Mauro Leoncini

The K-Neigh Protocol for Symmetric Topology Control in Ad Hoc Networks

We propose an approach to topology control based on the principle of maintaining the number of neighbors of every node equal to or slightly below a specific value k. The approach enforces symmetry on the resulting communication graph, thereby easing the operation of higher layer protocols. To evaluate the performance of our approach, we estimate the value of k that guarantees connectivity of the communication graph with high probability. We then define k-Neigh, a fully distributed, asynchronous, and localized protocol that follows the above approach and uses distance estimation. We prove that k-Neigh terminates at every node after a total of 2n messages have been exchanged (with n nodes in the network) and within strictly bounded time. Finally, we present simulations results which show that our approach is about 20% more energy-efficient than a widely-studied existing protocol.

The k-Neighbors Approach to Interference Bounded and Symmetric Topology Control in Ad Hoc Networks

Topology control, wherein nodes adjust their transmission ranges to conserve energy and reduce interference, is an important feature in wireless ad hoc networks. Contrary to most of the literature on topology control which focuses on reducing energy consumption, in this paper we tackle the topology control problem with the goal of limiting interference as much as possible, while keeping the communication graph connected with high probability. Our approach is based on the principle of maintaining the number of physical neighbors of every node equal to or slightly below a specific value k. As we will discuss in this paper, having a nontrivially bounded physical node degree allows a network topology with bounded interference to be generated. The proposed approach enforces symmetry on the resulting communication graph, thereby easing the operation of higher layer protocols. To evaluate the performance of our approach, we estimate the value of k that guarantees connectivity of the communication graph with high probability both theoretically and through simulation. We then define k-NEIGH, a fully distributed, asynchronous, and localized protocol that uses distance estimation. k-NEIGH guarantees logarithmically bounded physical degree at every node, is the most efficient known protocol (requiring 2n messages in total, where n is the number of nodes in the network), and relies on simpler assumptions than existing protocols. Furthermore, we verify through simulation that the network topologies produced by k-NEIGH show good performance in terms of node energy consumption and expected interference

On the Symmetric Range Assignment Problem in Wireless Ad Hoc Networks

In this paper we consider a constrained version of the range assignment problem for wireless ad hoc networks, where the value the node transmitting ranges must be assigned in such a way that the resulting communication graph is strongly connected and the energy cost is minimum. We impose the further requirement of symmetry on the resulting communication graph. We also consider a weaker notion of symmetry, in which only the existence of a set of symmetric edges that renders the communication graph connected is required. Our interest in these problems is motivated by the fact that a (weakly) symmetric range assignment can be more easily integrated with existing higher and lower-level protocols for ad hoc networks, which assume that all the nodes have the same transmitting range. We show that imposing symmetry does not change the complexity of the problem, which remains NP-hard in two and three-dimensional networks. We also show that a weakly symmetric range assignment can reduce the energy cost considerably with respect to the homogeneous case, in which all the nodes have the same transmitting range, and that no further (asymptotic) benefit is expected from the asymmetric range assignment. Hence, the results presented in this paper indicate that weak symmetry is a desirable property of the range assignment.

Analysis of a wireless sensor dropping problem in wide-area environmental monitoring

In this paper we study the following problem: we are given a certain region R to monitor and a requirement on the degree of coverage (DoC) of R to meet by a network of deployed sensors. The latter will be dropped by a moving vehicle, which can release sensors at arbitrary points within R. The node spatial distribution when sensors are dropped at a certain point is modeled by a probability density function F. The network designer is allowed to choose an arbitrary a set of drop points, and to release an arbitrary number of sensors at each point. Given this setting, we consider the problem of determining the optimal grid deployment strategy, i.e., the drop strategy in which release points are arranged in a grid such that (1) the DoC requirement is fulfilled and (2) the total number of deployed nodes n is minimum. This problem is relevant whenever manual node deployment is impossible or overly expensive, and partially controlled deployment is the only feasible choice. The main contribution of this paper is an accurate study of the interrelationships between environmental conditions, DoC requirement, and cost of the deployment. In particular, we show that, for a given value of /spl sigma/ and DoC requirement, optimal grid deployment strategies can be easily identified.

