at most 1) by removing at most B vertices. Assuming the randomised Exponential Time Hypothesis, we prove their conjecture for (I) all hereditary pattern classes H, and (II) all tree pattern classes, i.e., all classes H such that every H∈H is a tree. We also establish almost tight fine-grained upper and lower bounds for the case of hereditary patterns (I). |
| Author | Roth, Marc Goldberg, Leslie Ann |
| Author_xml | – sequence: 1 givenname: Leslie Ann surname: Goldberg fullname: Goldberg, Leslie Ann organization: Department of Computer Science, University of Oxford – sequence: 2 givenname: Marc surname: Roth fullname: Roth, Marc email: marc.roth.cs@gmail.com organization: Department of Computer Science, University of Oxford |
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| Cites_doi | 10.4230/LIPIcs.MFCS.2021.84 10.1007/978-3-662-47672-7_19 10.1145/3055399.3055502 10.4230/LIPIcs.ICALP.2021.108 10.1007/978-1-4471-5559-1 10.1137/1.9781611973730.111 10.1109/FOCS.2014.22 10.1007/978-3-642-39206-1_30 10.1016/j.ic.2005.05.001 10.1006/jcss.2000.1727 10.4230/LIPIcs.ESA.2021.34 10.1137/S0097539703427203 10.1098/rsif.2010.0063 10.1145/3038912.3052653 10.1007/978-3-319-21275-3 10.1145/3519935.3520075 10.1145/3520240 10.1007/978-3-319-21233-3_5 10.1145/210332.210337 10.1016/j.jctb.2018.03.007 10.1038/ncomms3241 10.1016/j.tcs.2004.08.008 10.1137/1.9781611973730.42 10.1007/978-3-540-70575-8_48 10.1007/s00453-021-00811-0 10.1093/bioinformatics/btn163 10.4230/LIPIcs.ICALP.2020.5 10.1007/s00453-021-00894-9 10.1007/3-540-29953-X 10.1137/0220053 10.1016/j.jctb.2008.06.004 10.1126/science.298.5594.824 10.1016/j.jcss.2006.04.007 10.1126/science.1089167 |
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| Keywords | Theory of computation Problems Subgraph counting Fine-grained complexity Parameterised complexity reductions and completeness Mathematics of computing Discrete mathematics Modular counting |
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| References | Flum, J., Grohe, M.: Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series. Springer (2006). https://doi.org/10.1007/3-540-29953-X TranNHChoiKPZhangLCounting motifs in the human interactomeNat. Commun.2013411810.1038/ncomms3241 GroheMMarxDOn tree width, bramble size, and expansionJ. Comb. Theory Ser. B2009991218228246782710.1016/j.jctb.2008.06.004 Curticapean, R., Marx, D.: Complexity of counting subgraphs: only the boundedness of the vertex-cover number counts. In: 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, Philadelphia, PA, USA, October 18–21, 2014, pp. 130–139. IEEE Computer Society (2014). https://doi.org/10.1109/FOCS.2014.22 DörflerJRothMSchmittJWellnitzPCounting induced subgraphs: An algebraic approach to #w[1]-hardnessAlgorithmica2022842379404438171610.1007/s00453-021-00894-9 AlonNYusterRZwickUColor-codingJ. ACM1995424844856141178710.1145/210332.210337 Chen, Y., Thurley, M., Weyer, M.: Understanding the complexity of induced subgraph isomorphisms. In: Proceedings of the 35th International Colloquium on Automata, Languages and Programming (ICALP), pp. 587–596. Springer (2008). https://doi.org/10.1007/978-3-540-70575-8_48 Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer (2013). https://doi.org/10.1007/978-1-4471-5559-1 Roth, M., Schmitt, J., Wellnitz, P.: Detecting and counting small subgraphs, and evaluating a parameterized Tutte polynomial: lower bounds via toroidal grids and Cayley graph expanders. CoRR arXiv:2011.03433 (2020) Curticapean, R., Dell, H., Husfeldt, T.: Modular counting of subgraphs: matchings, matching-splittable graphs, and paths. In: Mutzel, P., Pagh, R., Herman, G. (eds.) 29th Annual European Symposium on Algorithms, ESA 2021, September 6–8, 2021, Lisbon, Portugal (Virtual Conference), LIPIcs, vol. 204, pp. 1–17. Schloss Dagstuhl—Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.ESA.2021.34 ImpagliazzoRPaturiROn the complexity of k-satJ. Comput. Syst. Sci.2001622367375182059710.1006/jcss.2000.1727 AlonNDaoPHajirasoulihaIHormozdiariFCenk SahinalpSBiomolecular network motif counting and discovery by color codingBioinformatics20082413i241i24910.1093/bioinformatics/btn163 Curticapean, R.: Counting matchings of size k is w[1]-hard. