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We investigate the problem of drawing graphs in 2D and 3D such that their edges (or only their vertices) can be covered by few lines or planes. We insist on straight-line edges and crossing-free drawings. This problem has many connections to other challenging graph-drawing problems such as small-area or small-volume drawings, layered or track drawings, and… (More)

Obstacle representations of graphs have been investigated quite intensely over the last few years. We focus on graphs that can be represented by a single obstacle. Given a (topologically open) polygon C and a finite set P of points in general position in the complement of C, the visibility graph G C (P) has a vertex for each point in P and an edge pq for… (More)

It is well known that any graph admits a crossing-free straight-line drawing in R 3 and that any planar graph admits the same even in R 2. For d ∈ {2, 3}, let ρ 1 d (G) denote the minimum number of lines in R d that together can accommodate all edges of a drawing of G, where ρ 1 2 (G) is defined for planar graphs. We investigate the complexity of computing… (More)

- Thomas C. van Dijk, Martin Fink, Norbert Fischer, Fabian Lipp, Peter Markfelder, Alexander Ravsky +2 others
- ArXiv
- 2016

Introduction Classical force-directed algorithm Attracting forces: O(m) time with m = #edges Repulsive forces: Θ(n 2) time with n = #vertices Attracting forces: O(m) time with m = #edges Repulsive forces: Θ(n 2) time with n = #vertices Many speed-up techniques for force-directed algorithms known: Hierarchical O(n log n) force-calculation [Barnes & Hut,… (More)

Instances of optimization problems with multiple objectives can have several optimal solutions whose cost vectors are incomparable. This ambiguity leads to several reasonable notions for solving multiobjective problems. Each such notion defines a class of multivalued functions. We systematically investigate the computational complexity of these classes.… (More)

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