2,430 research outputs found
An Order-based Algorithm for Minimum Dominating Set with Application in Graph Mining
Dominating set is a set of vertices of a graph such that all other vertices
have a neighbour in the dominating set. We propose a new order-based randomised
local search (RLS) algorithm to solve minimum dominating set problem in
large graphs. Experimental evaluation is presented for multiple types of
problem instances. These instances include unit disk graphs, which represent a
model of wireless networks, random scale-free networks, as well as samples from
two social networks and real-world graphs studied in network science. Our
experiments indicate that RLS performs better than both a classical greedy
approximation algorithm and two metaheuristic algorithms based on ant colony
optimisation and local search. The order-based algorithm is able to find small
dominating sets for graphs with tens of thousands of vertices. In addition, we
propose a multi-start variant of RLS that is suitable for solving the
minimum weight dominating set problem. The application of RLS in graph
mining is also briefly demonstrated
Connectivity, Coverage and Placement in Wireless Sensor Networks
Wireless communication between sensors allows the formation of flexible sensor networks, which can be deployed rapidly over wide or inaccessible areas. However, the need to gather data from all sensors in the network imposes constraints on the distances between sensors. This survey describes the state of the art in techniques for determining the minimum density and optimal locations of relay nodes and ordinary sensors to ensure connectivity, subject to various degrees of uncertainty in the locations of the nodes
Approximating k-Connected m-Dominating Sets
A subset of nodes in a graph is a -connected -dominating set
(-cds) if the subgraph induced by is -connected and every
has at least neighbors in . In the -Connected
-Dominating Set (-CDS) problem the goal is to find a minimum weight
-cds in a node-weighted graph. For we obtain the following
approximation ratios. For general graphs our ratio improves the
previous best ratio and matches the best known ratio for unit
weights. For unit disc graphs we improve the ratio to
-- this is the
first sublinear ratio for the problem, and the first polylogarithmic ratio
when ; furthermore, we obtain ratio
for uniform
weights. These results are obtained by showing the same ratios for the Subset
-Connectivity problem when the set of terminals is an -dominating set
with
Analysing local algorithms in location-aware quasi-unit-disk graphs
A local algorithm with local horizon r is a distributed algorithm that runs in r synchronous communication rounds; here r is a constant that does not depend on the size of the network. As a consequence, the output of a node in a local algorithm only depends on the input within r hops from the node. We give tight bounds on the local horizon for a class of local algorithms for combinatorial problems on unit-disk graphs (UDGs). Most of our bounds are due to a refined analysis of existing approaches, while others are obtained by suggesting new algorithms. The algorithms we consider are based on network decompositions guided by a rectangular tiling of the plane. The algorithms are applied to matching, independent set, graph colouring, vertex cover, and dominating set. We also study local algorithms on quasi-UDGs, which are a popular generalisation of UDGs, aimed at more realistic modelling of communication between the network nodes. Analysing the local algorithms on quasi-UDGs allows one to assume that the nodes know their coordinates only approximately, up to an additive error. Despite the localisation error, the quality of the solution to problems on quasi-UDGs remains the same as for the case of UDGs with perfect location awareness. We analyse the increase in the local horizon that comes along with moving from UDGs to quasi-UDGs.Peer reviewe
Improved Approximation Algorithm for Minimum-Weight --Connected Dominating Set
The classical minimum connected dominating set (MinCDS) problem aims to find
a minimum-size subset of connected nodes in a network such that every other
node has at least one neighbor in the subset. This problem is drawing
considerable attention in the field of wireless sensor networks because
connected dominating sets can serve as virtual backbones of such networks.
Considering fault-tolerance, researchers developed the minimum -connected
-fold CDS (MinCDS) problem. Many studies have been conducted on
MinCDSs, especially those in unit disk graphs. However, for the minimum-weight
CDS (MinWCDS) problem in general graphs, algorithms with guaranteed
approximation ratios are rare. Guha and Khuller designed a
-approximation algorithm for MinWCDS, where is the
number of nodes. In this paper, we improved the approximation ratio to
for MinWCDS, where is the
maximum degree of the graph
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