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[ Abstract ]

[ Slides ]

In the last few years, the Internet has exponentially expanded to a worldwide network connecting several millions of users. Such an explosion deeply impacts on the available bandwidth of IP backbone networks. Network Engineers have been building very large scale networks at their best, trying to understand beforehand (planning) and react just in time to the network events. Recently, new emerging Traffic Engineering (TE) techniques enable Internet Service Providers (ISP) to route the traffic along the network, offering the best service to their users in terms of throughput and latency, moving traffic from congested links to less loaded areas of the network. In particular, the Multi-Protocol Label Switching (MPLS-TE) networks enable ISPs to adopt quality-of-service (QoS) policies, setting up constrained label switched paths (LSPs). Furthermore, network survivability techniques have been developed to guarantee seamless communication services in case of network failures. Traffic management and restoration strategies are usually adopted in order to make a backbone network survivable, i.e., the network traffic load has to be distributed in such a way that a failure has the minimum (eventually, null) impact when it occurs; moreover, the traffic demands affected by the failure have to be suitably restored. The talk concerns the problem of minimizing the maximum link utilization of IP telecommunication networks under the joint use of the traditional IS-IS/OPSF protocol and the MPLS-TE technology. Both working conditions and single link failure scenarios are addressed. A Linear Programming mathematical model is proposed that, while optimizing the network utilization, provides optimal user performance, efficient use of network resources, and 100% survivability in case of single link failure. The hybrid approach takes advantage of both IGP and MPLS-TE technologies providing a flexible tool for IP networks traffic engineers. The efficiency of the proposed appoach is validated by a wide experimentation performed on synthetic and real networks, both in working and failure conditions. The obtained results show that the maximum utilization of the network considerably reduces allowing a more efficient use of the network resources. Moreover, by setting a limited number of LSPs allows better results than those obtained by simply optimizing the IGP weights. However, using the hybrid approach, an optimized set of IGP weigths allows to further improve the network performance in case of failure.

[ Slides ]

It is well know that two states in a finite image Kripke frame are bisimilar iff they satisfy the same modal formulas, this is an instantiation of the Hennessy-Milner property. Coalgebras are a generalization of Kripke frames. In this talk we will use some elementary category theory to show how to generalize the Hennessy-Milner property to arbitrary coalgebras. Using this approach we will see that the Hennessy-Milner property is related to the existence of some solution set. Using this we will prove: The existence of a language with the Hennessy-Milner property for T-coalgebras is equivalent to the existence of a final T-coalgebra.

Monads are widely used in the writing of computations with side effects, as a powerful tool allowing for more concise and intuitive expressions. One might expect reasoning about them to be just as straightforward, but wishful thinking didn't make it happen. We try to address the issue by means of a plain example: the labelling of a tree with distinct labels. We take a simple algorithm using a modifiable state, and prove it correct using elementary techniques in a first go, and monads / applicative functors the second time around. We thus obtain a factorisation of the labelling routine, the proof of which suggests taking some liberty with the type system, so as to describe some intriguing properties of the state applicative functor in interaction with function composition.

We deploy some category theory to compare two fundamental approaches to programming. Namely, algebraic data types and structural recursion play a central role in functional programming as they allow programmers to define recursive data structures and operations on them uniformly by induction. Likewise, in concurrent programming (such as idealised object-oriented programming), recursive hierarchies of components play a central role for the same reason. There is a semantical correspondence between these two situations which we reveal and formalise categorically. In particular, we observe that (in some sense) well-defined programs with inductive data and coinductive behaviour are defined by a categorical distributive law of the structure of the data over the behaviour.

Evolutionary Algorithms (EAs) have been applied successfully to a wide range of static optimisation problems. Many real-world problems, however, possess numerous time-variant attributes that require a continuous adaptation of the proposed solution. These dynamic attributes pose many new challenges to the design and analysis of novel EAs. In this talk, I will start with an introduction to dynamic optimisation and will present some examples of dynamic optimisation problems as well as existing approaches that have been developed recently to address them. I will also present a formal problem definition, placing special emphasis on the underlying problem and the imposed dynamics. In the remainder of the talk I will focus on the impact of time-variance in the combinatorial domain and will present some results regarding the potential correlation of successive environmental states in the subset sum problem.

Over the past 20 years, the research on multiobjective evolutionary optimisation has received a growing interest. In this talk, I will introduce a recent new multiobjective approach, called decomposition-based multiobjective evolutionary algorithm (MOEA/D). It solves multiple single objective subproblems simultaneously by evolving a population. The optima of these subproblems correspond to a set of Pareto-optimal solutions. Under the framework of MOEA/D, it is very easy to incorporate other metaheuristics, such as simulated annealing, differential evolution, memetic algorithm, greedy randomized adaptive search, etc. Our experimental results show that MOEA/D is very promising to solve complex multiobjective optimisation problems.

[ Slides ]
We introduce two abstract notions of system of equations, called Equational System and Term Equational System. Equational Systems provide a very abstract notion of equation, which is general enough to represent non-classical notions of equations as needed in modern applications such as nominal algebras and pi-calculus algebras. For Equational Systems we present an explicit construction of free algebras under reasonably general conditions. Term Equational Systems (TESs) are given by a more concrete, yet still abstract notion of equation. For TESs, we provide two means of equational reasoning: reasoning by deduction and reasoning by rewriting. For the reasoning by deduction, a set of sound deduction rules is given, but we do not have a general completeness result for it. However, we have an internal completeness result for TESs that admit free algebras. Together with this result, by analyzing the explicit construction of free algebras given by the theory of Equational Systems, one may synthesize a sound and complete equational reasoning by rewritng. Existing systems that arise as TESs include:

• First-order equational logic and rewriting system;
• Nominal equational logics independently developed by Gabbay and Mathijssen, and Clouston and Pitts;
• Binding equational logic and rewriting system of Hamana;
• Combinatory reduction systems of Klop;
• Second-order abstract syntax of Marcelo Fiore.

This is joint work with Marcelo Fiore.

Large scale data applications like search engines require very efficient compression routines. Sometimes, even removing some bits per element can result in a significant improvement. Random access to compressed data also requires additional informations (and space). Using the above scenario as a working example, we introduce (fully) indexable dictionaries, succinct data structures for bitvectors supporting desirable operations in nearly minimal space. We then illustrate some of the latest results concerning FIDs, both in term of theory and of real life applications.