Maria J. Blesa

MALLBA: a library of skeletons for combinatorial optimisation

The MALLBA project tackles the resolution of combinatorial optimization problems using algorithmic skeletons implemented in C++. mallba offers three families of generic resolution methods: exact, heuristic and hybrid. Moreover, for each resolution method, MALLBA provides three different implementations: sequential, parallel for local area networks, and parallel for wide area networks (currently under development). This paper explains the architecture of the MALLBA library, presents some of its skeletons, and offers several computational results to show the viability of the approach.

New metaheuristic approaches for the edge-weighted k -cardinality tree problem

In this paper we propose three metaheuristic approaches, namely a Tabu Search, an Evolutionary Computation and an Ant Colony Optimization approach, for the edge-weighted k-cardinality tree (KCT) problem. This problem is an NP-hard combinatorial optimization problem that generalizes the well-known minimum weight spanning tree problem. Given an edge-weighted graph G = (V,E), it consists of finding a tree in G with exactly k ≤ |V| - 1 edges, such that the sum of the weights is minimal. First, we show that our new metaheuristic approaches are competitive by applying them to a set of existing benchmark instances and comparing the results to two different Tabu Search methods from the literature. The results show that these benchmark instances are not challenging enough for our metaheuristics. Therefore, we propose a diverse set of benchmark instances that are characterized by different features such as density and variance in vertex degree. We show that the performance of our metaheuristics depends on the characteristics of the tackled instance, as well as on the cardinality. For example, for low cardinalities the Ant Colony Optimization approach is best, whereas for high cardinalities the Tabu Search approach has advantages.

Efficient parallel LAN/WAN algorithms for optimization: the MALLBA project

The MALLBA project tackles the resolution of combinatorial optimization problems using generic algorithmic skeletons implemented in C++. A skeleton in the MALLBA library implements an optimization method in one of the three families of generic optimization techniques offered: exact, heuristic and hybrid. Moreover, for each of those methods, MALLBA provides three different implementations: sequential, parallel for Local Area Networks, and parallel for Wide Area Networks. This paper introduces the architecture of the MALLBA library, details some of the implemented skeletons, and offers computational results for some classical optimization problems to show the viability of our library. Among other conclusions, we claim that the design used to develop the optimization techniques included in the library is generic and efficient at the same time.

A Characterization of Universal Stability in the Adversarial Queuing Model

We study universal stability of directed and undirected graphs in the adversarial queuing model for static packet routing. In this setting, packets are injected in some edge and have to traverse a predefined path before leaving the system. Restrictions on the allowed packet trajectory provide a way to analyze stability under different packet trajectories. We consider five packet trajectories, two for directed graphs and three for undirected graphs, and provide polynomial time algorithms for testing universal stability when considering each of them. In each case we obtain a different characterization of the universal stability property in terms of a set of forbidden subgraphs. Thus we show that variations of the allowed packet trajectory lead to nonequivalent characterizations. Using those characterizations we are also able to provide polynomial time algorithms for testing stability under the \NTGLIS (Nearest To Go-Longest In System) protocol.

An ant colony optimization algorithm for DNA sequencing by hybridization

The reconstruction of DNA sequences from DNA fragments is one of the most challenging problems in computational biology. In recent years the specific problem of DNA sequencing by hybridization has attracted quite a lot of interest in the optimization community. Several metaheuristics such as tabu search and evolutionary algorithms have been applied to this problem. However, the performance of existing metaheuristics is often inferior to the performance of recently proposed constructive heuristics. On the basis of these new heuristics we develop an ant colony optimization algorithm for DNA sequencing by hybridization. An important feature of this algorithm is the implementation in a so-called multi-level framework. The computational results show that our algorithm is currently a state-of-the-art method for the tackled problem.

Beam search for the longest common subsequence problem

The longest common subsequence problem is a classical string problem that concerns finding the common part of a set of strings. It has several important applications, for example, pattern recognition or computational biology. Most research efforts up to now have focused on solving this problem optimally. In comparison, only few works exist dealing with heuristic approaches. In this work we present a deterministic beam search algorithm. The results show that our algorithm outperforms the current state-of-the-art approaches not only in solution quality but often also in computation time.

