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.
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.
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.
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.
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.
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.
14933759
Classifying matrices separating rows and columns
The classification problem transforms a set of N numbers in such a way that none of the first N/2 numbers exceeds any of the last N/2 numbers. A comparator network that solves the classification problem on a set of r numbers is commonly called an r-classifier. We show how the well-known Leighton's Columnsort algorithm can be modified to solve the classification problem of N=rs numbers, with 1 /spl les/ s /spl les/ r, using an r-classifier instead of an r-sorting network. Overall, the r-classifier is used O(s) times, namely, the same number of times that Columnsort applies an r-sorter. A hardware implementation is proposed that runs in optimal O(s+logr) time and uses an O(rlogr(s + logr)) work. The implementation shows that, when N= rlogr, there is a classifier network solving the classification problem on N numbers in the same O(logr) time and using the same O(rlogr) comparators as an r-classifier, thus saying a logr factor in the number of comparators over an (rlogr)-classifier.
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.
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.