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Hierarchical decompositions of graphs are interesting for algorithmic purposes. Many NP complete problems have linear complexity on graphs with tree-decompositions of bounded width. We investigate alternate hierarchical decompositions that apply to wider classes of graphs and still enjoy good algorithmic properties. These decompositions are motivated and… (More)

— This paper investigates theoretical aspects of the uneven energy depletion phenomenon recently noticed in sink-based wireless sensor networks. We consider uniformly distributed sensors, each sending roughly the same number of reports toward the closest sink. We assume an energy consumption model governed by the relation E = d α +c where d, (d ≤ t x), is… (More)

We present a linear time algorithm for unit interval graph recognition. The algorithm is simple and based on Breadth-First Search. It is also direct | it does not rst recognize the graph as an interval graph. Given a graph G, the algorithm produces an ordering of the vertices of the graph whenever G is a unit interval graph. This order corresponds to the… (More)

ÐAd hoc networks are self-organizing entities that are deployed on demand in support of various events including collaborative computing, multimedia classroom, disaster-relief, search-and-rescue, interactive mission planning, and law enforcement operations. One of the fundamental tasks that have to be addressed when setting up an ad hoc network (AHN, for… (More)

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, for short) if it contains no asteroidal triples. The motivation for this investigation was provided, in part, by the fact that the asteroidal triple-free graphs… (More)

A radio network is a distributed system with no central arbiter, consisting of ¡ radio transceivers, henceforth referred to as stations. We assume that the stations are identical and cannot be distinguished by serial or manufacturing number. The leader election problem asks to designate one of the station as leader. A leader election protocol is said to be… (More)

A graph is an interval graph if it is the intersection graph of intervals on a line. Interval graphs are known to be the intersection of chordal graphs and asteroidal triple-free graphs, two families where the well-known Lexicographic Breadth First Search (LBFS) plays an important algorithmic and structural role. In this paper we show that interval graphs… (More)

ÐNow that cellular networks are being called upon to support real-time interactive multimedia traffic such as video tele-conferencing, these networks must be able to provide their users with quality-of-service (QoS) guarantees. Although the QoS provisioning problem arises in wireline networks as well, mobility of hosts, scarcity of bandwidth, and channel… (More)

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,… (More)