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M.Z., Peleg, D. (eds.) Automata, Languages, and Programming—40th International Colloquium, ICALP 2013, Riga, Latvia, July 8–12, 2013, Proceedings, Part I, Lecture Notes in Computer Science, vol. 7965, pp. 352–363. Springer (2013). https://doi.org/10.1007/978-3-642-39206-1_30 Peyerimhoff, N., Roth, M., Schmitt, J., Stix, J., Vdovina, A., Wellnitz, P.: Parameterized counting and Cayley graph expanders. SIAM J. Discrete Math., to appear HarveyDJWoodDRThe treewidth of line graphsJ. Comb. Theory Ser. B2018132157179382030210.1016/j.jctb.2018.03.007 ChenJHuangXKanjIAXiaGStrong computational lower bounds via parameterized complexityJ. Comput. Syst. Sci.200672813461367227341210.1016/j.jcss.2006.04.007 Williams, V.V., Wang, J.R., Williams, R.R., Yu, H.: Finding four-node subgraphs in triangle time. In: Indyk, P. (ed.) Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4–6, 2015, pp. 1671–1680. SIAM (2015). https://doi.org/10.1137/1.9781611973730.111 Björklund, A., Dell, H., Husfeldt, T.: The parity of set systems under random restrictions with applications to exponential time problems. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) Automata, Languages, and Programming—42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6–10, 2015, Proceedings, Part I, Lecture Notes in Computer Science, vol. 9134, pp. 231–242. Springer (2015). https://doi.org/10.1007/978-3-662-47672-7_19 Abboud, A., Feller, S., Weimann, O.: On the fine-grained complexity of parity problems. In: Czumaj, A., Dawar, A., Merelli, E. (eds.) 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, July 8–11, 2020, Saarbrücken, Germany (Virtual Conference), LIPIcs, vol. 168, pp. 1–19. Schloss Dagstuhl—Leibniz-Zentrum für Informatik (2020). https://doi.org/10.4230/LIPIcs.ICALP.2020.5 Cygan, M., Fomin, F.V., Kowalik, L., Lokshtanov, D., Marx, D., Pilipczuk, M., Pilipczuk, M., Saurabh, S.: Parameterized Algorithms. Springer (2015). https://doi.org/10.1007/978-3-319-21275-3 Curticapean, R., Dell, H., Marx, D.: Homomorphisms are a good basis for counting small subgraphs. In: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (STOC), pp. 210–223. ACM (2017). https://doi.org/10.1145/3055399.3055502 Jansen, B.M.P., Marx, D.: Characterizing the easy-to-find subgraphs from the viewpoint of polynomial-time algorithms, kernels, and turing kernels. In: Indyk, P. (ed.) Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4–6, 2015, pp. 616–629. SIAM (2015). https://doi.org/10.1137/1.9781611973730.42 MiloRItzkovitzSKashtanNLevittRShen-OrrSAyzenshtatIShefferMAlonUSuperfamilies of evolved and designed networksScience200430356631538154210.1126/science.1089167 Peyerimhoff, N., Roth, M., Schmitt, J., Stix, J., Vdovina, A.: Parameterized (modular) counting and Cayley graph expanders. CoRR arXiv:2104.14596 (2021) DalmauVJonssonPThe complexity of counting homomorphisms seen from the other sideTheor. Comput. Sci.20043291–3315323210365510.1016/j.tcs.2004.08.008 Schiller, B., Jager, S., Hamacher, K., Strufe, T.: StreaM—a stream-based algorithm for counting motifs in dynamic graphs. In: