Results 1  10
of
735,836
A Weighted Planar Graph Separator
, 1998
"... Given a weighted planar graph, we construct a simple separating cycle C whose interior and exterior both weigh at most 2/3 of the total weight. The cycle C uses k jumps across the faces and ordinary edges with cost O(1/k) of the total edge cost. This theorem is the main component of a PTAS for the ..."
Abstract
 Add to MetaCart
Given a weighted planar graph, we construct a simple separating cycle C whose interior and exterior both weigh at most 2/3 of the total weight. The cycle C uses k jumps across the faces and ordinary edges with cost O(1/k) of the total edge cost. This theorem is the main component of a PTAS
Approximate minimum 2connected subgraphs in weighted planar graphs
, 2004
"... We consider the problems of finding the minimumweight 2connected spanning subgraph in edgeweighted planar graphs and its variations. We first give a PTAS for the problem of finding minimumweight 2edgeconnected spanning subgraphs where duplicate edges are allowed. Then we present a new greedy s ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We consider the problems of finding the minimumweight 2connected spanning subgraph in edgeweighted planar graphs and its variations. We first give a PTAS for the problem of finding minimumweight 2edgeconnected spanning subgraphs where duplicate edges are allowed. Then we present a new greedy
Approximation schemes for minimum 2connected spanning subgraphs in weighted planar graphs
 in Proc. of ESA
, 2005
"... Abstract. We present new approximation schemes for various classical problems of finding the minimumweight spanning subgraph in edgeweighted undirected planar graphs that are resistant to edge or vertex removal. We first give a PTAS for the problem of finding minimumweight 2edgeconnected spanni ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
Abstract. We present new approximation schemes for various classical problems of finding the minimumweight spanning subgraph in edgeweighted undirected planar graphs that are resistant to edge or vertex removal. We first give a PTAS for the problem of finding minimumweight 2edge
Counting minimum (s, t)cuts in weighted planar graphs in polynomial time
"... Abstract. We give an O(nd+n log n) algorithm computing the number of minimum (s, t)cuts in weighted planar graphs, where n is the number of vertices and d is the length of the shortest st path in the corresponding unweighted graph. Previously, Ball and Provan gave a polynomialtime algorithm for u ..."
Abstract
 Add to MetaCart
Abstract. We give an O(nd+n log n) algorithm computing the number of minimum (s, t)cuts in weighted planar graphs, where n is the number of vertices and d is the length of the shortest st path in the corresponding unweighted graph. Previously, Ball and Provan gave a polynomialtime algorithm
A polynomialtime approximation scheme for weighted planar graph TSP
 PROC. 9TH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS, PP 33–41
, 1998
"... Given a planar Rraph on n nodes with costs (weights) on its edges, define;he distance between nodes i &d 2 as ’ the length of the shortest path between i and i. Consider this as &I instance of me & TSP. For any E> 6, our algorithm finds a salesman tour of total cost at most (1 + E) t ..."
Abstract

Cited by 61 (13 self)
 Add to MetaCart
Given a planar Rraph on n nodes with costs (weights) on its edges, define;he distance between nodes i &d 2 as ’ the length of the shortest path between i and i. Consider this as &I instance of me & TSP. For any E> 6, our algorithm finds a salesman tour of total cost at most (1 + E
Contiguous minimum singlesourcemultisink cuts in weighted planar graphs
"... Abstract. We present a fast algorithm for uniform sampling of contiguous minimum cuts separating a source vertex from a set of sink vertices in a weighted undirected planar graph with n vertices embedded in the plane. The algorithm takes O(n) time per sample, after an initial O(n 3) preprocessing ti ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. We present a fast algorithm for uniform sampling of contiguous minimum cuts separating a source vertex from a set of sink vertices in a weighted undirected planar graph with n vertices embedded in the plane. The algorithm takes O(n) time per sample, after an initial O(n 3) preprocessing
Counting and sampling minimum (s, t)cuts in weighted planar graphs in polynomial time
"... We give an O(nd + n log n) algorithm computing the number of minimum (s, t)cuts in weighted planar graphs, where n is the number of vertices and d is the length of the shortest st path in the corresponding unweighted graph. Previously, Ball and Provan gave a polynomialtime algorithm for unweighte ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We give an O(nd + n log n) algorithm computing the number of minimum (s, t)cuts in weighted planar graphs, where n is the number of vertices and d is the length of the shortest st path in the corresponding unweighted graph. Previously, Ball and Provan gave a polynomialtime algorithm
Wiener Index, Diameter, and Stretch Factor of a Weighted Planar Graph in Subquadratic Time
, 2008
"... We solve three open problems: the existence of subquadratic time algorithms for computing the Wiener index (sum of APSP distances) and the diameter (maximum distance between any vertex pair) of a planar graph with nonnegative edge weights and the stretch factor of a plane geometric graph (maximum o ..."
Abstract
 Add to MetaCart
We solve three open problems: the existence of subquadratic time algorithms for computing the Wiener index (sum of APSP distances) and the diameter (maximum distance between any vertex pair) of a planar graph with nonnegative edge weights and the stretch factor of a plane geometric graph (maximum
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 627 (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
Results 1  10
of
735,836