par Knauer, Christian C.;Tiwary, Hans Raj 
;Werner, Daniel
Référence Leibniz international proceedings in informatics, 9, page (649-660)
Publication Publié, 2011
;Werner, DanielRéférence Leibniz international proceedings in informatics, 9, page (649-660)
Publication Publié, 2011
Article révisé par les pairs
| Résumé : | We study several canonical decision problems arising from some well-known theorems from combinatorial geometry. Among others, we show that computing the minimum size of a Caratheodory set and a Helly set and certain decision versions of the ham-sandwich cut problem are W[1]-hard (and NP-hard) if the dimension is part of the input. This is done by fpt-reductions (which are actually ptime-reductions) from the d-SUM problem. Our reductions also imply that the problems we consider cannot be solved in time no(d) (where n is the size of the input), unless the Exponential-Time Hypothesis (ETH) is false. The technique of embedding d-SUM into a geometric setting is conceptually much simpler than direct fpt-reductions from purely combinatorial W[1]-hard problems (like the clique problem) and has great potential to show (parameterized) hardness and (conditional) lower bounds for many other problems. © Christian Knauer, Hans Raj Tiwary, Daniel Werner. |
