research-article

Known algorithms on graphs of bounded treewidth are probably optimal

Authors:

Daniel Lokshtanov,

Saket SaurabhAuthors Info & Claims

SODA '11: Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms

Pages 777 - 789

Published: 23 January 2011 Publication History

Abstract

We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that SAT cannot be solved in (2 - ∈)ⁿm^O(1) time, we show that for any ∈ > 0;

• Independent Set cannot be solved in time (2 − ε)^tw(G) |V(G)|^O(1),

• Dominating Set cannot be solved in time (3 − ε)^tw(G) |V(G)|^O(1),

• Max Cut cannot be solved in time (2 − ε)^tw(G) |V(G)|^O(1),

• Odd Cycle Transversal cannot be solved in time (3 − ε)^tw(G) |V(G)|^O(1),

• For any q ≥ 3, q-Coloring cannot be solved in time (q − ε)^tw(G) |V(G)|^O(1),

• Partition Into Triangles cannot be solved in time (2 − ε)^tw(G) |V(G)|^O(1).

Our lower bounds match the running times for the best known algorithms for the problems, up to the ε in the base.

References

[1]

J. Alber and R. Niedermeier, Improved tree decomposition based algorithms for domination-like problems, in LATIN, 2002, pp. 613--628.

Digital Library

[2]

A. Björklund, T. Husfeldt, P. Kaski, and M. Koivisto, Fourier meets möbius: fast subset convolution, in STOC, 2007, pp. 67--74.

Digital Library

[3]

C. Calabro, R. Impagliazzo, and R. Paturi, The complexity of satisfiability of small depth circuits, in IWPEC, 2009, pp. 75--85.

Digital Library

[4]

J. Chen, X. Huang, I. A. Kanj, and G. Xia, On the computational hardness based on linear FPT-reductions, J. Comb. Optim., 11 (2006), pp. 231--247.

[5]

J. Chen, X. Huang, I. A. Kanj, and G. Xia, Strong computational lower bounds via parameterized complexity, J. Comput. Syst. Sci., 72 (2006), pp. 1346--1367.

Digital Library

[6]

E. D. Demaine, F. V. Fomin, M. T. Hajiaghayi, and D. M. Thilikos, Subexponential parameterized algorithms on bounded-genus graphs and -minor-free graphs, J. ACM, 52 (2005), pp. 866--893.

Digital Library

[7]

E. D. Demaine and M. Hajiaghayi, The bidimensionality theory and its algorithmic applications, Comput. J., 51 (2008), pp. 292--302.

Digital Library

[8]

D. Eppstein, Diameter and treewidth in minor-closed graph families, Algorithmica, 27 (2000), pp. 275--291.

[9]

S. Fiorini, N. Hardy, B. A. Reed, and A. Vetta, Planar graph bipartization in linear time, Discrete Applied Mathematics, 156 (2008).

Digital Library

[10]

J. Flum and M. Grohe, Parameterized Complexity Theory, Springer, Berlin, 2006.

Digital Library

[11]

F. Fomin, P. Golovach, D. Lokshtanov, and S. Saurabh, Algorithmic lower bounds for problems parameterized by clique-width, in SODA, 2010, pp. 493--502.

Digital Library

[12]

F. V. Fomin, S. Gaspers, S. Saurabh, and A. A. Stepanov, On two techniques of combining branching and treewidth, Algorithmica, 54 (2009), pp. 181--207.

Digital Library

[13]

R. Impagliazzo and R. Paturi, On the complexity of k-sat, J. Comput. Syst. Sci., 62 (2001), pp. 367--375.

Digital Library

[14]

R. Impagliazzo, R. Paturi, and F. Zane, Which problems have strongly exponential complexity?, J. Comput. Syst. Sci., 63 (2001), pp. 512--530.

Digital Library

[15]

J. Kleinberg and E. Tardos, Algorithm Design, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, 2005.

Digital Library

[16]

D. Lokshtanov, D. Marx, and S. Saurabh, Known algorithms on graphs of bounded treewidth are probably optimal, CoRR, abs/1007.5450 (2010).

[17]

D. Lokshtanov, S. Saurabh, and S. Sikdar, Simpler parameterized algorithm for oct, in IWOCA, 2009, pp. 380--384.

Digital Library

[18]

D. Marx, Can you beat treewidth?, in FOCS, 2007, pp. 169--179.

Digital Library

[19]

D. Marx, On the optimality of planar and geometric approximation schemes, in FOCS, 2007, pp. 338--348.

Digital Library

[20]

D. Mölle, S. Richter, and P. Rossmanith, Enumerate and expand: Improved algorithms for connected vertex cover and tree cover, Theory Comput. Syst., 43 (2008), pp. 234--253.

[21]

R. Niedermeier, Invitation to fixed-parameter algorithms, vol. 31 of Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, 2006.

[22]

M. Pătraşcu and R. Williams, On the possibility of faster sat algorithms, in Proc. 21st ACM/SIAM Symposium on Discrete Algorithms (SODA), 2010. To appear.

Digital Library

[23]

B. Reed, K. Smith, and A. Vetta, Finding odd cycle transversals, Operations Research Letters, 32 (2004), pp. 299--301.

Digital Library

[24]

A. D. Scott and G. B. Sorkin, Linear-programming design and analysis of fast algorithms for max 2-csp, Discrete Optimization, 4 (2007), pp. 260--287.

