Rajmohan Rajaraman

Topology control and routing in ad hoc networks: a survey

An ad hoc wireless network, or simply an ad hoc network, consists of a collection of geographically distributed nodes that communicate with one other over a wireless medium. An ad hoc network differs from cellular networks in that there is no wired infrastructure and the communication capabilities of the network are limited by the battery power of the network nodes. One of the original motivations for ad hoc networks is found in military applications. A classic example of ad hoc networking is network of war fighters and their mobile platforms in battlefields. Indeed, a wealth of early research in the area involved the development of packet-radio networks (PRNs) and survivable radio networks [16]. While military applications still dominate the research needs in ad hoc networking, the recent rapid advent of mobile telephony and plethora of personal digital assistants has brought to the fore a number of potential commercial applications of ad hoc networks. Examples are disaster relief, conferencing, home networking, sensor networks, personal area networks, and embedded computing applications [37].The lack of a fixed infrastructure in ad hoc networks implies that any computation on the network needs to be carried out in a decentralized manner. Thus, many of the important problems in ad hoc networking can be formulated as problems in distributed computing. However, there are certain characteristics of ad hoc networks that makes this study somewhat different than traditional work in distributed computing. In this article, we review some of the characteristic features of ad hoc networks, formulate problems and survey research work done in the area. We focus on two basic problem domains: topology control, the problem of computing and maintaining a connected topology among the network nodes, and routing. This article is not intended to be a comprehensive survey on ad hoc networking. The choice of the problems discussed in this article are somewhat biased by the research interests of the author.The remainder of this article is organized as follows. In Section 2, we describe various aspects relevant to modeling ad hoc networks. In Section 3, we discuss topology control. Since the nodes of an ad hoc network are often associated with points in 2-dimensional space, topology control is closely tied to computational geometry; we will briefly review this relationship and extant work in the area. In Section 4, we discuss routing protocols for ad hoc networks. After a brief overview of the many protocols that have been proposed, we discuss alternative approaches based on the adversarial network model.

Analysis of a Local Search Heuristic for Facility Location Problems

In this paper, we study approximation algorithms for several NP-hard facility location problems. We prove that a simple local search heuristic yields polynomial-time constant-factor approximation bounds for the metric versions of the uncapacitated k-median problem and the uncapacitated facility location problem. (For the k-median problem, our algorithms require a constant-factor blowup in the parameter k.) This local search heuristic was first proposed several decades ago, and has been shown to exhibit good practical performance in empirical studies. We also extend the above results to obtain constant-factor approximation bounds for the metric versions of capacitated k-median and facility location problems.

Mobility models for ad hoc network simulation

In this paper, we propose a novel general technique, based on renewal theory, for analyzing mobility models in ad hoc networks. Our technique enables an accurate derivation of the steady state distribution functions for node movement parameters such as distance and speed. We first apply our technique to the random waypoint model and provide alternative proofs for previous claims about the discrepancy between the steady state average speed and the average speed associated with the simulated distribution (Yoon, J et al., 2003). Our main contribution is a new methodology for simulating mobility which guarantees steady state for node movement distributions from the start of the simulation. Our methodology enables the correct and efficient simulation of a desired steady state distribution, and can be implemented in a manner transparent to the user. We support our claims through both formal proofs as well as extensive simulations.

Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems

We study the approximability of edge-disjoint paths and related problems. In the edge-disjoint paths problem (EDP), we are given a network G with source-sink pairs (si; ti), 1 i k, and the goal is to nd a largest subset of source-sink pairs that can be simultaneously connected in an edge-disjoint manner. We show that in directed networks, for any > 0, EDP is NP-hard to approximate within m 1=2 . We also design simple approximation algorithms that achieve essentially matching approximation guarantees for some generalizations of EDP. Another related class of routing problems that we study concerns EDP with the additional constraint that the routing paths be of bounded length. We show that, for any > 0, bounded length EDP is hard to approximate within m 1=2 even in undirected networks, and give an O( p m)-approximation algorithm for it. For directed networks, we show that even the single source-sink pair case (i.e. nd the maximum number of paths of bounded length between a given sourcesink pair) is hard to approximate within m 1=2 , for any > 0.

Placement algorithms for hierarchical cooperative caching

Consider a hierarchical network in which each node periodically issues a request for an object drawn from a fixed set of unit-size objects. Suppose further that the following conditions are satisfied: the frequency with which each node accesses each object is known; each node has a cache of known capacity; any cache can be accessed by any node; and any request is satisfied by the closest node with a copy of the desired object, at a cost proportional to the distance between the accessing node and the closest copy. In such an environment, it is desirable to fill the available cache space with copies of objects in such a way that the average access cost is minimized. We provide both exact and approximate polynomial-time algorithms for this hierarchical placement problem. Our exact algorithm is based on a reduction to min-cost flow, and does not appear to be practical for large problem sizes. Thus we are motivated to search for a faster approximation algorithm. Our main result is a simple constant-factor approximation algorithm for the hierarchical placement problem that admits an efficient distributed implementation.

On the Performance of IEEE 802.11 under Jamming

In this paper, we study the performance of the IEEE 802.11 MAC protocol under a range of jammers that covers both channel-oblivious and channel-aware jamming. We study two channel-oblivious jammers: a periodic jammer that jams deterministically at a specified rate, and a memoryless jammer whose signals arrive according to a Poisson process. We also develop new models for channel-aware jamming, including a reactive jammer that only jams non-colliding transmissions and an omniscient jammer that optimally adjusts its strategy according to current states of the participating nodes. Our study comprises of a theoretical analysis of the saturation throughput of 802.11 under jamming, an extensive simulation study, and a testbed to conduct real world experimentation of jamming IEEE 802.11 using GNU Radio and USRP platform. In our theoretical analysis, we use a discrete-time Markov chain analysis to derive formulae for the saturation throughput of IEEE 802.11 under memoryless, reactive and omniscient jamming. One of our key results is a characterization of optimal omniscient jamming that establishes a lower bound on the saturation throughput of 802.11 under arbitrary jammer attacks. We validate the theoretical analysis by means of Qualnet simulations. Finally, we measure the real-world performance of periodic and memoryless jammers using our GNU radio jammer prototype.

Approximation Algorithms for Data Placement Problems

We develop approximation algorithms for the problem of placing replicated data in arbitrary networks, where the nodes may both issue requests for data objects and have capacity for storing data objects so as to minimize the average data-access cost. We introduce the data placement problem to model this problem. We have a set of caches

Multi-query optimization for sensor networks

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A dynamic object replication and migration protocol for an Internet hosting service

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Online scheduling to minimize average stretch

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