Results 1  10
of
7,484
Upward Embeddings and Orientations of Undirected Planar Graphs
 Journal of Graph Algorithms and Applications
, 2001
"... An upward embedding of an embedded planar graph states, for each vertex v, which edges are incident to v \above" or \below" and, in turn, induces an upward orientation of the edges. In this paper we characterize the set of all upward embeddings and orientations of a plane graph by using a ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
An upward embedding of an embedded planar graph states, for each vertex v, which edges are incident to v \above" or \below" and, in turn, induces an upward orientation of the edges. In this paper we characterize the set of all upward embeddings and orientations of a plane graph by using a
More compact oracles for approximate distances in undirected planar graphs
 In SODA ’13
, 2013
"... Distance oracles are data structures that provide fast (possibly approximate) answers to shortestpath and distance queries in graphs. The tradeoff between the space requirements and the query time of distance oracles is of particular interest and the main focus of this paper. In FOCS‘01, Thorup int ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
introduced approximate distance oracles for planar graphs. He proved that, for any > 0 and for any planar graph on n nodes, there exists a (1 + )–approximate distance oracle using space O(n−1 logn) such that approximate distance queries can be answered in time O(−1). Ten years later, we give the first
Minimum s − t cut in undirected planar graphs when the source and the sink are close
 STACS
, 2011
"... ..."
A lineartime approximation scheme for TSP in undirected planar graphs with edgeweights
, 2009
"... We give an algorithm requiring O(c1/ǫ2n) time to find an ǫoptimal traveling salesman tour in the shortestpath metric defined by an undirected planar graph with nonnegative edgelengths. For the case of all lengths equal to 1, the time required is O(c 1/ǫ n). ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
We give an algorithm requiring O(c1/ǫ2n) time to find an ǫoptimal traveling salesman tour in the shortestpath metric defined by an undirected planar graph with nonnegative edgelengths. For the case of all lengths equal to 1, the time required is O(c 1/ǫ n).
An algorithm for drawing general undirected graphs
 Information Processing Letters
, 1989
"... Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, dataflow graphs, Petri nets, and entit ..."
Abstract

Cited by 698 (2 self)
 Add to MetaCart
Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, dataflow graphs, Petri nets
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
Abstract

Cited by 461 (1 self)
 Add to MetaCart
Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
Abstract

Cited by 628 (44 self)
 Add to MetaCart
as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar
Depth first search and linear graph algorithms
 SIAM JOURNAL ON COMPUTING
, 1972
"... The value of depthfirst search or "backtracking" as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components of an undirect ..."
Abstract

Cited by 1406 (19 self)
 Add to MetaCart
of an undirect graph are presented. The space and time requirements of both algorithms are bounded by k 1V + k2E d k for some constants kl, k2, and k a, where Vis the number of vertices and E is the number of edges of the graph being examined.
Routing with Guaranteed Delivery in ad hoc Wireless Networks
, 2001
"... We consider routing problems in ad hoc wireless networks modeled as unit graphs in which nodes are points in the plane and two nodes can communicate if the distance between them is less than some fixed unit. We describe the first distributed algorithms for routing that do not require duplication of ..."
Abstract

Cited by 849 (80 self)
 Add to MetaCart
We consider routing problems in ad hoc wireless networks modeled as unit graphs in which nodes are points in the plane and two nodes can communicate if the distance between them is less than some fixed unit. We describe the first distributed algorithms for routing that do not require duplication
Results 1  10
of
7,484