8,345 research outputs found
Local Approximation Schemes for Ad Hoc and Sensor Networks
We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1+Îľ)-approximation to the problems at hand for any given Îľ > 0. The time complexity of both algorithms is O(TMIS + log*! n/ÎľO(1)), where TMIS is the time required to compute a maximal independent set in the graph, and n denotes the number of nodes. We then extend these results to a more general class of graphs in which the maximum number of pair-wise independent nodes in every r-neighborhood is at most polynomial in r. Such graphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models, such as unit disk graphs or coverage area graphs
A PTAS for the minimum dominating set problem in unit disk graphs
We present a polynomial-time approximation scheme (PTAS) for the minimum dominating set problem in unit disk graphs. In contrast to previously known approximation schemes for the minimum dominating set problem on unit disk graphs, our approach does not assume a geometric representation of the vertices (specifying the positions of the disks in the plane) to be given as part of the input. \u
Approximating Minimum Independent Dominating Sets in Wireless Networks
We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth. Graphs of bounded growth are used to characterize wireless communication networks, and this class of graph includes many models known from the literature, e.g. (Quasi) Unit Disk Graphs. An independent dominating set is a dominating set in a graph that is also independent. It thus combines the advantages of both structures, and there are many applications that rely on these two structures e.g. in the area of wireless ad hoc networks. The presented approach yields a robust algorithm, that is, the algorithm accepts any undirected graph as input, and returns a (1+")- pproximate minimum dominating set, or a certificate showing that the input graph does not reflect a wireless network
On Sensor Network Localization Using SDP Relaxation
A Semidefinite Programming (SDP) relaxation is an effective computational
method to solve a Sensor Network Localization problem, which attempts to
determine the locations of a group of sensors given the distances between some
of them [11]. In this paper, we analyze and determine new sufficient conditions
and formulations that guarantee that the SDP relaxation is exact, i.e., gives
the correct solution. These conditions can be useful for designing sensor
networks and managing connectivities in practice.
Our main contribution is twofold: We present the first non-asymptotic bound
on the connectivity or radio range requirement of the sensors in order to
ensure the network is uniquely localizable. Determining this range is a key
component in the design of sensor networks, and we provide a result that leads
to a correct localization of each sensor, for any number of sensors. Second, we
introduce a new class of graphs that can always be correctly localized by an
SDP relaxation. Specifically, we show that adding a simple objective function
to the SDP relaxation model will ensure that the solution is correct when
applied to a triangulation graph. Since triangulation graphs are very sparse,
this is informationally efficient, requiring an almost minimal amount of
distance information. We also analyze a number objective functions for the SDP
relaxation to solve the localization problem for a general graph.Comment: 20 pages, 4 figures, submitted to the Fields Institute Communications
Series on Discrete Geometry and Optimizatio
Algorithms for Fast Aggregated Convergecast in Sensor Networks
Fast and periodic collection of aggregated data
is of considerable interest for mission-critical and continuous
monitoring applications in sensor networks. In the many-to-one
communication paradigm, referred to as convergecast, we focus
on applications wherein data packets are aggregated at each hop
en-route to the sink along a tree-based routing topology, and
address the problem of minimizing the convergecast schedule
length by utilizing multiple frequency channels. The primary
hindrance in minimizing the schedule length is the presence of
interfering links. We prove that it is NP-complete to determine
whether all the interfering links in an arbitrary network can
be removed using at most a constant number of frequencies.
We give a sufficient condition on the number of frequencies for
which all the interfering links can be removed, and propose a
polynomial time algorithm that minimizes the schedule length
in this case. We also prove that minimizing the schedule length
for a given number of frequencies on an arbitrary network is
NP-complete, and describe a greedy scheme that gives a constant
factor approximation on unit disk graphs. When the routing tree
is not given as an input to the problem, we prove that a constant
factor approximation is still achievable for degree-bounded trees.
Finally, we evaluate our algorithms through simulations and
compare their performance under different network parameters
Spanners for Geometric Intersection Graphs
Efficient algorithms are presented for constructing spanners in geometric
intersection graphs. For a unit ball graph in R^k, a (1+\epsilon)-spanner is
obtained using efficient partitioning of the space into hypercubes and solving
bichromatic closest pair problems. The spanner construction has almost
equivalent complexity to the construction of Euclidean minimum spanning trees.
The results are extended to arbitrary ball graphs with a sub-quadratic running
time.
For unit ball graphs, the spanners have a small separator decomposition which
can be used to obtain efficient algorithms for approximating proximity problems
like diameter and distance queries. The results on compressed quadtrees,
geometric graph separators, and diameter approximation might be of independent
interest.Comment: 16 pages, 5 figures, Late
Secure Clustering in DSN with Key Predistribution and WCDS
This paper proposes an efficient approach of secure clustering in distributed
sensor networks. The clusters or groups in the network are formed based on
offline rank assignment and predistribution of secret keys. Our approach uses
the concept of weakly connected dominating set (WCDS) to reduce the number of
cluster-heads in the network. The formation of clusters in the network is
secured as the secret keys are distributed and used in an efficient way to
resist the inclusion of any hostile entity in the clusters. Along with the
description of our approach, we present an analysis and comparison of our
approach with other schemes. We also mention the limitations of our approach
considering the practical implementation of the sensor networks.Comment: 6 page
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