Ant Colony Optimization for the Maximum Edge-Disjoint Paths Problem

Given a graph G representing a network topology, and a collection T={(s 1,t 1)...(s k ,t k )} of pairs of vertices in G representing connection request, the maximum edge-disjoint paths problem is an NP-hard problem which consists in determining the maximum number of pairs in T that can be routed in G by mutually edge-disjoint s i -t i paths. We propose an Ant Colony Optimization (aco) algorithm to solve this problem. aco algorithms are inspired by the foraging behavior of real ants, whose distributed nature makes them suitable for the application in network environments. Our current version is aimed for the application in static graphs. In comparison to a multi-start greedy approach, our algorithm has advantages especially when speed is an issue.

Finding Edge-disjoint Paths in Networks: An Ant Colony Optimization Algorithm

One of the basic operations in communication networks consists in establishing routes for connection requests between physically separated network nodes. In many situations, either due to technical constraints or to quality-of-service and survivability requirements, it is required that no two routes interfere with each other. These requirements apply in particular to routing and admission control in large-scale, high-speed and optical networks. The same requirements also arise in a multitude of other applications such as real-time communications, vlsi design, scheduling, bin packing, and load balancing. This problem can be modeled as a combinatorial optimization problem as follows. Given a graph G representing a network topology, and a collection T={(s1,t1)...(sk,tk)} of pairs of vertices in G representing connection request, the maximum edge-disjoint paths problem is an NP-hard problem that consists in determining the maximum number of pairs in T that can be routed in G by mutually edge-disjoint si−ti paths. We propose an ant colony optimization (aco) algorithm to solve this problem. aco algorithms are approximate algorithms that are inspired by the foraging behavior of real ants. The decentralized nature of these algorithms makes them suitable for the application to problems arising in large-scale environments. First, we propose a basic version of our algorithm in order to outline its main features. In a subsequent step we propose several extensions of the basic algorithm and we conduct an extensive parameter tuning in order to show the usefulness of those extensions. In comparison to a multi-start greedy approach, our algorithm generates in general solutions of higher quality in a shorter amount of time. In particular the run-time behaviour of our algorithm is one of its important advantages.

The impact of failure management on the stability of communication networks

In this work we deal with communication networks in which links may fail. We propose an adversarial model for describing the traffic pattern occurring in this type of faulty systems and study properties concerning their stability, especially under (nontrivial) underloaded worse-case scenarios. We show that, depending on how the system is organized and prepared to deal with failures, the dynamics of the system change and thus the conditions for stability. We propose three different ways of failure management and study how they influence on the stability of faulty communication networks under the adversarial model proposed. We show that some failure managements can provoke the instability of even very simple networks.

Adversarial Queueing Model for Continuous Network Dynamics

Abstract In this paper we initiate the generalization of the Adversarial Queueing Theory (aqt) model to capture the dynamics of continuous scenarios in which the usually assumed synchronicity of the evolution is not required anymore. We propose an asynchronous model, named continuousaqt (caqt), in which packets can have arbitrary lengths, and the network links may have different speeds (or bandwidths) and propagation delays. With respect to the standard aqt model, these new features turn out to be significant for the stability of packet scheduling policies that take them into account, but not so much for the stability of networks. From the network point of view, we show that networks with directed acyclic topologies are universally stable, i.e., stable independently of the scheduling policies and traffic patterns used in it. Interestingly enough, this even holds for traffic patterns that make links to be fully loaded. Finally, it turns out that the set of universally stable networks remains the same as in the aqt model and, therefore, the property of universal stability of networks is decidable in polynomial time. Concerning packet scheduling policies, we show that the well-known lis, sis, ftgand nfsscheduling policies remain universally stable in the caqt model. We introduce other scheduling policies that, although being universally stable in the aqt model, they are unstable under the caqt model.