We present a general framework and algorithmic approach for incremental approximation algorithms. The framework handles cardinality constrained minimization problems, such as the k-median and k-MST problems. Given some notion of ordering on solutions of different cardinalities k, we give solutions for all values of k such that the solutions respect the ordering and such that for any k, our solution is close in value to the value of an optimal solution of cardinality k. For instance, for the k-median problem, the notion of ordering is set inclusion, and our incremental algorithm produces solutions such that for any k and $k'$, $k

Motivated by applications in grid computing and project management, we study multiprocessor scheduling in scenarios where there is uncertainty in the successful execution of jobs when assigned to processors. We consider the problem of multiprocessor scheduling under uncertainty, in which we are given n unit-time jobs and m machines, a directed acyclic graph C giving the dependencies among the jobs, and for every job j and machine i, the probability pij of the successful completion of job j when scheduled on machine i in any given particular step. The goal of the problem is to find a schedule that minimizes the expected makespan, that is, the expected completion time of all the jobs.

We introduce a notion of universality in the context of optimization problems with partial information. Universality is a framework for dealing with uncertainty by guaranteeing a certain quality of goodness for all possible completions of the partial information set. Universal variants of optimization problems can be defined that are both natural and well-motivated. We consider universal versions of three classical problems: TSP, Steiner Tree and Set Cover.We present a polynomial-time algorithm to find a universal tour on a given metric space over n vertices such that for any subset of the vertices, the sub-tour induced by the subset is within O(log4n/log log n) of an optimal tour for the subset. Similarly, we show that given a metric space over n vertices and a root vertex, we can find a universal spanning tree such that for any subset of vertices containing the root, the sub-tree induced by the subset is within O(log4n/log log n) of an optimal Steiner tree for the subset. Our algorithms rely on a new notion of sparse partitions, that may be of independent interest. For the special case of doubling metrics, which includes both constant-dimensional Euclidean and growth-restricted metrics, our algorithms achieve an O(log n) upper bound. We complement our results for the universal Steiner tree problem with a lower bound of Ω(log n/log log n) that holds even for n vertices on the plane. We also show that a slight generalization of the universal Steiner Tree problem is coNP-hard and present nearly tight upper and lower bounds for a universal version of Set Cover.

In this paper, we investigate the resiliency to jamming of data protocols, such as IP, over WLAN. We show that, on existing WLAN, an adversary can successfully jam data packets at a very low energy cost. Such attacks allow a set of adversary nodes disseminated over an area to prevent communication, partition an ad hoc network or force packets to be routed over adversary chosen paths. The ratio of the jamming pulses duration to the transmission duration can be as low as 10−4. We investigate and analyze the performance of combining a cryptographic interleaver with various coding schemes to improve the robustness of wireless LANs for IP packets transmission 1. A concatenated code that is simple to decode and can maintain a low frame error rate (FER) under a jamming effort ratio of 15%. We argue that LDPC codes will be very suitable to prevent this type of jamming. We investigate the theoretical limits by analyzing the performance derived from upper bounds on binary error-control codes. We also propose an efficient anti-jamming technique for IEEE802.11b based on Reed–Solomon codes. Copyright © 2004 John Wiley & Sons, Ltd.

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.