32558867
Linear Time Algorithms for Dominating Pairs in Asteroidal Triple-free Graphs
An independent set of three of vertices is called an asteroidal triple if between each, pair in the triple there exists a path that avoids the neighbourhood of the third. A graph is asteroidal triple-free (AT-free, for short) 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 three. 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.
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.
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.
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.
37000292
Wings and perfect graphs
Abstract An edge uv of a graph G is called a wing if there exists a chordless path with vertices u , v , x , y and edges uv , vx , xy . The wing-graph W ( G ) of a graph G is a graph having the same vertex set as G ; uv is an edge in W ( G ) if and only if uv is a wing in G . A graph G is saturated if G is isomorphic to W ( G ). A star-cutset in a graph G is a non-empty set of vertices such that G — C is disconnected and some vertex in C is adjacent to all the remaining vertices in C . V. Chvatal proposed to call a graph unbreakable if neither G nor its complement contain a star-cutset. We establish several properties of unbreakable graphs using the notions of wings and saturation. In particular, we obtain seven equivalent versions of the Strong Perfect Graph Conjecture.
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.
11087297
Fairness in DQDB revisited: a new solution
The main contribution of this work is to a new way of looking at fairness in a DQDB system. Our scheme is very simple and efficient to implement and compares favorably with the leading rate-controlled schemes proposed in the literature. In addition, simulation results show that in the presence of non-uniform loads, such as a file server being brought up, our scheme converges rapidly to a fair steady state.<<ETX>>
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.
9333297
A two-zone hybrid routing protocol for mobile ad hoc networks
Recently, an elegant routing protocol, the zone routing protocol (ZRP), was proposed to provide a hybrid routing framework that is locally proactive and globally reactive, with the goal of minimizing the sum of the proactive and reactive control overhead. The key idea of ZRP is that each node proactively advertises its link state over a fixed number of hops, called the zone radius. These local advertisements provide each node with an updated view of its routing zone - the collection of all nodes and links that are reachable within the zone radius. The nodes on the boundary of the routing zone are called peripheral nodes and play an important role in the reactive zone-based route discovery. The main contribution of this work is to propose a novel hybrid routing protocol - the two-zone routing protocol (TZRP) - as a nontrivial extension of ZRP. In contrast with the original ZRP where a single zone serves a dual purpose, TZRP aims to decouple the protocol's ability to adapt to traffic characteristics from its ability to adapt to mobility. In support of this goal, in TZRP each node maintains two zones: a crisp zone and a fuzzy zone. By adjusting the sizes of these two zones independently, a lower total routing control overhead can be achieved. Extensive simulation results show that TZRP is a general MANET routing framework that can balance the trade offs between various routing control overheads more effectively than ZRP in a wide range of network conditions.