Afonso Ferreira

Building a reference combinatorial model for MANETs

Wireless technologies and the deployment of mobile and nomadic services are driving the emergence of complex ad hoc networks that have a highly dynamic behavior. Modeling such dynamics and creating a reference model on which results could be compared and reproduced, was stated as a fundamental issue by a recent NSF workshop on networking. In this article we show how the modeling of time-changes unsettles old questions and allows for new insights into central problems in networking, such as routing metrics, connectivity, and spanning trees. Such modeling is made possible through evolving graphs, a simple combinatorial model that helps capture the behavior or dynamic networks over time.

Efficient Parallel Graph Algorithms For Coarse Grained Multicomputers and BSP

In this paper, we present deterministic parallel algorithms for the coarse grained multicomputer (CGM) and bulk-synchronous parallel computer (BSP) models which solve the following well known graph problems: (1) list ranking, (2) Euler tour construction, (3) computing the connected components and spanning forest, (4) lowest common ancestor preprocessing, (5) tree contraction and expression tree evaluation, (6) computing an ear decomposition or open ear decomposition, (7) 2-edge connectivity and biconnectivity (testing and component computation), and (8) cordai graph recognition (finding a perfect elimination ordering). The algorithms for Problems 1–7 require O(log p) communication rounds and linear sequential work per round. Our results for Problems 1 and 2 hold for arbitrary ratios \(\frac{n}{p}\), i.e. they are fully scalable, and for Problems 3–8 it is assumed that \(\frac{n}{p} \geqslant p^ \in ,{\mathbf{ }} \in {\mathbf{ }} > 0\), which is true for all commercially available multiprocessors. We view the algorithms presented as an important step towards the final goal of O(1) communication rounds. Note that, the number of communication rounds obtained in this paper is independent of n and grows only very slowly with respect to p. Hence, for most practical purposes, the number of communication rounds can be considered as constant. The result for Problem 1 is a considerable improvement over those previously reported. The algorithms for Problems 2–7 are the first practically relevant deterministic parallel algorithms for these problems to be used for commercially available coarse grained parallel machines.

Complexity of connected components in evolving graphs and the computation of multicast trees in dynamic networks

New technologies and the deployment of mobile and nomadic services are driving the emergence of complex communications networks, that have a highly dynamic behavior. This naturally engenders new route-discovery problems under changing conditions over these networks. Unfortunately, the temporal variations in the topology of dynamic networks are hard to be effectively captured in a classical graph model. In this paper, we use evolving graphs, which helps capture the dynamic characteristics of such networks, in order to compute multicast trees with minimum overall transmission time for a class of wireless mobile dynamic networks. We first show that computing different types of strongly connected components in evolving digraphs is NP-Complete, and then propose an algorithm to build all rooted directed minimum spanning trees in strongly connected dynamic networks.

Characterizing topological assumptions of distributed algorithms in dynamic networks

Besides the complexity in time or in number of messages, a common approach for analyzing distributed algorithms is to look at their assumptions on the underlying network. This paper focuses on the study of such assumptions in dynamic networks, where the connectivity is expected to change, predictably or not, during the execution. Our main contribution is a theoretical framework dedicated to such analysis. By combining several existing components (local computations, graph relabellings, and evolving graphs), this framework allows to express detailed properties on the network dynamics and to prove that a given property is necessary, or sufficient, for the success of an algorithm. Consequences of this work include (i) the possibility to compare distributed algorithms on the basis of their topological requirements, (ii) the elaboration of a formal classification of dynamic networks with respect to these properties, and (iii) the possibility to check automatically whether a network trace belongs to one of the classes, and consequently to know which algorithm should run on it.

Performance Evaluation of Dynamic Networks using an Evolving Graph Combinatorial Model

The highly dynamic behavior of wireless networks make them very difficult to evaluate, e.g. as far as the performance of routing algorithms is concerned. However, some of these networks, such as intermittent wireless sensors networks, periodic or cyclic networks, and low Earth orbit (LEO) satellites systems have more predictable dynamics, as the temporal variations in the network topology are somehow deterministic. Recently, a graph theoretic model-the evolving graphs-was proposed to help capture the dynamic behavior of these networks, in view of the construction of least cost routing and other algorithms. The algorithms and insights obtained through this model are theoretically very efficient and intriguing. However, there is no study on the uses of these theoretical results into practical situations. Therefore, the objective of this work is to analyze the applicability of the evolving graph theory in the construction of efficient routing protocols in realistic scenarios. In this paper, we used the NS2 network simulator to first implement an evolving graph based routing protocol, and then to evaluate such protocol compared to three major ad-hoc protocols (DSDV, DSR, AODV). Interestingly, our experiments showed that evolving graphs have all the potentials to be an effective and powerful tool in the development of algorithms for dynamic networks, with predictable dynamics at least. In order to make this model widely applicable, however, some practical issues still have to be addressed and incorporated into the model, like stochastically predictable behavior. We also discuss such issues in this paper, as a result of our experience

BOUNDING THE PROBABILITY OF SUCCESS OF STOCHASTIC METHODS FOR GLOBAL OPTIMIZATION

Abstract In this paper, we establish some bounds for the probability that stimulated annealing produces an optimal or near-optimal solution. Such bounds are given for both asymptotical and finite number of steps in the algorithm, and they depend only on the instance of the problem to be treated. Then we compare its performance with a randomized local search, showing that actually simulated annealing behaves worse than such a very simple global optimization technique. Furthermore, since many parallel implementations of simulated annealing exist, we also address its behavior in the parallel model of computation. Even in this case, similar bounds hold and we can prove that the most simple parallel version of randomized local search is more likely to find optimal or near-optimal solutions than any version of parallel simulated annealing.

Fractional Path Coloring with Applications to WDM Networks

This paper addresses the natural relaxation of the path coloring problem, in which one needs to color directed paths on a symmetric directed graph with a minimum number of colors, in such a way that paths using the same arc of the graph have different colors. This classic combinatorial problem finds applications in the minimization of the number of wavelengths in wavelength division multiplexing (WDM) all-optical networks.

A parallel time/hardware tradeoff T.H=O(2/sup n/2/) for the knapsack problem

A parallel algorithm for solving the knapsack problem on a single-instruction, multiple-data machine with shared memory is presented. The shared memory allows concurrent reading while concurrent writing is forbidden. The knapsack problem is of size n, which the algorithm solves in time T=O(n*(2/sup n/2/)/sup epsilon /) when P=O((2/sup n/2/)/sup (1- epsilon )/), 0 >

ON THE REAL POWER OF LOOSELY COUPLED PARALLEL ARCHITECTURES

We propose new models of SIMD distributed memory parallel computers. We define concurrent read/write access also for machines other than PRAM. Our goal is to unify the description of abstract models of parallel machines with the aim of building a complexity theory where all models can be soundly compared. As an example, we introduce the Hypercube Random Access Machine with concurrent read/write capabilities, and show that it can solve some problems faster than the PRAM.

Topologies for optical interconnection networks based on the optical transpose interconnection system

Many results exist in the literature describing technological and theoretical advances in optical network topologies and design. However, an essential effort has yet to be made in linking those results together. We propose a step in this direction by giving optical layouts for several graph-theoretical topologies studied in the literature, using the optical transpose interconnection system (OTIS) architecture. These topologies include the family of partitioned optical passive star (POPS) and stack-Kautz networks as well as a generalization of the Kautz and the de Bruijn digraphs.