Proceedings of the 2nd International Conference on Algorithms for Computational Biology (AlCoB), pp. 53–67 (2015). https://doi.org/10.1007/978-3-319-21233-3_5 MiloRShen-OrrSItzkovitzSKashtanNChklovskiiDAlonUNetwork motifs: simple building blocks of complex networksScience2002298559482482710.1126/science.298.5594.824 KuchaievOMilenkovićTMemiševićVHayesWPržuljNTopological network alignment uncovers biological function and phylogenyJ. R. Soc. Interface20107501341135410.1098/rsif.2010.0063 Bulatov, A.A., Kazeminia, A.: Complexity classification of counting graph homomorphisms modulo a prime number. In: Leonardi, S., Gupta, A. (eds.) STOC ’22: 54th Annual ACM SIGACT Symposium on Theory of Computing, Rome, Italy, June 20–24, 2022, pp. 1024–1037. ACM (2022). https://doi.org/10.1145/3519935.3520075 Peyerimhoff, N., Roth, M., Schmitt, J., Stix, J., Vdovina, A.: Parameterized (modular) counting and Cayley graph expanders. In: Bonchi, F., Puglisi, S.J. (eds.) 46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021, August 23–27, 2021, Tallinn, Estonia, LIPIcs, vol. 202, pp. 1–15. Schloss Dagstuhl—Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.MFCS.2021.84 Roth, M., Schmitt, J., Wellnitz, P.: Detecting and counting small subgraphs, and evaluating a parameterized Tutte polynomial: lower bounds via toroidal grids and Cayley graph expanders. In: Bansal, N., Merelli, E., Worrell, J. (eds.) 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, July 12–16, (2021), Glasgow, Scotland (Virtual Conference), LIPIcs, vol. 198, pp. 1–16. Schloss Dagstuhl—Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.ICALP.2021.108 ChenJChorBFellowsMHuangXJuedesDWKanjIAXiaGTight lower bounds for certain parameterized NP-hard problemsInf. Comput.20052012216231216571610.1016/j.ic.2005.05.001 BeraSKGishbolinerLLevanzovYSeshadhriCShapiraACounting subgraphs in degenerate graphsJ. ACM2022693121444853210.1145/3520240 BressanMFaster algorithms for counting subgraphs in sparse graphsAlgorithmica202183825782605428947010.1007/s00453-021-00811-0 FlumJGroheMThe parameterized complexity of counting problemsSIAM J. Comput.2004334892922206533810.1137/S0097539703427203 TodaSPP is as hard as the polynomial-time hierarchySIAM J. Comput.1991205865877111565510.1137/0220053 Tsourakakis, C.E., Pachocki, J., Mitzenmacher, M.: Scalable motif-aware graph clustering. In: Proceedings of the 26th International Conference on World Wide Web (WWW), pp. 1451–1460 (2017). https://doi.org/10.1145/3038912.3052653 O Kuchaiev (1178_CR25) 2010; 7 NH Tran (1178_CR35) 2013; 4 1178_CR15 1178_CR37 1178_CR14 1178_CR36 R Milo (1178_CR26) 2002; 298 J Chen (1178_CR8) 2005; 201 1178_CR18 M Grohe (1178_CR21) 2009; 99 R Impagliazzo (1178_CR23) 2001; 62 J Dörfler (1178_CR17) 2022; 84 M Bressan (1178_CR6) 2021; 83 DJ Harvey (1178_CR22) 2018; 132 SK Bera (1178_CR4) 2022; 69 J Chen (1178_CR9) 2006; 72 1178_CR31 1178_CR30 1178_CR13 V Dalmau (1178_CR16) 2004; 329 1178_CR12 1178_CR11 1178_CR33 S Toda (1178_CR34) 1991; 20 1178_CR10 1178_CR32 1178_CR28 1178_CR1 N Alon (1178_CR3) 1995; 42 1178_CR29 J Flum (1178_CR19) 2004; 33 1178_CR7 R Milo (1178_CR27) 2004; 303 1178_CR5 N Alon (1178_CR2) 2008; 24 1178_CR20 1178_CR24 |
