Dear all, You all are cordially invited. Location: Freie Universität Berlin Takustr. 9 14195 Berlin Time: Monday, June 20 - 14:15 Lecture: Wolfgang Mulzer (Freie Universität Berlin) Title: Long Alternating Paths Exist Abstract:Let P be a set of 2n points in convex position, such that n points are colored red and n points are colored blue. A non-crossing alternating path on P of length l is a sequence p_1, ..., p_l of l points from P so that (i) all points are pairwise distinct; (ii) any two consecutive points p_i, p_{i+1} have different colors; and (iii) any two segments p_i p_{i+1} and p_j p_{j+1} have disjoint relative interiors, for i /= j. We show that there is an absolute constant eps > 0, independent of n and of the coloring, such that P always admits a non-crossing alternating path of length at least (1 + eps)n. The result is obtained through a slightly stronger statement: there always exists a non-crossing bichromatic separated matching on at least (1 + eps)n points of P. This is a properly colored matching whose segments are pairwise disjoint and intersected by a common line. For both versions, this is the first improvement of the easily obtained lower bound of n by an additive term linear in n. The best known published upper bounds are asymptotically of order 4n/3 + o(n). Based on joint work with Pavel Valtr. Coffee & Tea Break : Room 134 - 1st Floor Time: Monday, June 20 - 16:00 s.t. Colloquium: Michaela Borzechowski (Freie Universität Berlin) Title: Unique Sink Orientations of Grids is in Unique End of Potential Line Abstract:The complexity classes Unique End of Potential Line (UEOPL) and its promise version PUEOPL were introduced in 2018 by Fearnly et al. PUEOPL captures search problems where the instances are promised to have a unique solution. UEOPL captures total search versions of these promise problems. The promise problems can be made total by defining violations that are returned as a short certificate of an unfulfilled promise. GridUSO is the problem of finding the sink in a grid with a unique sink orientation. It was introduced by Gärtner et al. in 2008. We describe a promise preserving reduction from GridUSO to UniqueForwardEOPL, a UEOPL-complete problem. Thus, we show that GridUSO is in UEOPL and its promise version is in PUEOPL. |