Università della Svizzera italiana

On the hausdorff and other cluster Voronoi diagrams

Khramtcova, Elena ; Papadopoulou, Evanthia (Dir.)

Thèse de doctorat : Università della Svizzera italiana, 2016 ; 2016INFO005.

The Voronoi diagram is a fundamental geometric structure that encodes proximity information. Given a set of geometric objects, called sites, their Voronoi diagram is a subdivision of the underlying space into maximal regions, such that all points within one region have the same nearest site. Problems in diverse application domains (such as VLSI CAD, robotics, facility location, etc.) demand...

Università della Svizzera italiana

Voronoi diagrams in the max-norm : algorithms, implementation, and applications

Dey, Sandeep Kumar ; Papadopoulou, Evanthia (Dir.)

Thèse de doctorat : Università della Svizzera italiana, 2015 ; 2015INFO007.

Voronoi diagrams and their numerous variants are well-established objects in computational geometry. They have proven to be extremely useful to tackle geometric problems in various domains such as VLSI CAD, Computer Graphics, Pattern Recognition, Information Retrieval, etc. In this dissertation, we study generalized Voronoi diagram of line segments as motivated by applications in VLSI Computer...

Università della Svizzera italiana

Higher-order Voronoi diagrams of polygonal objects

Zavershynskyi, Maksym ; Papadopoulou, Evanthia (Dir.)

Thèse de doctorat : Università della Svizzera italiana, 2014 ; 2014INFO009.

Higher-order Voronoi diagrams are fundamental geometric structures which encode the k-nearest neighbor information. Thus, they aid in computations that require proximity information beyond the nearest neighbor. They are related to various favorite structures in computational geometry and are a fascinating combinatorial problem to study. While higher-order Voronoi diagrams of points have been...