Defining Equitable Geographic Districts in Road Networks via Stable Matching
@article{Eppstein2017DefiningEG, title={Defining Equitable Geographic Districts in Road Networks via Stable Matching}, author={David Eppstein and Michael T. Goodrich and Doruk Korkmaz and Nil Mamano}, journal={Proceedings of the 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems}, year={2017} }
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…
10 Citations
On the computational tractability of a geographic clustering problem arising in redistricting
- MathematicsFORC
- 2021
If the diameter of the graph is moderately small and the number of districts is very small, the algorithm is useable, and it is shown that, under a complexity-theoretic assumption, no algorithms with running time of the form $O(c^wn^{k+1})$ exist.
Stable-Matching Voronoi Diagrams: Combinatorial Complexity and Algorithms
- Computer Science, MathematicsICALP
- 2018
This paper shows that a stable-matching Voronoi diagram of $n$ point sites has $O(n^{2+\varepsilon})$ faces and edges, for any $0$, and shows that this bound is almost tight by giving a family of diagrams with $\Theta(n^2)$ face and edges.
Reactive Proximity Data Structures for Graphs
- Computer ScienceLATIN
- 2018
This work presents novel reactive proximity data structures for graphs of polynomial expansion, i.e., the class of graphs with small separators, such as planar graphs and road networks, and experimentally compares their data structure to Dijkstra's algorithm.
Balanced power diagrams for redistricting
- MathematicsArXiv
- 2017
We propose a method for redistricting, decomposing a geographical area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are compact…
Euclidean TSP, Motorcycle Graphs, and Other New Applications of Nearest-Neighbor Chains
- Computer Science, MathematicsArXiv
- 2019
We show new applications of the nearest-neighbor chain algorithm, a technique that originated in agglomerative hierarchical clustering. We apply it to a diverse class of geometric problems: we…
Parallel Cover Trees and their Applications
- Computer ScienceSPAA
- 2022
This paper shows highly parallel and work-efficient cover tree algorithms that can handle batch insertions (and thus construction) and batch deletions and uses three key ideas to guarantee work-efficiency: the prefix-doubling scheme, a careful design to limit the graph size on which it applies MIS, and a strategy to propagate information among different levels in the cover tree.
Computing β-Stretch Paths in Drawings of Graphs
- MathematicsSWAT
- 2020
The βSP quantifies a notion of “near straightness” for paths in a graph G, motivated by gerrymandered regions in a map, where edges of G represent natural geographical/political boundaries that may be chosen to bound election districts.
New Applications of Nearest-Neighbor Chains: Euclidean TSP and Motorcycle Graphs
- Computer ScienceISAAC
- 2019
New applications of the nearest-neighbor chain algorithm are shown, a technique that originated in agglomerative hierarchical clustering that is used to construct the greedy multi-fragment tour for Euclidean TSP and for Steiner TSP in planar graphs in O(n √ n log n) time.
Graphical Models of Pandemic
- Computer SciencemedRxiv
- 2021
Both COVID-19 and novel pandemics challenge those of us within the modeling community, specifically in establishing suitable relations between lifecycles, scales, and existing methods. Herein we…
Balanced centroidal power diagrams for redistricting
- MathematicsSIGSPATIAL/GIS
- 2018
The solution is, in a well-defined sense, a locally optimal solution to the problem of choosing centers in the plane and choosing an assignment of people to those 2-d centers so as to minimize the sum of squared distances subject to the assignment being balanced.
References
SHOWING 1-10 OF 49 REFERENCES
Weighted Voronoi region algorithms for political districting
- Computer ScienceMath. Comput. Model.
- 2007
Studying (non-planar) road networks through an algorithmic lens
- Computer ScienceGIS '08
- 2008
This paper studies real-world road networks from an algorithmic perspective, focusing on empirical studies that yield useful properties of road networks that can be exploited in the design of fast…
A Stable Marriage of Poisson and Lebesgue
- Mathematics
- 2006
Let be a discrete set in R d . Call the elements of centers. The well-known Voronoi tessellation partitions R d into polyhedral regions (of varying sizes) by allocating each site of R d to the…
Going off-road: transversal complexity in road networks
- Computer Science, MathematicsGIS
- 2009
By viewing road networks as multiscale-dispersed graphs, it is shown that a random line will cross the edges of such a graph O(√n) times on average, which allows for point location and ray-shooting navigational queries with respect to road networks in O( √n log n) expected time.
Reactive Proximity Data Structures for Graphs
- Computer ScienceLATIN
- 2018
This work presents novel reactive proximity data structures for graphs of polynomial expansion, i.e., the class of graphs with small separators, such as planar graphs and road networks, and experimentally compares their data structure to Dijkstra's algorithm.
Fully Dynamic Algorithms for Maintaining Shortest Paths Trees
- Computer Science, MathematicsJ. Algorithms
- 2000
We propose fully dynamic algorithms for maintaining the distances and the shortest paths from a single source in either a directed or an undirected graph with positive real edge weights, handling…
Shortest Path Tree Computation in Dynamic Graphs
- Computer ScienceIEEE Transactions on Computers
- 2009
This work correct and extend a few state-of-the-art dynamic SPT algorithms to handle multiple edge weight updates and compares them with the well-known static Dijkstra algorithm.
On Dynamic Shortest Paths Problems
- Computer Science, MathematicsAlgorithmica
- 2010
Reductions that show that the incremental and decremental single-source shortest-paths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static all-pairs shortest- Paths problem.
Dynamic Planar Voronoi Diagrams for General Distance Functions and their Algorithmic Applications
- Computer ScienceSODA
- 2017
A new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions, and a randomized incremental construction algorithm for computing the lowest k levels in an arrangement of bivariate algebraic functions is developed.