| References_xml | – reference: TodaSPP is as hard as the polynomial-time hierarchySIAM J. Comput.1991205865877111565510.1137/0220053 – reference: Roth, M., Schmitt, J., Wellnitz, P.: Detecting and counting small subgraphs, and evaluating a parameterized Tutte polynomial: lower bounds via toroidal grids and Cayley graph expanders. CoRR arXiv:2011.03433 (2020) – reference: DörflerJRothMSchmittJWellnitzPCounting induced subgraphs: An algebraic approach to #w[1]-hardnessAlgorithmica2022842379404438171610.1007/s00453-021-00894-9 – reference: AlonNDaoPHajirasoulihaIHormozdiariFCenk SahinalpSBiomolecular network motif counting and discovery by color codingBioinformatics20082413i241i24910.1093/bioinformatics/btn163 – reference: AlonNYusterRZwickUColor-codingJ. ACM1995424844856141178710.1145/210332.210337 – reference: Jansen, B.M.P., Marx, D.: Characterizing the easy-to-find subgraphs from the viewpoint of polynomial-time algorithms, kernels, and turing kernels. In: Indyk, P. (ed.) Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4–6, 2015, pp. 616–629. SIAM (2015). https://doi.org/10.1137/1.9781611973730.42 – reference: Curticapean, R., Dell, H., Marx, D.: Homomorphisms are a good basis for counting small subgraphs. In: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (STOC), pp. 210–223. ACM (2017). https://doi.org/10.1145/3055399.3055502 – reference: Flum, J., Grohe, M.: Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series. Springer (2006). https://doi.org/10.1007/3-540-29953-X – reference: Peyerimhoff, N., Roth, M., Schmitt, J., Stix, J., Vdovina, A.: Parameterized (modular) counting and Cayley graph expanders. In: Bonchi, F., Puglisi, S.J. (eds.) 46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021, August 23–27, 2021, Tallinn, Estonia, LIPIcs, vol. 202, pp. 1–15. Schloss Dagstuhl—Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.MFCS.2021.84 – reference: Williams, V.V., Wang, J.R., Williams, R.R., Yu, H.: Finding four-node subgraphs in triangle time. In: Indyk, P. (ed.) Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4–6, 2015, pp. 1671–1680. SIAM (2015). https://doi.org/10.1137/1.9781611973730.111 – reference: FlumJGroheMThe parameterized complexity of counting problemsSIAM J. Comput.2004334892922206533810.1137/S0097539703427203 – reference: ChenJHuangXKanjIAXiaGStrong computational lower bounds via parameterized complexityJ. Comput. Syst. Sci.200672813461367227341210.1016/j.jcss.2006.04.007 – reference: MiloRShen-OrrSItzkovitzSKashtanNChklovskiiDAlonUNetwork motifs: simple building blocks of complex networksScience2002298559482482710.1126/science.298.5594.824 – reference: GroheMMarxDOn tree width, bramble size, and expansionJ. Comb. Theory Ser. B2009991218228246782710.1016/j.jctb.2008.06.004 – reference: ImpagliazzoRPaturiROn the complexity of k-satJ. Comput. Syst. Sci.2001622367375182059710.1006/jcss.2000.1727 – reference: Cygan, M., Fomin, F.V., Kowalik, L., Lokshtanov, D., Marx, D., Pilipczuk, M., Pilipczuk, M., Saurabh, S.: Parameterized Algorithms. Springer (2015). https://doi.org/10.1007/978-3-319-21275-3 – reference: Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer (2013). https://doi.org/10.1007/978-1-4471-5559-1 – reference: ChenJChorBFellowsMHuangXJuedesDWKanjIAXiaGTight lower bounds for certain parameterized NP-hard problemsInf. Comput.20052012216231216571610.1016/j.ic.2005.05.001 – reference: BeraSKGishbolinerLLevanzovYSeshadhriCShapiraACounting subgraphs in degenerate graphsJ. ACM2022693121444853210.1145/3520240 – reference: TranNHChoiKPZhangLCounting motifs in the human interactomeNat. Commun.2013411810.1038/ncomms3241 – reference: Chen, Y., Thurley, M., Weyer, M.: Understanding the complexity of induced subgraph isomorphisms. In: Proceedings of the 35th International Colloquium on Automata, Languages and Programming (ICALP), pp. 587–596. Springer (2008). https://doi.org/10.1007/978-3-540-70575-8_48 – reference: BressanMFaster algorithms for counting subgraphs in sparse graphsAlgorithmica202183825782605428947010.1007/s00453-021-00811-0 – reference: Curticapean, R., Dell, H., Husfeldt, T.: Modular counting of subgraphs: