@misc{KrumkeLauraLipmannetal., author = {Krumke, Sven and Laura, Luigi and Lipmann, Maarten and Marchetti-Spaccamela, Alberto and Paepe, Willem de and Poensgen, Diana and Stougie, Leen}, title = {Non-Abusiveness Helps: An O(1)-Competitive Algorithm for Minimizing the Maximum Flow Time in the Online Traveling Salesman Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7038}, number = {02-36}, abstract = {In the online traveling salesman problem \$OLTSP\$ requests for visits to cities arrive online while the salesman is traveling. We study the \$F{\_max}-OLTSP\$ where the objective is to minimize the maximum flow time. This objective is particularly interesting for applications. Unfortunately, there can be no competitive algorithm, neither deterministic nor randomized. Hence, competitive analysis fails to distinguish online algorithms. Not even resource augmentation which is helpful in scheduling works as a remedy. This unsatisfactory situation motivates the search for alternative analysis methods. We introduce a natural restriction on the adversary for the \$F{\_max}-OLTSP\$ on the real line. A \emph{non-abusive adversary} may only move in a direction if there are yet unserved requests on this side. Our main result is an algorithm which achieves a constant competitive ratio against the non-abusive adversary.}, language = {en} } @misc{KrumkeLipmannPaepeetal., author = {Krumke, Sven and Lipmann, Maarten and Paepe, Willem de and Poensgen, Diana and Rambau, J{\"o}rg and Stougie, Leen and Woeginger, Gerhard}, title = {How to Cut a Cake Almost Fairly}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6905}, number = {02-23}, abstract = {In the cake cutting problem, \$n\ge2\$ players want to cut a cake into \$n\$ pieces so that every player gets a ``fair'' share of the cake by his own measure. We describe a protocol with \$n-1\$~cuts in which each player can enforce to get a share of at least~\$1/(2n-2)\$. Moreover we show that no protocol with \$n-1\$~cuts can guarantee a better fraction.}, language = {en} }