Results 1 
4 of
4
Plane geometric graph augmentation: a generic perspective
, 2011
"... Graph augmentation problems are motivated by network design, and have been studied extensively in optimization. We consider augmentation problems over plane geometric graphs, that is, graphs given with a crossingfree straightline embedding in the plane. The geometric constraints on the possible ne ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Graph augmentation problems are motivated by network design, and have been studied extensively in optimization. We consider augmentation problems over plane geometric graphs, that is, graphs given with a crossingfree straightline embedding in the plane. The geometric constraints on the possible new edges render some of the simplest augmentation problems intractable, and in many cases only extremal results are known. We survey recent results, highlight common trends, and gather numerous conjectures and open problems.
Realization of simply connected polygonal linkages and recognition of unit disk contact trees
"... Abstract. We wish to decide whether a simply connected flexible polygonal structure can be realized in Euclidean space. Two models are considered: polygonal linkages (bodyandjoint framework) and contact graphs of unit disks in the plane. (1) We show that it is strongly NPhard to decide whether a ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We wish to decide whether a simply connected flexible polygonal structure can be realized in Euclidean space. Two models are considered: polygonal linkages (bodyandjoint framework) and contact graphs of unit disks in the plane. (1) We show that it is strongly NPhard to decide whether a given polygonal linkage is realizable in the plane when the bodies are convex polygons and their contact graph is a tree; the problem is weakly NPhard already for a chain of rectangles, but efficiently decidable for a chain of triangles hinged at distinct vertices. (2) We also show that it is strongly NPhard to decide whether a given tree is the contact graph of interiordisjoint unit disks in the plane. 1