Bi-Criteria and Approximation Algorithms for Restricted Matchings

In this work we study approximation algorithms for the \textit{Bounded Color Matching} problem (a.k.a. Restricted Matching problem) which is defined as follows: given a graph in which each edge $e$ has a color $c_e$ and a profit $p_e \in \mathbb{Q}^+$, we want to compute a maximum (cardinality or profit) matching in which no more than $w_j \in \mathbb{Z}^+$ edges of color $c_j$ are present. This kind of problems, beside the theoretical interest on its own right, emerges in multi-fiber optical networking systems, where we interpret each unique wavelength that can travel through the fiber as a color class and we would like to establish communication between pairs of systems. We study approximation and bi-criteria algorithms for this problem which are based on linear programming techniques and, in particular, on polyhedral characterizations of the natural linear formulation of the problem. In our setting, we allow violations of the bounds $w_j$ and we model our problem as a bi-criteria problem: we have two objectives to optimize namely (a) to maximize the profit (maximum matching) while (b) minimizing the violation of the color bounds. We prove how we can "beat" the integrality gap of the natural linear programming formulation of the problem by allowing only a slight violation of the color bounds. In particular, our main result is \textit{constant} approximation bounds for both criteria of the corresponding bi-criteria optimization problem

Metrics on semistable and numerically effective Higgs bundles

We provide notions of numerical effectiveness and numerical flatness for Higgs vector bundles on compact K\"ahler manifolds in terms of fibre metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they admit filtrations whose quotients are stable flat Higgs bundles. We compare these definitions with those previously given in the case of projective varieties. Finally we study the relations between numerically effectiveness and semistability, establishing semistability criteria for Higgs bundles on projective manifolds of any dimension.Comment: 25 pages. Changes in the expositio

Boundary Exchange Algebras and Scattering on the Half Line

Some algebraic aspects of field quantization in space-time with boundaries are discussed. We introduce an associative algebra, whose exchange properties are inferred from the scattering processes in integrable models with reflecting boundary conditions on the half line. The basic properties of this algebra are established and the Fock representations associated with certain involutions are derived. We apply these results for the construction of quantum fields and for the study of scattering on the half line.Comment: Enlarged version, to appear in Comm. Math. Phys. Tex file, macros included, no figures, 32 page

Testing complete positivity

We study the modified dynamical evolution of the neutral kaon system under the condition of complete positivity. The accuracy of the data from planned future experiments is expected to be sufficiently precise to test such a hypothesis.Comment: 12 pages, latex, no figures, to appear in Mod. Phys. Lett.

Multistage Switching Architectures for Software Routers

Software routers based on personal computer (PC) architectures are becoming an important alternative to proprietary and expensive network devices. However, software routers suffer from many limitations of the PC architecture, including, among others, limited bus and central processing unit (CPU) bandwidth, high memory access latency, limited scalability in terms of number of network interface cards, and lack of resilience mechanisms. Multistage PC-based architectures can be an interesting alternative since they permit us to i) increase the performance of single software routers, ii) scale router size, iii) distribute packet manipulation and control functionality, iv) recover from single-component failures, and v) incrementally upgrade router performance. We propose a specific multistage architecture, exploiting PC-based routers as switching elements, to build a high-speed, largesize,scalable, and reliable software router. A small-scale prototype of the multistage router is currently up and running in our labs, and performance evaluation is under wa

Cellular Automaton for Realistic Modelling of Landslides

A numerical model is developed for the simulation of debris flow in landslides over a complex three dimensional topography. The model is based on a lattice, in which debris can be transferred among nearest neighbors according to established empirical relationships for granular flows. The model is then validated by comparing a simulation with reported field data. Our model is in fact a realistic elaboration of simpler ``sandpile automata'', which have in recent years been studied as supposedly paradigmatic of ``self-organized criticality''. Statistics and scaling properties of the simulation are examined, and show that the model has an intermittent behavior.Comment: Revised version (gramatical and writing style cleanup mainly). Accepted for publication by Nonlinear Processes in Geophysics. 16 pages, 98Kb uuencoded compressed dvi file (that's the way life is easiest). Big (6Mb) postscript figures available upon request from [email protected] / [email protected]