K-Boost: a scalable algorithm for high-quality clustering of microarray gene expression data.

Microarray technology for profiling gene expression levels is a popular tool in modern biological research. Applications range from tissue classification to the detection of metabolic networks, from drug discovery to time-critical personalized medicine. Given the increase in size and complexity of the data sets produced, their analysis is becoming problematic in terms of time/quality trade-offs. Clustering genes with similar expression profiles is a key initial step for subsequent manipulations and the increasing volumes of data to be analyzed requires methods that are at the same time efficient (completing an analysis in minutes rather than hours) and effective (identifying significant clusters with high biological correlations). In this paper, we propose K-Boost, a clustering algorithm based on a combination of the furthest-point-first (FPF) heuristic for solving the metric k-center problem, a stability-based method for determining the number of clusters, and a k-means-like cluster refinement. K-Boost runs in O (|N| x k) time, where N is the input matrix and k is the number of proposed clusters. Experiments show that this low complexity is usually coupled with a very good quality of the computed clusterings, which we measure using both internal and external criteria. Supporting data can be found as online Supplementary Material at www.liebertonline.com.

Approximation algorithms for a hierarchically structured bin packing problem

In this paper we study a variant of the bin packing problem in which the items to be packed are structured as the leaves of a tree. The problem is motivated by document organization and retrieval. We show that the problem is NP-hard and we give approximation algorithms for the general case and for the particular case in which all the items have the same size.

An STDMA-based framework for QoS provisioning in wireless mesh networks

Providing strong QoS guarantees for wireless multi-hop networks is very challenging, due to many factors such as use of a shared communication medium, variability in wireless link quality, and so on. However, wireless mesh technology gives the opportunity to alleviate some of these problems, due to lack of mobility in the wireless infrastructure, and presence of natural centralization points in the network. The main contribution of this paper is the definition of a simple framework that exploits these features to provide provable, strong QoS guarantees to network clients. In particular, admitted clients are guaranteed a certain minimum bandwidth and maximum delay on their connections. The framework is based on STDMA scheduling at the MAC layer, which is periodically executed at the network manager to adapt to changes in traffic demand. While scheduling computation is centralized, admission control is performed locally at the wireless backbone nodes, thus reducing signaling. We propose two bandwidth distribution and related admission control policies, which are at opposite ends of the network utilization/spatial fairness trade-off. Through extensive simulations, we show that the proposed framework achieves its design goals of providing strong QoS guarantees to VoIP clients while not sacrificing throughput in a realistic mesh network scenario, also in presence of highly unbalanced load at the backbone nodes. To the best of our knowledge, this is the first proposal with similar features for wireless mesh networks.

FPF-SB: a scalable algorithm for microarray gene expression data clustering

Efficient and effective analysis of large datasets from microarray gene expression data is one of the keys to time-critical personalized medicine. The issue we address here is the scalability of the data processing software for clustering gene expression data into groups with homogeneous expression profile. In this paper we propose FPF-SB, a novel clustering algorithm based on a combination of the Furthest-Point-First (FPF) heuristic for solving the k- center problem and a stability-based method for determining the number of clusters k. Our algorithm improves the state of the art: it is scalable to large datasets without sacrificing output quality.

Checking robust nonsingularity of tridiagonal matrices in linear time

In this paper we present a linear time algorithm for checking whether a tridiagonal matrix will become singular under certain perturbations of its coefficients. The problem is known to be NP-hard for general matrices. Our algorithm can be used to get perturbation bounds on the solutions to tridiagonal systems.

Parallel Complexity of Linear System Solution

This book presents the most important parallel algorithms for the solution of linear systems. Despite the evolution and significance of the field of parallel solution of linear systems, no book is completely dedicated to the subject. People interested in the themes covered by this book belong to two different groups: numerical linear algebra and theoretical computer science, and this is the first effort to produce a useful tool for both. The book is organized as follows: after introducing the general features of parallel algorithms and the most important models of parallel computation, the authors analyze the complexity of solving linear systems in the circuit, PRAM, distributed, and VLSI models. The approach covers both the general case (i.e. dense linear systems without structure) and many important special cases (i.e. banded, sparse, Toeplitz, circulant linear systems).