Abstract-A framework for integrated multicast and unicast routing in mobile ad hoc networks (MANETs) is introduced. It is based on interest-defined mesh enclaves that are connected components of a MANET spanning the sources and receivers of unicast or multicast flows. The Protocol for Routing in Interest-defined Mesh Enclaves (PRIME) is presented to implement the proposed framework for integrated routing in MANETs. PRIME establishes meshes that are activated and deactivated by the presence or absence of interest in individual destination nodes and groups and confines most of the signaling overhead within regions of interest (enclaves) in such meshes. The routes established in PRIME are shown to be free of permanent loops. Experimental results based on extensive simulations show that PRIME attains similar or better data delivery and end-to-end delays than traditional unicast and multicast routing schemes for MANETs (AODV, OLSR, ODMRP). The experiments also show that signaling in PRIME is far more scalable than the one used by traditional multicast and unicast routing protocols such as AODV, OLSR, or ODMRP.Index Terms-Interest-driven routing, mobile ad hoc network (MANET), multicast routing, unicast routing.
The vertex k-center problem is a classical NP-Hard optimization problem with application to Facility Location and Clustering among others. This problem consists in finding a subset C ⊆ V of an input graph G = (V , E), such that the distance from the farthest vertex in V to its nearest center in C is minimized, where |C| ≤ k, with k ∈ Z + as part of the input. Many heuristics, metaheuristics, approximation algorithms, and exact algorithms have been developed for this problem. This paper presents an analytical study and experimental evaluation of the most representative approximation algorithms for the vertex k-center problem. For each of the algorithms under consideration and using a common notation, we present proofs of their corresponding approximation guarantees as well as examples of tight instances of such approximation bounds, including a novel tight example for a 3-approximation algorithm. Lastly, we present the results of extensive experiments performed over de facto benchmark data sets for the problem which includes instances of up to 71009 vertices. INDEX TERMS Approximation algorithms, k-center problem, polynomial time heuristics. I. INTRODUCTION Perhaps one of the first center selection problems for which there is historical register is the following: ''given three points in the plane, find a fourth point such that the sum of its distances to the three points is minimized'' [1]. Given its simplicity, it is hard to establish who first stated this problem. However, this problem is usually associated to Pierre de Fermat, who asked this question around 1636, and its first registered solution is associated to Evangelista Torricelli [1]. An extension of this problem is known as the Weber's problem, where the points have an associated cost and the goal is to locate not 1 but k centers [1]. By adding new properties and restrictions to a basic k-center problem, the collection of k-center problems have become larger over the years. One of the basic center selection problems that more directly gave rise to many other center problems is known The associate editor coordinating the review of this manuscript and approving it for publication was Diego Oliva.
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