Digital Library

[25]

A. Takahashi, S. Ueno, and Y. Kajitani, Mixed searching and proper-path-width, Theor. Comput. Sci., 137 (1995), pp. 253--268.

Digital Library

[26]

J. A. Telle and A. Proskurowski, Practical algorithms on partial k-trees with an application to domination-like problems, in WADS, 1993, pp. 610--621.

Digital Library

[27]

D. M. Thilikos, M. J. Serna, and H. L. Bodlaender, Cutwidth i: A linear time fixed parameter algorithm, J. Algorithms, 56 (2005), pp. 1--24.

Digital Library

[28]

J. M. M. van Rooij, H. L. Bodlaender, and P. Rossmanith, Dynamic programming on tree decompositions using generalised fast subset convolution, in ESA, 2009, pp. 566--577.

[29]

J. M. M. van Rooij, J. Nederlof, and T. C. van Dijk, Inclusion/exclusion meets measure and conquer, in ESA, 2009, pp. 554--565.

Cited By

Lagerkvist VWahlström M(2021)The (Coarse) Fine-Grained Structure of NP-Hard SAT and CSP ProblemsACM Transactions on Computation Theory10.1145/349233614:1(1-54)Online publication date: 15-Dec-2021
https://dl.acm.org/doi/10.1145/3492336
Abboud ABringmann KHermelin DShabtay DChan T(2019)SETH-based lower bounds for subset sum and bicriteria pathProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310438(41-57)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.5555/3310435.3310438
Pilipczuk MPilipczuk MWrochna M(2019)Edge Bipartization Faster than $$2^k$$2kAlgorithmica10.1007/s00453-017-0319-z81:3(917-966)Online publication date: 1-Mar-2019
https://dl.acm.org/doi/10.1007/s00453-017-0319-z
Show More Cited By

Known algorithms on graphs of bounded treewidth are probably optimal

Recommendations

Known Algorithms on Graphs of Bounded Treewidth Are Probably Optimal

We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that n-variable m-...
Restricted space algorithms for isomorphism on bounded treewidth graphs

The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time. We give restricted space algorithms for these problems proving the following results:*Isomorphism for ...
DYNAMIC PROGRAMMING ON GRAPHS WITH BOUNDED TREEWIDTH

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

SODA '11: Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms

January 2011

1785 pages

Program Chair:
Dana Randall
Georgia Institute of Technology

Sponsors

SIAM Activity Group on Discrete Mathematics
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 23 January 2011

Check for updates

Qualifiers

Research-article

Conference

SODA '11

Sponsor:

SIGACT

SODA '11: 22nd ACM-SIAM Symposium on Discrete Algorithms

January 23 - 25, 2011

California, San Francisco

Acceptance Rates

Overall Acceptance Rate 411 of 1,322 submissions, 31%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

33
Total Citations
View Citations
171
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 20 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Lagerkvist VWahlström M(2021)The (Coarse) Fine-Grained Structure of NP-Hard SAT and CSP ProblemsACM Transactions on Computation Theory10.1145/349233614:1(1-54)Online publication date: 15-Dec-2021
https://dl.acm.org/doi/10.1145/3492336
Abboud ABringmann KHermelin DShabtay DChan T(2019)SETH-based lower bounds for subset sum and bicriteria pathProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310438(41-57)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.5555/3310435.3310438
Pilipczuk MPilipczuk MWrochna M(2019)Edge Bipartization Faster than $$2^k$$2kAlgorithmica10.1007/s00453-017-0319-z81:3(917-966)Online publication date: 1-Mar-2019
https://dl.acm.org/doi/10.1007/s00453-017-0319-z
Curticapean RLindzey NNederlof JCzumaj A(2018)A tight lower bound for counting hamiltonian cycles via matrix rankProceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3174304.3175340(1080-1099)Online publication date: 7-Jan-2018
https://dl.acm.org/doi/10.5555/3174304.3175340
Abboud ABringmann KDell HNederlof JDiakonikolas IKempe DHenzinger M(2018)More consequences of falsifying SETH and the orthogonal vectors conjectureProceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3188745.3188938(253-266)Online publication date: 20-Jun-2018
https://dl.acm.org/doi/10.1145/3188745.3188938
Lokshtanov DMarx DSaurabh S(2018)Known Algorithms on Graphs of Bounded Treewidth Are Probably OptimalACM Transactions on Algorithms10.1145/317044214:2(1-30)Online publication date: 16-Apr-2018
https://dl.acm.org/doi/10.1145/3170442
Cygan MKratsch SNederlof J(2018)Fast Hamiltonicity Checking Via Bases of Perfect MatchingsJournal of the ACM10.1145/314822765:3(1-46)Online publication date: 13-Mar-2018
https://dl.acm.org/doi/10.1145/3148227
Cygan MMarx DPilipczuk MPilipczuk M(2017)Hitting forbidden subgraphs in graphs of bounded treewidthInformation and Computation10.1016/j.ic.2017.04.009256:C(62-82)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1016/j.ic.2017.04.009
Curticapean RMarx D(2016)Tight conditional lower bounds for counting perfect matchings on graphs of bounded treewidth, cliquewidth, and genusProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884548(1650-1669)Online publication date: 10-Jan-2016
https://dl.acm.org/doi/10.5555/2884435.2884548
Socała A(2016)Tight Lower Bound for the Channel Assignment ProblemACM Transactions on Algorithms10.1145/287650512:4(1-19)Online publication date: 2-Sep-2016
https://dl.acm.org/doi/10.1145/2876505
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents