2,993 research outputs found
Edge Routing with Ordered Bundles
Edge bundling reduces the visual clutter in a drawing of a graph by uniting
the edges into bundles. We propose a method of edge bundling drawing each edge
of a bundle separately as in metro-maps and call our method ordered bundles. To
produce aesthetically looking edge routes it minimizes a cost function on the
edges. The cost function depends on the ink, required to draw the edges, the
edge lengths, widths and separations. The cost also penalizes for too many
edges passing through narrow channels by using the constrained Delaunay
triangulation. The method avoids unnecessary edge-node and edge-edge crossings.
To draw edges with the minimal number of crossings and separately within the
same bundle we develop an efficient algorithm solving a variant of the
metro-line crossing minimization problem. In general, the method creates clear
and smooth edge routes giving an overview of the global graph structure, while
still drawing each edge separately and thus enabling local analysis
Motion Planning for Unlabeled Discs with Optimality Guarantees
We study the problem of path planning for unlabeled (indistinguishable)
unit-disc robots in a planar environment cluttered with polygonal obstacles. We
introduce an algorithm which minimizes the total path length, i.e., the sum of
lengths of the individual paths. Our algorithm is guaranteed to find a solution
if one exists, or report that none exists otherwise. It runs in time
, where is the number of robots and is the total
complexity of the workspace. Moreover, the total length of the returned
solution is at most , where OPT is the optimal solution cost. To
the best of our knowledge this is the first algorithm for the problem that has
such guarantees. The algorithm has been implemented in an exact manner and we
present experimental results that attest to its efficiency
Approximate Euclidean shortest paths in polygonal domains
Given a set of pairwise disjoint simple polygonal obstacles
in defined with vertices, we compute a sketch of
whose size is independent of , depending only on and the
input parameter . We utilize to compute a
-approximate geodesic shortest path between the two given points
in time. Here, is a user
parameter, and is a small positive constant (resulting from the time
for triangulating the free space of using the algorithm in
\cite{journals/ijcga/Bar-YehudaC94}). Moreover, we devise a
-approximation algorithm to answer two-point Euclidean distance
queries for the case of convex polygonal obstacles.Comment: a few updates; accepted to ISAAC 201
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