matchings, matching-splittable graphs, and paths. In: Mutzel, P., Pagh, R., Herman, G. (eds.) 29th Annual European Symposium on Algorithms, ESA 2021, September 6–8, 2021, Lisbon, Portugal (Virtual Conference), LIPIcs, vol. 204, pp. 1–17. Schloss Dagstuhl—Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.ESA.2021.34 – reference: Schiller, B., Jager, S., Hamacher, K., Strufe, T.: StreaM—a stream-based algorithm for counting motifs in dynamic graphs. In: Proceedings of the 2nd International Conference on Algorithms for Computational Biology (AlCoB), pp. 53–67 (2015). https://doi.org/10.1007/978-3-319-21233-3_5 – reference: HarveyDJWoodDRThe treewidth of line graphsJ. Comb. Theory Ser. B2018132157179382030210.1016/j.jctb.2018.03.007 – reference: Abboud, A., Feller, S., Weimann, O.: On the fine-grained complexity of parity problems. In: Czumaj, A., Dawar, A., Merelli, E. (eds.) 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, July 8–11, 2020, Saarbrücken, Germany (Virtual Conference), LIPIcs, vol. 168, pp. 1–19. Schloss Dagstuhl—Leibniz-Zentrum für Informatik (2020). https://doi.org/10.4230/LIPIcs.ICALP.2020.5 – reference: MiloRItzkovitzSKashtanNLevittRShen-OrrSAyzenshtatIShefferMAlonUSuperfamilies of evolved and designed networksScience200430356631538154210.1126/science.1089167 – reference: Curticapean, R.: Counting matchings of size k is w[1]-hard. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M.Z., Peleg, D. (eds.) Automata, Languages, and Programming—40th International Colloquium, ICALP 2013, Riga, Latvia, July 8–12, 2013, Proceedings, Part I, Lecture Notes in Computer Science, vol. 7965, pp. 352–363. Springer (2013). https://doi.org/10.1007/978-3-642-39206-1_30 – reference: DalmauVJonssonPThe complexity of counting homomorphisms seen from the other sideTheor. Comput. Sci.20043291–3315323210365510.1016/j.tcs.2004.08.008 – reference: Tsourakakis, C.E., Pachocki, J., Mitzenmacher, M.: Scalable motif-aware graph clustering. In: Proceedings of the 26th International Conference on World Wide Web (WWW), pp. 1451–1460 (2017). https://doi.org/10.1145/3038912.3052653 – reference: Bulatov, A.A., Kazeminia, A.: Complexity classification of counting graph homomorphisms modulo a prime number. In: Leonardi, S., Gupta, A. (eds.) STOC ’22: 54th Annual ACM SIGACT Symposium on Theory of Computing, Rome, Italy, June 20–24, 2022, pp. 1024–1037. ACM (2022). https://doi.org/10.1145/3519935.3520075 – reference: KuchaievOMilenkovićTMemiševićVHayesWPržuljNTopological network alignment uncovers biological function and phylogenyJ. R. Soc. Interface20107501341135410.1098/rsif.2010.0063 – reference: Peyerimhoff, N., Roth, M., Schmitt, J., Stix, J., Vdovina, A., Wellnitz, P.: Parameterized counting and Cayley graph expanders. SIAM J. Discrete Math., to appear – reference: Peyerimhoff, N., Roth, M., Schmitt, J., Stix, J., Vdovina, A.: Parameterized (modular) counting and Cayley graph expanders. CoRR arXiv:2104.14596 (2021) – reference: Roth, M., Schmitt, J., Wellnitz, P.: Detecting and counting small subgraphs, and evaluating a parameterized Tutte polynomial: lower bounds via toroidal grids and Cayley graph expanders. In: Bansal, N., Merelli, E., Worrell, J. (eds.) 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, July 12–16, (2021), Glasgow, Scotland (Virtual Conference), LIPIcs, vol. 198, pp. 1–16. Schloss Dagstuhl—Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.ICALP.2021.108 – reference: Curticapean, R., Marx, D.: Complexity of counting subgraphs: only the boundedness of the vertex-cover number counts. In: 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, Philadelphia, PA, USA, October 18–21, 2014, pp. 130–139. IEEE Computer Society (2014). https://doi.org/10.1109/FOCS.2014.22 – reference: Björklund, A., Dell, H., Husfeldt, T.: The parity of set systems under random restrictions with applications to exponential time problems. