Results 1  10
of
92
Approximation Algorithms for Disjoint Paths Problems
, 1996
"... The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for w ..."
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Cited by 139 (0 self)
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The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for which very little is known from the point of view of approximation algorithms. It has recently been brought into focus in work on problems such as VLSI layout and routing in highspeed networks; in these settings, the current lack of understanding of the disjoint paths problem is often an obstacle to the design of practical heuristics.
Diameter and Treewidth in MinorClosed Graph Families
, 1999
"... It is known that any planar graph with diameter D has treewidth O(D), and this fact has been used as the basis for several planar graph algorithms. We investigate the extent to which similar relations hold in other graph families. We show that treewidth is bounded by a function of the diameter in a ..."
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Cited by 82 (3 self)
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It is known that any planar graph with diameter D has treewidth O(D), and this fact has been used as the basis for several planar graph algorithms. We investigate the extent to which similar relations hold in other graph families. We show that treewidth is bounded by a function of the diameter in a minorclosed family, if and only if some apex graph does not belong to the family. In particular, the O(D) bound above can be extended to boundedgenus graphs. As a consequence, we extend several approximation algorithms and exact subgraph isomorphism algorithms from planar graphs to other graph families.
Dominating Sets in Planar Graphs: BranchWidth and Exponential Speedup
, 2002
"... Graph minors theory, developed by Robertson & Seymour, provides a list of powerful theoretical results and tools. However, the wide spread opinion in Graph Algorithms community about this theory is that it is mainly of theoretical importance. ..."
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Cited by 65 (13 self)
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Graph minors theory, developed by Robertson & Seymour, provides a list of powerful theoretical results and tools. However, the wide spread opinion in Graph Algorithms community about this theory is that it is mainly of theoretical importance.
A simpler linear time algorithm for embedding graphs into an arbitrary surface and the genus of graphs of bounded treewidth
, 2008
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Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
 In 46th Annual IEEE Symposium on Foundations of Computer Science
, 2005
"... At the core of the seminal Graph Minor Theory of Robertson and Seymour is a powerful structural theorem capturing the structure of graphs excluding a fixed minor. This result is used throughout graph theory and graph algorithms, but is existential. We develop a polynomialtime algorithm using topolog ..."
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Cited by 42 (12 self)
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At the core of the seminal Graph Minor Theory of Robertson and Seymour is a powerful structural theorem capturing the structure of graphs excluding a fixed minor. This result is used throughout graph theory and graph algorithms, but is existential. We develop a polynomialtime algorithm using topological graph theory to decompose a graph into the structure guaranteed by the theorem: a cliquesum of pieces almostembeddable into boundedgenus surfaces. This result has many applications. In particular, we show applications to developing many approximation algorithms, including a 2approximation to graph coloring, constantfactor approximations to treewidth and the largest grid minor, combinatorial polylogarithmicapproximation to halfintegral multicommodity flow, subexponential fixedparameter algorithms, and PTASs for many minimization and maximization problems, on graphs excluding a fixed minor. 1.
Object Location Using Path Separators
, 2006
"... We study a novel separator property called kpath separable. Roughly speaking, a kpath separable graph can be recursively separated into smaller components by sequentially removing k shortest paths. Our main result is that every minor free weighted graph is kpath separable. We then show that kpat ..."
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Cited by 35 (11 self)
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We study a novel separator property called kpath separable. Roughly speaking, a kpath separable graph can be recursively separated into smaller components by sequentially removing k shortest paths. Our main result is that every minor free weighted graph is kpath separable. We then show that kpath separable graphs can be used to solve several object location problems: (1) a smallworldization with an average polylogarithmic number of hops; (2) an (1 + ε)approximate distance labeling scheme with O(log n) space labels; (3) a stretch(1 + ε) compact routing scheme with tables of polylogarithmic space; (4) an (1+ε)approximate distance oracle with O(n log n) space and O(log n) query time. Our results generalizes to much wider classes of weighted graphs, namely to boundeddimension isometric sparable graphs.
Fixedparameter algorithms for the (k, r)center in planar graphs and map graphs
 ACM TRANSACTIONS ON ALGORITHMS
, 2003
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Highly Connected Sets and the Excluded Grid Theorem
, 2000
"... We present a short proof of the excluded grid theorem of Robertson and Seymour, the fact that a graph has no large grid minor if and only if it has small treewidth. We further propose a very simple obstruction to small treewidth inspired by that proof, showing that a graph has small treewidth if ..."
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Cited by 28 (1 self)
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We present a short proof of the excluded grid theorem of Robertson and Seymour, the fact that a graph has no large grid minor if and only if it has small treewidth. We further propose a very simple obstruction to small treewidth inspired by that proof, showing that a graph has small treewidth if and only if it contains no large highly connected set of vertices.
Excluding Any Graph as a Minor Allows a Low TreeWidth 2Coloring
, 2001
"... This article proves the conjecture of Thomas that, for every graph G, there is an integer k such that every graph with no minor isomorphic to G has a 2coloring of either its vertices or its edges where each color induces a graph of treewidth at most k. Some generalizations are also proved. ..."
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Cited by 28 (2 self)
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This article proves the conjecture of Thomas that, for every graph G, there is an integer k such that every graph with no minor isomorphic to G has a 2coloring of either its vertices or its edges where each color induces a graph of treewidth at most k. Some generalizations are also proved.