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 1549-6325 10.1115/3170942

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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 n-variable m-clause 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, q-COLORING 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.

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