Known Algorithms on Graphs of Bounded Treewidth Are Probably Optimal
Lokshtanov, D and Marx, Dániel and Saurabh, S (2018) Known Algorithms on Graphs of Bounded Treewidth Are Probably Optimal. ACM TRANSACTIONS ON ALGORITHMS, 14 (2). ISSN 15496325 10.1115/3170942

Text
Lokshtanov_13_3424372_ny.pdf Download (975kB)  Preview 
Abstract
We obtain a number of lower bounds on the running time of algoritluns 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 nvariable mclause SAT cannot be solved in time (2  epsilon)(n) m(O(1)), we show that for any epsilon > 0: INDEPENDENT SET cannot be solved ill time (2  epsilon)(tw(G))vertical bar V(G)vertical bar(O(1)), DOMINATING SET cannot be solved in time (3  epsilon)(tw(G))vertical bar V(G)vertical bar(O(1)), MAX CUT cannot be solved in time (2  epsilon)(tw(G))vertical bar V(G)vertical bar(O(1)), ODD CYCLE TRANSVERSAL cannot be solved in lime (3  epsilon)(tw(G))vertical bar V(G)vertical bar(O(1)) For ally fixed q >= 3, qCOLORING cannot be solved in time (q  epsilon)(tw(G)) vertical bar V(G)vertical bar(O(1)), PARTITION INTO TRIANGLES cannot be solved in time (2  epsilon)(tw(G))vertical bar V(G)vertical bar(O(1)). Our lower bounds match the running times for the best known algoritluns for the problems, up to the epsilon in the base.
Item Type:  Article 

Uncontrolled Keywords:  COMPLEXITY; LOWER BOUNDS; WIDTH; Treewidth; Planar; SAT; SETH; 
Subjects:  Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány 
Divisions:  Informatics Laboratory 
SWORD Depositor:  MTMT Injector 
Depositing User:  MTMT Injector 
Date Deposited:  08 Jan 2019 20:59 
Last Modified:  21 Jul 2019 13:32 
URI:  https://eprints.sztaki.hu/id/eprint/9567 
Update Item 