39112817
Asteroidal Triple-Free Graphs
An independent set of three vertices such that each pair is joined by a path that avoids the neighborhood of the third is called an asteroidal triple. A graph is asteroidal triple-free (AT-free) if it contains no asteroidal triples. The motivation for this investigation was provided, in part, by the fact that the AT-free graphs provide a common generalization of interval, permutation, trapezoid, and cocomparability graphs. The main contribution of this work is to investigate and reveal fundamental structural properties of AT-free graphs. Specifically, we show that every connected AT-free graph contains a dominating pair, that is, a pair of vertices such that every path joining them is a dominating set in the graph. We then provide characterizations of AT-free graphs in terms of dominating pairs and minimal triangulations. Subsequently, we state and prove a decomposition theorem for AT-free graphs. An assortment of other properties of AT-free graphs is also provided. These properties generalize known structural properties of interval, permutation, trapezoid, and cocomparability graphs.
5840834
Asteroidal Triple-Free Graphs
Many families of perfect graphs such as interval graphs, permutation graphs, trapezoid graphs and cocomparability graphs demonstrate a type of linear ordering of their vertex sets. These graphs are all subfamilies of a class of graphs called the asteroidal triple-free graphs. (An independent triple {x, y, z} is called an asteroidal triple (AT, for short) if between any pair in the triple there exists a path that avoids the neighbourhood of the third vertex.) In this paper we argue that the property of being AT-free is what is enforcing the linear ordering of the vertex sets. To justify this claim, we present various structural properties and characterizations of AT-free graphs.
7817544
P-Components and the Homogeneous Decomposition of Graphs
In this paper we introduce and investigate the notion of p-connectedness. As it turns out, this concept leads naturally to a unique tree representation for arbitrary graphs: the leaves of this tree are the p-connected components along with weak vertices, that is, vertices of the graph that belong to no p-connected component. We then show how to refine this decomposition to obtain a new decomposition that extends the well-known modular decomposition.
205001978
A Linear Time Algorithm to Compute a Dominating Path in an AT-Free Graph
Abstract An independent set { x , y , z } is called an asteroidal triple if between any pair in the triple there exists a path that avoids the neighborhood of the third. A graph is referred to as AT-free if it does not contain an asteroidal triple. We present a simple linear-time algorithm to compute a dominating path in a connected AT-free graph.
37426117
On the Closure of Triangle-Free Graphs Under Substitution
On dit qu'un graphe G se construit a partir de deux graphes G 1 et G 2 par substitution,si,pour un sommet donne w de G 1 ,G apparait en supprimant w et en rendant,par la suite,les sommets de G 2 adjacents a tous les voisins de w dans G 1 .On presente ici une caracterisation par configurations interdites de la fermeture de graphes sans triangles sous substitution.
11519290
Linear Time Algorithms for Dominating Pairs in Asteroidal Triple-free Graphs
An independent set of three vertices is called an asteroidal triple if between each pair in the triple there exists a path that avoids the neighborhood of the third. A graph is asteroidal triple-free (AT-free) if it contains no asteroidal triple. The motivation for this investigation is provided, in part, by the fact that AT-free graphs offer a common generalization of interval, permutation, trapezoid, and cocomparability graphs. 
Previously, the authors have given an existential proof of the fact that every connected AT-free graph contains a dominating pair, that is, a pair of vertices such that every path joining them is a dominating set in the graph. The main contribution of this paper is a constructive proof of the existence of dominating pairs in connected AT-free graphs. The resulting simple algorithm, based on the well-known lexicographic breadth-first search, can be implemented to run in time linear in the size of the input, whereas the best algorithm previously known for this problem has complexity O(|V|3) for input graph G=(V,E). In addition, we indicate how our algorithm can be extended to find, in time linear in the size of the input, all dominating pairs in a connected AT-free graph with diameter greater than 3. A remarkable feature of the extended algorithm is that, even though there may be O(|V|2) dominating pairs, the algorithm can compute and represent them in linear time.
6823924
Some observations on using meta-heuristics for efficient location management in mobile computing networks
With the increase in global wireless communication, there is a need for efficient network management strategies. Location management in a mobile network involves keeping track of mobile host (MH) cell locations. MHs perform location updates to inform the network of their location. When a call arrives for an MH, the network uses its last known cell location and a paging strategy to find that host. Current location management techniques do not consider host-mobility patterns or call arrival rates. This paper describes a selective update strategy that is modeled on the characteristics of a network, such as, topology, host mobility patterns and connection request rates. Then, a genetic algorithm is used to solve the location management problem that involves the search of a large solution space. The aim of the work is to determine whether genetic algorithms can be applied successfully to solve this problem, and to evaluate their efficiency in solving this class of optimization problems. Results from the selective update strategy show improvements over alternative algorithms. The location management optimization problem is shown to be well adapted to the workings of the genetic algorithm. The proposed solution also saves power, processing time, and network bandwidth.
45508612
A unifying look at clustering in mobile ad hoc networks
In recent years, a significant number of clustering schemes have been proposed in the literature. Most of them treat cluster initialization and cluster maintenance differently as if they were two entirely different undertakings. The main contribution of this work is a unifying way of looking at clustering in MANET. We make an important point: there is no difference between cluster initialization and cluster maintenance, and one algorithm should gracefully blend into the other. To illustrate the feasibility of this concept, we propose a novel tree-based clustering algorithm for MANET based on a number of properties of diameter-2 graphs. The algorithm is cluster-centric and, unlike the vast majority of algorithms in the literature, works in the presence of node mobility. Extensive simulation results show the effectiveness of our algorithm when compared to other clustering schemes proposed in the recent literature. Copyright © 2004 John Wiley & Sons, Ltd.
2805859
A time-optimal solution for the path cover problem on cographs
We show that the notoriously difficult problem of finding and reporting the smallest number of vertex-disjoint paths that cover the vertices of a graph can be solved time- and work-optimally for cographs. Our result implies that for this class of graphs the task of finding a Hamiltonian path can be solved time- and work-optimally in parallel.It was open for more than 10 years to find a time- and work-optimal parallel solution for this important problem. Our contribution is to offer an optimal solution to this important problem. We begin by showing that any algorithm that solves an instance of size n of the problem must take ?(logn) time on the CREW, even if an infinite number of processors are available. We then go on to show that this time lower bound is tight by devising an EREW algorithm that, given an n-vertex cograph G represented by its cotree, finds and reports all the paths in a minimum path cover in O(logn) time using n/logn processors.
7945895
Wireless sensor networks: leveraging the virtual infrastructure
Overlaying a virtual infrastructure over a physical network is a time-honored strategy for conquering scale. We design a general-purpose virtual architecture for wireless sensor networks and show that it can be leveraged by a number of different protocols.
5533650
The hierarchical cliques interconnection network
The fully connected network possesses extremely good topological, fault-tolerant, and embedding properties. However, due to its high degree, the fully connected network has not been an attractive candidate for building parallel computers. On the other hand, tree-based networks are popular as parallel computer networks, even though they suffer from poor fault-tolerance and embedding properties. The hierarchical cliques interconnection network described in this paper incorporates positive features of the fully connected network and the tree network. In other words, the hierarchical cliques possess such desirable properties as low diameter, low degree, self routing, versatile embedding, good fault-tolerance and strong resilience. Hierarchical cliques can efficiently embed most important networks and possess a scalable, modular structure. Further, by combining hierarchical cliques with fat trees congestion in the upper levels can be alleviated.