2,393 research outputs found
Approximation Algorithmic Performance for CEDS in Wireless Network
A well-organized design of routing protocols in wireless networks, the connected dominating set (CDS) is widely used as a virtual backbone. To construct the CDS with its size as minimum, many heuristic, meta-heuristic, greedy, approximation and distributed algorithmic approaches have been anticipated. These approaches are concentrated on deriving independent set and then constructing the CDS using UDG, Steiner tree and these algorithms perform well only for the graphs having smaller number of nodes. For the networks that are generated in a fixed simulation area. This paper provides a novel approach for constructing the CDS, based on the concept of total edge dominating set. Since the total dominating set is the best lower bound for the CDS, the proposed approach reduces the computational complexity to construct the CDS through the number of iterations. The conducted simulation reveals that the proposed approach finds better solution than the recently developed approaches when important factors of network such as transmission radio range and area of network density varies
Approximation Algorithms for Connected Dominating Sets
The dominating set problem in graphs asks for a minimum size subset of
vertices with the following property: each vertex is required to either be
in the dominating set, or adjacent to some node in the dominating set.
We focus on the question of finding a {\em connected dominating set}
of minimum size, where the graph induced by vertices in the dominating
set is required to be {\em connected} as well.
This problem arises in network testing, as well as in wireless communication.
Two polynomial time algorithms that achieve approximation factors
of are presented, where is the maximum degree,
and is the harmonic function.
This question also arises in relation to the traveling tourist problem,
where one is looking for the shortest tour such that each vertex is either
visited, or has at least one of its neighbors visited.
We study a generalization of the problem when the vertices have weights,
and give an algorithm which achieves a performance ratio of .
We also consider the more general problem of
finding a connected dominating set of
a specified subset of vertices and provide an
approximation factor. To prove the bound we also develop an optimal
approximation algorithm for the unit node weighted Steiner tree problem.
(Also cross-referenced as UMIACS-TR-96-47
Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices
We study the Steiner Tree problem, in which a set of terminal vertices needs
to be connected in the cheapest possible way in an edge-weighted graph. This
problem has been extensively studied from the viewpoint of approximation and
also parametrization. In particular, on one hand Steiner Tree is known to be
APX-hard, and W[2]-hard on the other, if parameterized by the number of
non-terminals (Steiner vertices) in the optimum solution. In contrast to this
we give an efficient parameterized approximation scheme (EPAS), which
circumvents both hardness results. Moreover, our methods imply the existence of
a polynomial size approximate kernelization scheme (PSAKS) for the considered
parameter.
We further study the parameterized approximability of other variants of
Steiner Tree, such as Directed Steiner Tree and Steiner Forest. For neither of
these an EPAS is likely to exist for the studied parameter: for Steiner Forest
an easy observation shows that the problem is APX-hard, even if the input graph
contains no Steiner vertices. For Directed Steiner Tree we prove that
approximating within any function of the studied parameter is W[1]-hard.
Nevertheless, we show that an EPAS exists for Unweighted Directed Steiner Tree,
but a PSAKS does not. We also prove that there is an EPAS and a PSAKS for
Steiner Forest if in addition to the number of Steiner vertices, the number of
connected components of an optimal solution is considered to be a parameter.Comment: 23 pages, 6 figures An extended abstract appeared in proceedings of
STACS 201
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