Alexander Ravsky

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Given a planar graph G on n vertices, let fix (G) denote the maximum k such that any straight line drawing of G with possible edge crossings can be made crossing-free by moving at most n − k vertices to new positions. Let v̄(G) denote the maximum possible number of collinear vertices in a crossingfree straight line drawing of G. In view of the relation fix(More)
Given a planar graph G, we consider drawings of G in the plane where edges are represented by straight line segments (which possibly intersect). Such a drawing is specified by an injective embedding π of the vertex set of G into the plane. Let fix(G, π) be the maximum integer k such that there exists a crossing-free redrawing π′ of G which keeps k vertices(More)
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)
Given a planar graph G, we consider drawings of G in the plane where edges are represented by straight line segments (which possibly intersect). Such a drawing is specified by an injective embedding π of the vertex set of G into the plane. Let fix(G, π) be the maximum integer k such that there exists a crossing-free redrawing π of G which keeps k vertices(More)
It is well known that any graph admits a crossing-free straight-line drawing in R3 and that any planar graph admits the same even in R2. For a graph G and d ∈ {2, 3}, let ρd(G) denote the minimum number of lines in Rd that together can cover all edges of a drawing of G. For d = 2, G must be planar. We investigate the complexity of computing these parameters(More)
Storyline visualizations help visualize encounters of the characters in a story over time. Each character is represented by an xmonotone curve that goes from left to right. A meeting is represented by having the characters that participate in the meeting run close together for some time. In order to keep the visual complexity low, rather than just(More)
Given a drawing of a graph, its visual complexity is defined as the number of geometrical entities in the drawing, for example, the number of segments in a straight-line drawing or the number of arcs in a circular-arc drawing (in 2D). Recently, Chaplick et al. [4] introduced a different measure for the visual complexity, the affine cover number, which is(More)
In their seminal work, Mustafa and Ray [25] showed that a wide class of geometric set cover (SC) problems admit a PTAS via local search, which appears to be the most powerful approach known for such problems. Their result applies if a naturally defined “exchange graph” for two feasible solutions is planar and is based on subdividing this graph via a planar(More)
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