scispace - formally typeset
Search or ask a question
Author

David Eppstein

Other affiliations: McGill University, University of Passau, Princeton University  ...read more
Bio: David Eppstein is an academic researcher from University of California, Irvine. The author has contributed to research in topics: Planar graph & Time complexity. The author has an hindex of 67, co-authored 672 publications receiving 20584 citations. Previous affiliations of David Eppstein include McGill University & University of Passau.


Papers
More filters
Journal ArticleDOI
TL;DR: 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, maximum inscribed polygons, and genealogical relationship discovery are described.
Abstract: We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest paths from a given source s to each vertex in the graph, in total time O(m + n log n + kn). We describe applications to dynamic programming problems including the knapsack problem, sequence alignment, maximum inscribed polygons, and genealogical relationship discovery.

1,413 citations

Proceedings ArticleDOI
20 Nov 1994
TL;DR: 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.
Abstract: We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m+n log n+k). We can also find the k shortest paths from a given source s to each vertex in the graph, in total time O(m+n log n+kn). We describe applications to dynamic programming problems including the knapsack problem, sequence alignment, and maximum inscribed polygons. >

750 citations

Book ChapterDOI
01 Sep 1992

603 citations

Proceedings ArticleDOI
22 Jan 1995
TL;DR: In this paper, the subgraph isomorphism problem in planar graphs is solved in linear time, for any pattern of constant size, by partitioning the planar graph into pieces of small tree-width, and applying dynamic programming within each piece.
Abstract: 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 tree-width, and applying dynamic programming within each piece. The same methods can be used to solve other planar graph problems including connectivity, diameter, girth, induced subgraph isomorphism, and shortest paths.

448 citations

Journal ArticleDOI
TL;DR: In this paper, a graph on a planar point set is constructed by sampling a smooth curve densely enough, and the graph on the samples is a polygonalization of the curve, with no extraneous edges.

386 citations


Cited by
More filters
Journal ArticleDOI

[...]

08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Proceedings ArticleDOI
22 Jan 2006
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

7,116 citations

Journal ArticleDOI
TL;DR: A modularity matrix plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations, and a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong are proposed.
Abstract: We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as ``modularity'' over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.

4,559 citations

Proceedings ArticleDOI
23 May 1998
TL;DR: In this paper, the authors present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces, for data sets of size n living in R d, which require space that is only polynomial in n and d.
Abstract: We present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces. For data sets of size n living in R d , the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree. The article is based on the material from the authors' STOC'98 and FOCS'01 papers. It unifies, generalizes and simplifies the results from those papers.

4,478 citations

Journal ArticleDOI
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
Abstract: Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

4,236 citations