Results 1 
7 of
7
Multimedia Communication
 Proceedings of the IEEE
, 1997
"... : Multimedia communication deals with the transfer, the protocols, services and mechanisms of discrete media data (such as text and graphics) and continuous media data (like audio and video) in/over digital networks. Such a communication requires all involved components to be capable of handling a w ..."
Abstract

Cited by 41 (0 self)
 Add to MetaCart
: Multimedia communication deals with the transfer, the protocols, services and mechanisms of discrete media data (such as text and graphics) and continuous media data (like audio and video) in/over digital networks. Such a communication requires all involved components to be capable of handling a welldefined quality of service. The most important quality of service parameters are used to request (1) the required capacities of the involved resources, (2) compliance to endtoend delay and jitter as timing restrictions, and (3) restriction of the loss characteristics. In this paper we describe the necessary issues and we study the ability of current networks and communication systems to support distributed multimedia applications. Further, we discuss upcoming approaches and systems which promise to provide the necessary mechanisms and consider which issues are missing for a complete multimedia communication infrastructure. Keywords: multimedia, communication, quality of service, reser...
Equivalence of Local Treewidth and Linear Local Treewidth and its Algorithmic Applications
 In Proceedings of the 15th ACMSIAM Symposium on Discrete Algorithms (SODA’04
, 2003
"... We solve an open problem posed by Eppstein in 1995 [14, 15] and reenforced by Grohe [16, 17] concerning locally bounded treewidth in minorclosed families of graphs. A graph has bounded local treewidth if the subgraph induced by vertices within distance r of any vertex has treewidth bounded by a f ..."
Abstract

Cited by 28 (10 self)
 Add to MetaCart
We solve an open problem posed by Eppstein in 1995 [14, 15] and reenforced by Grohe [16, 17] concerning locally bounded treewidth in minorclosed families of graphs. A graph has bounded local treewidth if the subgraph induced by vertices within distance r of any vertex has treewidth bounded by a function of r (not n). Eppstein characterized minorclosed families of graphs with bounded local treewidth as precisely minorclosed families that minorexclude an apex graph, where an apex graph has one vertex whose removal leaves a planar graph. In particular, Eppstein showed that all apexminorfree graphs have bounded local treewidth, but his bound is doubly exponential in r, leaving open whether a tighter bound could be obtained. We improve this doubly exponential bound to a linear bound, which is optimal. In particular, any minorclosed graph family with bounded local treewidth has linear local treewidth. Our bound generalizes previously known linear bounds for special classes of graphs proved by several authors. As a consequence of our result, we obtain substantially faster polynomialtime approximation schemes for a broad class of problems in apexminorfree graphs, improving the running time from .
Graphs Excluding a Fixed Minor have Grids as Large as Treewidth, with Combinatorial and Algorithmic Applications through Bidimensionality
, 2005
"... We prove that any Hminorfree graph, for a fixed graph H, of treewidth w has an Ω(w) × Ω(w) grid graph as a minor. Thus grid minors suffice to certify that Hminorfree graphs have large treewidth, up to constant factors. This strong relationship was previously known for the special cases of plana ..."
Abstract

Cited by 19 (7 self)
 Add to MetaCart
We prove that any Hminorfree graph, for a fixed graph H, of treewidth w has an Ω(w) × Ω(w) grid graph as a minor. Thus grid minors suffice to certify that Hminorfree graphs have large treewidth, up to constant factors. This strong relationship was previously known for the special cases of planar graphs and boundedgenus graphs, and is known not to hold for general graphs. The approach of this paper can be viewed more generally as a framework for extending combinatorial results on planar graphs to hold on Hminorfree graphs for any fixed H. Our result has many combinatorial consequences on bidimensionality theory, parametertreewidth bounds, separator theorems, and bounded local treewidth; each of these combinatorial results has several algorithmic consequences including subexponential fixedparameter algorithms and approximation algorithms.
The Price of Connectedness in Expansions
"... Expansion is the way of generalizing different graph layout and searching problems. We initiate the study of connected expansion which naturally arises in a number of applications. Our main ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
Expansion is the way of generalizing different graph layout and searching problems. We initiate the study of connected expansion which naturally arises in a number of applications. Our main
Algorithmic graph minor theory: Improved grid minor bounds and wagner’s contraction
 Proceedings of the Third International Conference on Distributed Computing and Internet Technology
, 2006
"... ..."
Exponential Speedup of FixedParameter Algorithms for Classes of Graphs Excluding SingleCrossing Graphs as Minors
, 2002
"... We present a fixedparameter algorithm that constructively solves the kdominating set problem on any class of graphs excluding a singlecrossing graph (a graph that can be drawn in the plane with at most one crossing) as a minor in O(4 9.55 √ k n O(1) ) time. Examples of such graph classes are the ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
We present a fixedparameter algorithm that constructively solves the kdominating set problem on any class of graphs excluding a singlecrossing graph (a graph that can be drawn in the plane with at most one crossing) as a minor in O(4 9.55 √ k n O(1) ) time. Examples of such graph classes are the K3,3minorfree graphs and the K5minorfree graphs. As a consequence, we extend our results to several other problems such as vertex cover, edge dominating set, independent set, cliquetransversal set, kernels in digraphs, feedback vertex set, and a collection of vertexremoval problems. Our work generalizes and extends the recent results of exponential speedup in designing fixedparameter algorithms on planar graphs due to Alber et al. to other (nonplanar) classes of graphs.
Bidimensionality, Map Graphs, and Grid Minors
, 2005
"... In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and the size of the largest grid minor. These bounds improve the ..."
Abstract
 Add to MetaCart
In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and the size of the largest grid minor. These bounds improve the running times of a broad class of fixedparameter algorithms. Our novel technique of using approximate maxmin relations between treewidth and size of grid minors is powerful, and we show how it can also be used, e.g., to prove a linear relation between the treewidth of a boundedgenus graph and the treewidth of its dual.