27,426 research outputs found
The (k,l) Coredian tree for Ad Hoc Networks
In this paper, we present a new efficient strategy for constructing a wireless tree network containing n nodes of diameter ∆ while satisfying the QoS requirements such as bandwidth and delay. Given a tree network T , a coredian path is a path in T that minimizes the centdian function, a k-coredian tree is a subtree of T with k leaves that minimizes the centdian function, and a (k, l)-coredian tree is a subtree of T with k leaves and diameter l at most that minimizes the centdian function. The (k, l)-coredian tree can serve as a backbone for a network, where the internal nodes belong to the backbone and the leaves serve as the heads of the clusters covering the rest of the network. We show that a coredian path can be constructed at O(∆) time with O(n) messages and a k-coredian tree can be constructed at O(k∆) time with O(kn) messages. We provide an O(n 2 ) time construction algorithm for the (k, l)-coredian tree that requires O(n 2 ) messages. We also give upper and lower bounds for a number of nodes covered by the k cluster heads in random geometric graph using critical transmission range of connected network. Finally, simulation is presented for various values of n and k
Bandwidth and density for block graphs
The bandwidth of a graph G is the minimum of the maximum difference between
adjacent labels when the vertices have distinct integer labels. We provide a
polynomial algorithm to produce an optimal bandwidth labeling for graphs in a
special class of block graphs (graphs in which every block is a clique), namely
those where deleting the vertices of degree one produces a path of cliques. The
result is best possible in various ways. Furthermore, for two classes of graphs
that are ``almost'' caterpillars, the bandwidth problem is NP-complete.Comment: 14 pages, 9 included figures. Note: figures did not appear in
original upload; resubmission corrects thi
Bandwidth, expansion, treewidth, separators, and universality for bounded degree graphs
We establish relations between the bandwidth and the treewidth of bounded
degree graphs G, and relate these parameters to the size of a separator of G as
well as the size of an expanding subgraph of G. Our results imply that if one
of these parameters is sublinear in the number of vertices of G then so are all
the others. This implies for example that graphs of fixed genus have sublinear
bandwidth or, more generally, a corresponding result for graphs with any fixed
forbidden minor. As a consequence we establish a simple criterion for
universality for such classes of graphs and show for example that for each
gamma>0 every n-vertex graph with minimum degree ((3/4)+gamma)n contains a copy
of every bounded-degree planar graph on n vertices if n is sufficiently large
Static Data Structure for Discrete Advance Bandwidth Reservations on the Internet
In this paper we present a discrete data structure for reservations of
limited resources. A reservation is defined as a tuple consisting of the time
interval of when the resource should be reserved, , and the amount of the
resource that is reserved, , formally .
The data structure is similar to a segment tree. The maximum spanning
interval of the data structure is fixed and defined in advance. The granularity
and thereby the size of the intervals of the leaves is also defined in advance.
The data structure is built only once. Neither nodes nor leaves are ever
inserted, deleted or moved. Hence, the running time of the operations does not
depend on the number of reservations previously made. The running time does not
depend on the size of the interval of the reservation either. Let be the
number of leaves in the data structure. In the worst case, the number of
touched (i.e. traversed) nodes is in any operation , hence the
running time of any operation is also
Optimal Replica Placement in Tree Networks with QoS and Bandwidth Constraints and the Closest Allocation Policy
This paper deals with the replica placement problem on fully homogeneous tree
networks known as the Replica Placement optimization problem. The client
requests are known beforehand, while the number and location of the servers are
to be determined. We investigate the latter problem using the Closest access
policy when adding QoS and bandwidth constraints. We propose an optimal
algorithm in two passes using dynamic programming
The Effect of Planarization on Width
We study the effects of planarization (the construction of a planar diagram
from a non-planar graph by replacing each crossing by a new vertex) on
graph width parameters. We show that for treewidth, pathwidth, branchwidth,
clique-width, and tree-depth there exists a family of -vertex graphs with
bounded parameter value, all of whose planarizations have parameter value
. However, for bandwidth, cutwidth, and carving width, every graph
with bounded parameter value has a planarization of linear size whose parameter
value remains bounded. The same is true for the treewidth, pathwidth, and
branchwidth of graphs of bounded degree.Comment: 15 pages, 6 figures. To appear at the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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