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) Automata, Languages, and Programming—42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6–10, 2015, Proceedings, Part I, Lecture Notes in Computer Science, vol. 9134, pp. 231–242. Springer (2015). https://doi.org/10.1007/978-3-662-47672-7_19 – ident: 1178_CR28 doi: 10.4230/LIPIcs.MFCS.2021.84 – ident: 1178_CR5 doi: 10.1007/978-3-662-47672-7_19 – ident: 1178_CR13 doi: 10.1145/3055399.3055502 – ident: 1178_CR32 doi: 10.4230/LIPIcs.ICALP.2021.108 – ident: 1178_CR18 doi: 10.1007/978-1-4471-5559-1 – ident: 1178_CR30 – ident: 1178_CR37 doi: 10.1137/1.9781611973730.111 – ident: 1178_CR14 doi: 10.1109/FOCS.2014.22 – ident: 1178_CR11 doi: 10.1007/978-3-642-39206-1_30 – volume: 201 start-page: 216 issue: 2 year: 2005 ident: 1178_CR8 publication-title: Inf. Comput. doi: 10.1016/j.ic.2005.05.001 – volume: 62 start-page: 367 issue: 2 year: 2001 ident: 1178_CR23 publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.2000.1727 – ident: 1178_CR12 doi: 10.4230/LIPIcs.ESA.2021.34 – volume: 33 start-page: 892 issue: 4 year: 2004 ident: 1178_CR19 publication-title: SIAM J. Comput. doi: 10.1137/S0097539703427203 – volume: 7 start-page: 1341 issue: 50 year: 2010 ident: 1178_CR25 publication-title: J. R. Soc. Interface doi: 10.1098/rsif.2010.0063 – ident: 1178_CR36 doi: 10.1145/3038912.3052653 – ident: 1178_CR15 doi: 10.1007/978-3-319-21275-3 – ident: 1178_CR7 doi: 10.1145/3519935.3520075 – volume: 69 start-page: 1 issue: 3 year: 2022 ident: 1178_CR4 publication-title: J. ACM doi: 10.1145/3520240 – ident: 1178_CR33 doi: 10.1007/978-3-319-21233-3_5 – volume: 42 start-page: 844 issue: 4 year: 1995 ident: 1178_CR3 publication-title: J. ACM doi: 10.1145/210332.210337 – volume: 132 start-page: 157 year: 2018 ident: 1178_CR22 publication-title: J. Comb. Theory Ser. B doi: 10.1016/j.jctb.2018.03.007 – ident: 1178_CR29 – ident: 1178_CR31 – volume: 4 start-page: 1 issue: 1 year: 2013 ident: 1178_CR35 publication-title: Nat. Commun. doi: 10.1038/ncomms3241 – volume: 329 start-page: 315 issue: 1–3 year: 2004 ident: 1178_CR16 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2004.08.008 – ident: 1178_CR24 doi: 10.1137/1.9781611973730.42 – ident: 1178_CR10 doi: 10.1007/978-3-540-70575-8_48 – volume: 83 start-page: 2578 issue: 8 year: 2021 ident: 1178_CR6 publication-title: Algorithmica doi: 10.1007/s00453-021-00811-0 – volume: 24 start-page: i241 issue: 13 year: 2008 ident: 1178_CR2 publication-title: Bioinformatics doi: 10.1093/bioinformatics/btn163 – ident: 1178_CR1 doi: 10.4230/LIPIcs.ICALP.2020.5 – volume: 84 start-page: 379 issue: 2 year: 2022 ident: 1178_CR17 publication-title: Algorithmica doi: 10.1007/s00453-021-00894-9 – ident: 1178_CR20 doi: 10.1007/3-540-29953-X – volume: 20 start-page: 865 issue: 5 year: 1991 ident: 1178_CR34 publication-title: SIAM J. Comput. doi: 10.1137/0220053 – volume: 99 start-page: 218 issue: 1 year: 2009 ident: 1178_CR21 publication-title: J. Comb. Theory Ser. B doi: 10.1016/j.jctb.2008.06.004 – volume: 298 start-page: 824 issue: 5594 year: 2002 ident: 1178_CR26 publication-title: Science doi: 10.1126/science.298.5594.824 – volume: 72 start-page: 1346 issue: 8 year: 2006 ident: 1178_CR9 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2006.04.007 – volume: 303 start-page: 1538 issue: 5663 year: 2004 ident: 1178_CR27 publication-title: Science doi: 10.1126/science.1089167 |
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