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.
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.
7611602
Spatiotemporal multicast in sensor networks
Sensor networks often involve the monitoring of mobile phenomena. We believe this task can be facilitated by a spatiotemporal multicast protocol which we call "mobicast". Mobicast is a novel spatiotemporal multicast protocol that distributes a message to nodes in a delivery zone that evolves over time in some predictable manner. A key advantage of mobicast lies in its ability to provide reliable and just-in-time message delivery to mobile delivery zones on top of a random network topology. Mobicast can in theory achieve good spatiotemporal delivery guarantees by limiting communication to a mobile forwarding zone whose size is determined by the global worst-case value associated with a compactness metric defined over the geometry of the network (under a reasonable set of assumptions). In this work, we first studied the compactness properties of sensor networks with uniform distribution. The results of this study motivate three approaches for improving the efficiency of spatiotemporal multicast in such networks. First, spatiotemporal multicast protocols can exploit the fundamental tradeoff between delivery guarantees and communication overhead in spatiotemporal multicast. Our results suggest that in such networks, a mobicast protocol can achieve relatively high savings in message forwarding overhead by slightly relaxing the delivery guarantee, e.g., by optimistically choosing a forwarding zone that is smaller than the one needed for a 100% delivery guarantee. Second, spatiotemporal multicast may exploit local compactness values for higher efficiency for networks with non uniform spatial distribution of compactness. Third, for random uniformly distributed sensor network deployment, one may choose a deployment density to best support spatiotemporal communication. We also explored all these directions via simulation and results are presented in this paper.
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.
2136742
Exploiting efficient data mining techniques to enhance intrusion detection systems
Security is becoming a critical part of organizational information systems. Intrusion detection system (IDS) is an important detection that is used as a countermeasure to preserve data integrity and system availability from attacks. Data mining is being used to clean, classify, and examine large amount of network data to correlate common infringement for intrusion detection. The main reason for using data mining techniques for intrusion detection systems is due to the enormous volume of existing and newly appearing network data that require processing. The amount of data accumulated each day by a network is huge. Several data mining techniques such as clustering, classification, and association rules are proving to be useful for gathering different knowledge for intrusion detection. This paper presents the idea of applying data mining techniques to intrusion detection systems to maximize the effectiveness in identifying attacks, thereby helping the users to construct more secure information systems.
9704136
Detecting region outliers in meteorological data
Spatial outliers are the spatial objects with distinct features from their surrounding neighbors. Detection of spatial outliers helps reveal important and valuable information from large spatial data sets. In the field of meteorology, for example, spatial outliers can be associated with disastrous natural events such as tornadoes, hurricane, and forest fires. Previous study of spatial outlier mainly focuses on point data. However, in the meteorological data or other applications, spatial outliers are frequently represented in region, i.e., a group of points, with two dimensions or even three dimensions, and the previous point-based approaches may not be appropriate to be used. As region outliers are commonly multi-scale objects, wavelet analysis is an effective tool to study them. In this paper, we propose a wavelet analysis based approach to detect region outliers. We discuss the region outlier detection problem and design a suite of algorithms to effectively discover them. The algorithms were implemented and evaluated with a real-world meteorological data set.
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.