Describes efficient sequential and parallel algorithms for orienting the edges of an undirected planar graph so that each vertex has few outgoing edges. From such an orientation one can test in constant time whether a given edge exists. One consequence is a parallel algorithm to list all subgraphs isomorphic to K3 or K4. More recently this paper has been cited for its applications to scheduling update operations in parallel finite element methods.
(BibTeX -- Citations -- CiteSeer -- ACM DL)
The complement of a minimum spanning tree is a maximum spanning tree in the dual graph. By applying this fact we can use a modified form of Sleator and Tarjan's dynamic tree data structure to update the MST in logarithmic time per update.
(BibTeX -- Citations -- CiteSeer -- ACM DL)
It was known that planar graphs have O(n) subgraphs isomorphic to K3 or K4. This paper characterizes the subgraphs for which such a linear bound holds: they are exactly the 3-connected planar graphs. Please note that the Tech. Rep. version had a bug (in a supposed generalization of the result to nonplanar graph families) which was corrected in the journal version.
(BibTeX -- Citations -- CiteSeer -- ACM DL)
Replaces portions of a hierarchical separator decomposition with smaller certificates to achieve fast update times for various dynamic planar graph problems. Applications include finding the k best spanning trees of a planar graph.
(BibTeX -- Citations -- MIT hypertext bibliography)
First half of journal version of Separator based sparsification for dynamic planar graph algorithms.
Second half of journal version of Separator based sparsification for dynamic planar graph algorithms.
Uses an idea of Baker to cover a planar graph with subgraphs of low treewidth. As a consequence, any fixed pattern can be found as a subgraph in linear time; the same methods can be used to solve other planar graph problems including vertex connectivity, diameter, girth, induced subgraph isomorphism, and shortest paths. A companion paper presents a result announced in the conference version of this paper, that exactly characterizes the minor-closed graph families for which the same techniques apply.
(BibTeX -- Citations -- Citations from MIT hypertext bibliography -- CiteSeer (SODA) -- CiteSeer (JGAA))
It was known that planar graphs have the diameter-treewidth property: there is a function f(D) such that any planar graph with diameter D has treewidth at most f(D). (Actually, f(D)=O(D).) We characterize the other minor-closed families with this property: F has the diameter-treewidth property if and only if there is a graph G, formed by adding a vertex to a planar graph, that is not in F. Families with the diameter-treewidth property include bounded-genus graphs (for which again f(D)=O(D)) and K3,a-free graphs. As a consequence, various efficient planar subgraph isomorphism and approximation algorithms can be extended to these families. Some of these results were announced in the conference version of "subgraph isomorphism for planar graphs and related problems" but not included in the journal version.
Graph Theory -- Publications -- David Eppstein -- Theory Group -- Inf. & Comp. Sci. -- UC Irvine
Semi-automatically filtered from a common source file.