Separating a Voronoi Diagram via Local Search

Given a set P of n points in R^dwe show how to insert a set Z of O(n^(1-1/d)) additional points, such that P can be broken into two sets P1 and P2of roughly equal size, such that in the Voronoi diagram V(P u Z), the cells of P1 do not touch the cells of P2; that is, Z separates P1 from P2 in the Voronoi diagram (and also in the dual Delaunay triangulation). In addition, given such a partition (P1,P2) of Pwe present an approximation algorithm to compute a minimum size separator realizing this partition. We also present a simple local search algorithm that is a PTAS for approximating the optimal Voronoi partition

Cognition-enabled robot manipulation in human environments: requirements, recent work, and open problems

Due to copyright restrictions, the access to the full text of this article is only available via subscription.Service robots are expected to play an important role in our daily lives as our companions in home and work environments in the near future. An important requirement for fulfilling this expectation is to equip robots with skills to perform everyday manipulation tasks, the success of which is crucial for most home chores, such as cooking, cleaning, and shopping. Robots have been used successfully for manipulation tasks in wellstructured and controlled factory environments for decades. Designing skills for robots working in uncontrolled human environments raises many potential challenges in various subdisciplines, such as computer vision, automated planning, and human-robot interaction. In spite of the recent progress in these fields, there are still challenges to tackle. This article outlines problems in different research areas related to mobile manipulation from the cognitive perspective, reviews recently published works and the state-of-the-art approaches to address these problems, and discusses open problems to be solved to realize robot assistants that can be used in manipulation tasks in unstructured human environments.TÜBİTA