We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.
LIPIcs - Leibniz International Proceedings in Informatics. 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)
Doi
Abstract
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 hs 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 n^{o(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
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.