Notes on Parameterized Complexity, Dagstuhl, June 2012.
Notes on Parameterized Complexity, Dagstuhl, June 2012.
Notes on Parameterized Complexity, Dagstuhl, June 2012.
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THE MODERN INCARNATION<br />
◮ This is the exciting thing of the last decade.<br />
◮ The development of tools to match (up to O) upper and<br />
lower bounds, beginning with Cai and Juedes.<br />
◮ M[1] =FPT or ETH implying tight membership of XP.<br />
◮ Perhaps not known by every<strong>on</strong>e:<br />
sd = inf{ɛ | ∃O ∗ (2 ɛn ) algorithm for n variable d −CNFSAT}.<br />
◮ Clearly sd ≤ sd+1. We can define s∞ = limd→∞ sd.<br />
◮ Impagliazzo and Paturi noted that ETH means that<br />
infinitely many sd < sd+1.<br />
◮ SETH is that s∞ = 1.<br />
◮ Can be used for str<strong>on</strong>g lower bounds, see Cygan, Dell,<br />
Lokshtanov, Marx, Nederlof, Okamoto, Paturi, Saurabh,<br />
Wahlström applied to SET SPLITTING and HITTING SET.
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