• Publications
  • Influence
Finding the k shortest paths
  • D. Eppstein
  • Mathematics, Computer Science
    Proceedings 35th Annual Symposium on Foundations…
  • 20 November 1994
TLDR
K shortest paths are given for finding the k shortest paths connecting a pair of vertices in a digraph, and applications to dynamic programming problems including the knapsack problem, sequence alignment, and maximum inscribed polygons are described.
The Crust and the beta-Skeleton: Combinatorial Curve Reconstruction
TLDR
Two different graphs are given that, in this sense, reconstruct smooth curves: a simple new construction which is called the crust, and the β-skeleton, using a specific value of β.
Reset Sequences for Monotonic Automata
TLDR
A new algorithm based on breadth-first search is presented that runs in faster asymptotic time than Natarajan’s algorithms, and in addition finds the shortest possible reset sequence if such a sequence exists.
Provably good mesh generation
TLDR
It is shown how to triangulate a planar point set or a polygonally bounded domain with triangles of bounded aspect ratio, and how to produce a linear-size Delaunay triangulation of a multidimensional point set by adding a linear number of extra points.
Listing All Maximal Cliques in Sparse Graphs in Near-optimal Time
TLDR
There exists a nearly-optimal fixed-parameter tractable algorithm for enumerating all maximal cliques, parametrized by degeneracy, and this algorithm matches the Θ(d(n − d)3 d/3) worst-case output size of the problem whenever n − d = Ω(n).
Subgraph isomorphism in planar graphs and related problems
We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small
Listing All Maximal Cliques in Large Sparse Real-World Graphs
We implement a new algorithm for listing all maximal cliques in sparse graphs due to Eppstein, Loffler, and Strash (ISAAC 2010) and analyze its performance on a large corpus of real-world graphs. Our
Sparsification-a technique for speeding up dynamic graph algorithms
The authors provide data structures that maintain a graph as edges are inserted and deleted, and keep track of the following properties: minimum spanning forests, best swap, graph connectivity, and
Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions
TLDR
The algorithm simulates the sequence of collisions between edges and vertices during the shrinking process, using a technique of Eppstein for maintaining extrema of binary functions to reduce the problem of finding successive interactions to two dynamic range query problems.
Diameter and Treewidth in Minor-Closed Graph Families
TLDR
It is shown that treewidth is bounded by a function of the diameter in a minor-closed family, if and only if some apex graph does not belong to the family, and the O(D) bound above can be extended to bounded-genus graphs.
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