Known Algorithms on Graphs of Bounded Treewidth are Probably Optimal
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\epsilon)^{n}m^{O(1)} time, we show that for any e > 0; {\sc Independent Set} cannot be solved in (2e)^{tw(G)}V(G)^{O(1)} time, {\sc Dominating Set} cannot be solved in (3e)^{tw(G)}V(G)^{O(1)} time, {\sc Max Cut} cannot be solved in (2e)^{tw(G)}V(G)^{O(1)} time, {\sc Odd Cycle Transversal} cannot be solved in (3e)^{tw(G)}V(G)^{O(1)} time, For any $q \geq 3$, $q${\sc Coloring} cannot be solved in (qe)^{tw(G)}V(G)^{O(1)} time, {\sc Partition Into Triangles} cannot be solved in (2e)^{tw(G)}V(G)^{O(1)} time. Our lower bounds match the running times for the best known algorithms for the problems, up to the e in the base.
 Publication:

arXiv eprints
 Pub Date:
 July 2010
 arXiv:
 arXiv:1007.5450
 Bibcode:
 2010arXiv1007.5450L
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Complexity;
 Computer Science  Discrete Mathematics