9975325
On the Structure of Graphs with Few P4s
Abstract We present new classes of graphs for which the isomorphism problem can be solved in polynomial time. These graphs are characterized by containing — in some local sense — only a small number of induced paths of length three. As it turns out, every such graph has a unique tree representation: the internal nodes correspond to three types of graph operations, while the leaves are basic graphs with a simple structure. The paper extends and generalizes known results about cographs, P4-reducible graphs, and P4-sparse graphs.
9433006
No antitwins in minimal imperfect graphs
Abstract It is customary to call vertices x and y twins if every vertex distinct from x and y is adjacent either to both of them or to neither of them. By analogy, we shall call vertices x and y antitwins if every vertex distinct from x and y is adjacent to precisely one of them. Lovasz proved that no minimal imperfect graph has twins. The purpose of this note is to prove the analogous statement for antitwins.
44940446
Weak bipolarizable graphs
We characterize a new class of perfectly orderable graphs and give a polynomial-time recognition algorithm, together with linear-time optimization algorithms for this class of graphs.
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.
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.
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.
932666
Q-Win – A New Admission and Handoff Management Scheme for Multimedia LEO Satellite Networks
Low Earth Orbit (LEO) satellite networks are deployed as an enhancement to terrestrial wireless networks in order to provide broadband services to users regardless of their location. In addition to global coverage, these satellite systems support communications with hand-held devices and offer low cost-per-minute access cost, making them promising platform for Personal Communication Services (PCS). LEO satellites are expected to support multimedia traffic and to provide their users with the negotiated Quality of Service (QoS). However, the limited bandwidth of the satellite channel, satellite rotation around the Earth and mobility of end-users makes QoS provisioning and mobility management a challenging task. One important mobility problem is the intra-satellite handoff management. The main contribution of this work is to propose Q-Win, a novel call admission and handoff management scheme for LEO satellite networks. A key ingredient in our scheme is a companion predictive bandwidth allocation strategy that exploits the topology of the network and contributes to maintaining high bandwidth utilization. Our bandwidth allocation scheme is specifically tailored to meet the QoS needs of multimedia connections. The performance of Q-Win is compared to that of two recent schemes proposed in the literature. Simulation results show that our scheme offers low call dropping probability, providing for reliable handoff of on-going calls, good call blocking probability for new call requests, while maintaining bandwidth utilization high.
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.
42702929
A Fair Resource Allocation Protocol for Multimedia Wireless Networks
Wireless networks are expected to support real-time interactive multimedia traffic and must be able, therefore, to provide their users with quality-of-service (QoS) guarantees. Although the QoS provisioning problem arises in wireline networks as well, mobility of hosts and scarcity of bandwidth makes QoS provisioning a challenging task in wireless networks. It has been noticed that multimedia applications can tolerate and gracefully adapt to transient fluctuations in the QoS that they receive from the network. The additional flexibility afforded by the ability of multimedia applications to tolerate and adapt to transient changes in QoS can be exploited by protocol designers to significantly improve the overall performance of wireless systems. This paper presents a fair resource allocation protocol for multimedia wireless networks that uses a combination of bandwidth reservation and bandwidth borrowing to provide network users with QoS in terms of guaranteed bandwidth, call blocking, and call dropping probabilities. Our view of fairness was inspired by the well-known max-min fairness allocation protocol for wireline networks. Simulation results are presented that compare our protocol to similar schemes.
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.