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An approximation algorithm for the total covering problem

100%
Hatami P.
Discussiones Mathematicae Graph Theory
|
2007
|
tom 27
|
nr 3
553-558
EN
We introduce a 2-factor approximation algorithm for the minimum total covering number problem.
2
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An efficient connected dominating set algorithm in wsns based on the induced tree of the crossed cube

88%
Zhang J., Xu L., Zhou S.-m., Wu W., Ye X.
International Journal of Applied Mathematics and Computer Science
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2015
|
tom 25
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nr 2
295-309
EN
The connected dominating set (CDS) has become a well-known approach for constructing a virtual backbone in wireless sensor networks. Then traffic can forwarded by the virtual backbone and other nodes turn off their radios to save energy. Furthermore, a smaller CDS incurs fewer interference problems. However, constructing a minimum CDS is an NP-hard problem, and thus most researchers concentrate on how to derive approximate algorithms. In this paper, a novel algorithm based on the induced tree of the crossed cube (ITCC) is presented. The ITCC is to find a maximal independent set (MIS), which is based on building an induced tree of the crossed cube network, and then to connect the MIS nodes to form a CDS. The priority of an induced tree is determined according to a new parameter, the degree of the node in the square of a graph. This paper presents the proof that the ITCC generates a CDS with a lower approximation ratio. Furthermore, it is proved that the cardinality of the induced trees is a Fibonacci sequence, and an upper bound to the number of the dominating set is established. The simulations show that the algorithm provides the smallest CDS size compared with some other traditional algorithms.
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Selected multicriteria shortest path problems: an analysis of complexity, models and adaptation of standard algorithms

75%
Tarapata Z.
International Journal of Applied Mathematics and Computer Science
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2007
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tom 17
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nr 2
269-287
EN
The paper presents selected multicriteria (multiobjective) approaches to shortest path problems. A classification of multi-objective shortest path (MOSP) problems is given. Different models of MOSP problems are discussed in detail. Methods of solving the formulated optimization problems are presented. An analysis of the complexity of the presented methods and ways of adapting of classical algorithms for solving multiobjective shortest path problems are described. A comparison of the effectiveness of solving selected MOSP problems defined as mathematical programming problems (using the CPLEX 7.0 solver) and multi-weighted graph problems (using modified Dijkstra's algorithm) is given. Experimental results of using the presented methods for multicriteria path selection in a terrain-based grid network are given.
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