17738179
Perfect edge domination and efficient edge domination in graphs
Let G = (V,E) be a finite and undirected graph without loops and multiple edges. An edge is said to dominate itself and any edge adjacent to it. A subset D of E is called a perfect edge dominating set if every edge of E \ D is dominated by exactly one edge in D and an efficient edge dominating set if every edge of E is dominated by exactly one edge in D. The perfect (efficient) edge domination problem is to find a perfect (efficient) edge dominating set of minimum size in G. Suppose that each edge e is associated with a real number w(e) as its weight. Then, the weighted perfect (efficient) edge domination problem is to calculate a perfect (efficient) edge dominating set D such that the weight w(D) of D is minimum, where w(D)=Σe∈D w(e). In this paper, we show that the perfect (efficient) edge domination problem is NP-complete on bipartite (planar bipartite) graphs. Moreover, we present linear-time algorithms to solve the weighted perfect (efficient) edge domination problem on generalized series-parallel graphs and chordal graphs.
15221618
Weighted efficient domination problem on some perfect graphs
Abstract Given a simple graph G =( V , E ), a vertex v ∈ V is said to dominate itself and all vertices adjacent to it. A subset D of V is called an efficient dominating set of G if every vertex in V is dominated by exactly one vertex in D . The efficient domination problem is to find an efficient dominating set of G with minimum cardinality. Suppose that each vertex v ∈ V is associated with a weight. Then, the weighted efficient domination problem is to find an efficient dominating set with the minimum weight in G . In this paper, we show that the efficient domination problem is NP-complete for planar bipartite graphs and chordal bipartite graphs. Assume that a permutation diagram of a bipartite permutation graph and a one-vertex-extension ordering of a distance-hereditary graph are given in advance. Then, we give O (| V |) time algorithms for the weighted efficient domination problem on bipartite permutation graphs and distance-hereditary graphs.
7343346
Solving the Weighted Efficient Edge Domination Problem on Bipartite Permutation Graphs
Abstract Given a simple graph G = (V,E), an edge (u, v)ϵ E is said to dominate itself and any edge (u,x) or (v,x), where xϵ V. A subset D⊂-E is called an efficient edge dominating set of G if all edges in E are dominated by exactly one edge of D. The efficient edge domination problem is to find an efficient edge dominating set of minimum size in G. Suppose that each edge eϵ E is associated with a real number w(e), called the weight of e. The weighted efficient edge domination problem is to calculate an efficient edge dominating set D of G such that the weight w(D) of D is minimum, where w(D) = ∑{w(e)¦eϵD} . In this paper, we show that the problem of determining whether G has an efficient edge dominating set is NP-complete when G is restricted to a bipartite graph. Consequently, the decision problem of efficient (vertex) domination remains NP-complete for the line graphs of bipartite graphs. Moreover, we present a linear time algorithm to solve the weighted efficient edge domination problem on bipartite permutation graphs, which form a subclass of bipartite graphs, using the technique of dynamic programming.
6194551
Algorithms for spatial outlier detection
A spatial outlier is a spatially referenced object whose non-spatial attribute values are significantly different from the values of its neighborhood. Identification of spatial outliers can lead to the discovery of unexpected, interesting, and useful spatial patterns for further analysis. One drawback of existing methods is that normal objects tend to be falsely detected as spatial outliers when their neighborhood contains true spatial outliers. We propose a suite of spatial outlier detection algorithms to overcome this disadvantage. We formulate the spatial outlier detection problem in a general way and design algorithms which can accurately detect spatial outliers. In addition, using a real-world census data set, we demonstrate that our approaches can not only avoid detecting false spatial outliers but also find true spatial outliers ignored by existing methods.
30370540
On (d, 2)-dominating numbers of binary undirected de Bruijn graphs
Abstract In this paper, we show that: (i) For n-dimensional undirected binary de Bruijn graphs, UB(n), n⩾4, there is a vertex x=x 1 x 1 x 1 ⋯ x 1 x 1 (x1=1 or 0) such that for any other vertex t there exist at least two internally disjoint paths of length at most n−1 between x and t in UB(n), i.e., the (n−1,2)-dominating number of UB(n) is equal to one. (ii) For n⩾5, let S={100⋯01,011⋯10}. For any other vertex t there exist at least two internally disjoint paths of length at most n−2 between t and S in UB(n), i.e., the (n−2,2)-dominating number of UB(n) is no more than 2.
6432483
Evaluating GML support for spatial databases
This work presents a study on Geography Markup Language (GML), the issues that arise from using GML for spatial databases and solutions that have been proposed. We concentrate on three aspects of GML, including storage, parsing, and querying. GML is an XML encoding for storing geographic data. It has been developed by the OpenGIS as a medium for uniform geographic data storage and exchange among diverse applications. The underlying concepts of XML therefore can also be applied to GML data. This results in both advantages and disadvantages, which are discussed In the work. GML is a comparatively new language in the field of geographic information systems and still in its developmental stage. Most of the data processing techniques need to be further developed in order for GML to be an efficient medium for geographic data storage and processing.
15346536
Distance-two labelings of graphs
For given positive integers j ≥ k, an L(j,k)-labeling of a graph G is a function f : V (G) → {0, 1, 2,...} such that |f(u) - f(v)| ≥ j when dG(u, v) = 1 and |f(u) - f(v)| ≥ k when dG(u, v) = 2. The L(j, k)-labeling number λj,k(G) of G is defined as the minimum m such that there is an L(j, k)-labeling f of G with f(V(G)) ⊆ {0, 1, 2,....,m}. For a graph G of maximum degree Δ ≥ 1 it is the case that λj,k(G) ≥ j + (Δ - 1)k. The purpose of this paper is to study the structures of graphs G with maximum degree Δ ≥ 1 and λj,k(G) = j + (Δ - 1)k.
17196005
Analysis of payment transaction security in mobile commerce
Mobile payment is the process of two parties exchanging financial value using a mobile device in return for goods or services. This paper is an analysis of the security issues in mobile payment for m-commerce. We introduce m-commerce and mobile payment, discuss the public key infrastructure as a basis for secure mobile technologies, and study the features for different security technologies employed in current m-commerce market, including WAP, SIM application toolkit and J2M. In addition, we compare the effectiveness of these security technologies in supporting a secure mobile payment, and discuss research issues to enhance the security of mobile payment for large scale deployment of m-commerce.