1,061 research outputs found
Defining Equitable Geographic Districts in Road Networks via Stable Matching
We introduce a novel method for defining geographic districts in road
networks using stable matching. In this approach, each geographic district is
defined in terms of a center, which identifies a location of interest, such as
a post office or polling place, and all other network vertices must be labeled
with the center to which they are associated. We focus on defining geographic
districts that are equitable, in that every district has the same number of
vertices and the assignment is stable in terms of geographic distance. That is,
there is no unassigned vertex-center pair such that both would prefer each
other over their current assignments. We solve this problem using a version of
the classic stable matching problem, called symmetric stable matching, in which
the preferences of the elements in both sets obey a certain symmetry. In our
case, we study a graph-based version of stable matching in which nodes are
stably matched to a subset of nodes denoted as centers, prioritized by their
shortest-path distances, so that each center is apportioned a certain number of
nodes. We show that, for a planar graph or road network with nodes and
centers, the problem can be solved in time, which improves
upon the runtime of using the classic Gale-Shapley stable matching
algorithm when is large. Finally, we provide experimental results on road
networks for these algorithms and a heuristic algorithm that performs better
than the Gale-Shapley algorithm for any range of values of .Comment: 9 pages, 4 figures, to appear in 25th ACM SIGSPATIAL International
Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL
2017) November 7-10, 2017, Redondo Beach, California, US
The Skip Quadtree: A Simple Dynamic Data Structure for Multidimensional Data
We present a new multi-dimensional data structure, which we call the skip
quadtree (for point data in R^2) or the skip octree (for point data in R^d,
with constant d>2). Our data structure combines the best features of two
well-known data structures, in that it has the well-defined "box"-shaped
regions of region quadtrees and the logarithmic-height search and update
hierarchical structure of skip lists. Indeed, the bottom level of our structure
is exactly a region quadtree (or octree for higher dimensional data). We
describe efficient algorithms for inserting and deleting points in a skip
quadtree, as well as fast methods for performing point location and approximate
range queries.Comment: 12 pages, 3 figures. A preliminary version of this paper appeared in
the 21st ACM Symp. Comp. Geom., Pisa, 2005, pp. 296-30
Choosing Colors for Geometric Graphs via Color Space Embeddings
Graph drawing research traditionally focuses on producing geometric
embeddings of graphs satisfying various aesthetic constraints. After the
geometric embedding is specified, there is an additional step that is often
overlooked or ignored: assigning display colors to the graph's vertices. We
study the additional aesthetic criterion of assigning distinct colors to
vertices of a geometric graph so that the colors assigned to adjacent vertices
are as different from one another as possible. We formulate this as a problem
involving perceptual metrics in color space and we develop algorithms for
solving this problem by embedding the graph in color space. We also present an
application of this work to a distributed load-balancing visualization problem.Comment: 12 pages, 4 figures. To appear at 14th Int. Symp. Graph Drawing, 200
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