research-article

Known Algorithms on Graphs of Bounded Treewidth Are Probably Optimal

Authors:

Daniel Lokshtanov,

Saket SaurabhAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 14, Issue 2

Article No.: 13, Pages 1 - 30

https://doi.org/10.1145/3170442

Published: 16 April 2018 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 n-variable m-clause SAT cannot be solved in time (2-ϵ)ⁿm^O(1), we show that for any ϵ > 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 fixed 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.

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Index Terms

Known Algorithms on Graphs of Bounded Treewidth Are Probably Optimal
1. Theory of computation
  1. Design and analysis of algorithms
    1. Parameterized complexity and exact algorithms

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 14, Issue 2

April 2018

339 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3196491

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2018 ACM.

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Publication History

Published: 16 April 2018

Accepted: 01 November 2017

Revised: 01 October 2017

Received: 01 March 2017

Published in TALG Volume 14, Issue 2

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Bergen Research Foundation and the University of Bergen through project “BeHard”
ERC Starting Grant PaPaAlg
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Consolidator Grant SYSTEMATICGRAPH

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Cited By

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Focke JMarx DRzążewski P(2024)Counting List Homomorphisms from Graphs of Bounded Treewidth: Tight Complexity BoundsACM Transactions on Algorithms10.1145/364081420:2(1-32)Online publication date: 13-Feb-2024
https://dl.acm.org/doi/10.1145/3640814
Bodlaender HGroenland CNederlof JSwennenhuis C(2024)Parameterized problems complete for nondeterministic FPT time and logarithmic spaceInformation and Computation10.1016/j.ic.2024.105195300:COnline publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1016/j.ic.2024.105195
Bodlaender HGroenland CJacob HJaffke LLima P(2024)XNLP-Completeness for Parameterized Problems on Graphs with a Linear StructureAlgorithmica10.1007/s00453-024-01274-9Online publication date: 4-Nov-2024
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Harutyunyan ALampis MMelissinos N(2024)Digraph Coloring and Distance to AcyclicityTheory of Computing Systems10.1007/s00224-022-10103-x68:4(986-1013)Online publication date: 1-Aug-2024
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Andreev NBliznets IKundu MSaurabh STripathi VVerma S(2024)Parameterized Complexity of Paired DominationCombinatorial Algorithms10.1007/978-3-031-63021-7_40(523-536)Online publication date: 22-Jun-2024
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Hegerfeld FKratsch S(2023)Tight Algorithms for Connectivity Problems Parameterized by Modular-TreewidthGraph-Theoretic Concepts in Computer Science10.1007/978-3-031-43380-1_28(388-402)Online publication date: 23-Sep-2023
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