The secret santa problem.

Consider a digraph where the vertices represent people and an arc (i, j) represents the possibility of i giving a gift to j. The basic question we pose is whether there is an anonymity-preserving “gift assignment” such that each person makes and receives exactly one gift, and such that no person i can infer the remaining gift assignments from the fact that i is assigned to give a gift to j. We formalize this problem as a graph property involving vertex disjoint circuit covers, give a polynomial algorithm to decide this property for any given graph and provide a computational validation of the algorithm

Combinatorial optimization based recommender systems.

Recommender systems exploit a set of established user preferences to predict topics or products that a new user might like [2]. Recommender systems have become an important research area in the field of information retrieval. Many approaches have been developed in recent years and the interest is very high. However, despite all the efforts, recommender systems are still in need of further development and more advanced recommendation modelling methods, as these systems must take into account additional requirements on user preferences, such as geographic search and social networking. This fact, in particular, implies that the recommendation must be much more “personalized” than it used to be. In this paper, we describe the recommender system used in the “DisMoiOu”(“TellMeWhere” in French) on-line service (http://dismoiou.fr), which provides the user with advice on places that may be of interest to him/her; the definition of “interest” in this context is personalized taking into account the geographical position of the user (for example when the service is used with portable phones such as the Apple iPhone), his/her past ratings, and the ratings of his/her neighbourhood in a known social network. Using the accepted terminology [6], DisMoiOu is mainly a Collaborative Filtering System (CFS): it employs opinions collected from similar users to suggest likely places. By contrast with existing recommender systems, ours puts together the use of a graph theoretical model [4] and that of combinatorial optimization methods [1]. Broadly speaking, we encode known relations between users and places and users and other users by means of weighted graphs. We then define essential components of the system by means of combinatorial optimization problems on a reformulation of these graphs, which are finally used to derive a ranking on the recommendations associated to pairs (user,place). Preliminary computational results on the three classical evaluation parameters for recommender systems (accuracy, recall, precision [3]) show that our system performs well with respect to accuracy and recall, but precision results need to be improved

Compact relaxations for polynomial programming problems

Reduced RLT constraints are a special class of Reformulation- Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform rRLT constraint generation so as to reduce the number of inequality constraints in the relaxation, thereby making it more compact and faster to solve. We present some computational results validating our approach

The Anonymous subgraph problem.

Many problems can be modeled as the search for a subgraph S- A with specifi�c properties, given a graph G = (V;A). There are applications in which it is desirable to ensure also S to be anonymous. In this work we formalize an anonymity property for a generic family of subgraphs and the corresponding decision problem. We devise an algorithm to solve a particular case of the problem and we show that, under certain conditions, its computational complexity is polynomial. We also examine in details several specifi�c family of subgraphs

The anonymous subgraph problem

In this work we address the Anonymous Subgraph Problem (ASP). The problem asks to decide whether a directed graph contains anonymous subgraphs of a given family. This problem has a number of practical applications and here we describe three of them (Secret Santa Problem, anonymous routing, robust paths) that can be formulated as ASPs. Our main contributions are (i) a formalization of the anonymity property for a generic family of subgraphs, (ii) an algorithm to solve the ASP in time polynomial in the size of the graph under a set of conditions, and (iii) a thorough evaluation of our algorithms using various tests based both on randomly generated graphs and on real-world instances

On the composition of convex envelopes for quadrilinear terms

International audienceWithin the framework of the spatial Branch-and-Bound algorithm for solving Mixed-Integer Nonlinear Programs, different convex relaxations can be obtained for multilinear terms by applying associativity in different ways. The two groupings ((x1x2)x3)x4 and (x1x2x3)x4 of a quadrilinear term, for example, give rise to two different convex relaxations. In [6] we prove that having fewer groupings of longer terms yields tighter convex relaxations. In this paper we give an alternative proof of the same fact and perform a computational study to assess the impact of the tightened convex relaxation in a spatial Branch-and-Bound setting

A Storm of Feasibility Pumps for Nonconvex MINLP

One of the foremost difficulties in solving Mixed Integer Nonlinear Programs, either with exact or heuristic methods, is to find a feasible point. We address this issue with a new feasibility pump algorithm tailored for nonconvex Mixed Integer Nonlinear Programs. Feasibility pumps are algorithms that iterate between solving a continuous relaxation and a mixed-integer relaxation of the original problems. Such approaches currently exist in the literature for Mixed-Integer Linear Programs and convex Mixed-Integer Nonlinear Programs: both cases exhibit the distinctive property that the continuous relaxation can be solved in polynomial time. In nonconvex Mixed Integer Nonlinear Programming such a property does not hold, and therefore special care has to be exercised in order to allow feasibility pumps algorithms to rely only on local optima of the continuous relaxation. Based on a new, high level view of feasibility pumps algorithms as a special case of the well-known successive projection method, we show that many possible different variants of the approach can be developed, depending on how several different (orthogonal) implementation choices are taken. A remarkable twist of feasibility pumps algorithms is that, unlike most previous successive projection methods from the literature, projection is "naturally" taken in two different norms in the two different subproblems. To cope with this issue while retaining the local convergence properties of standard successive projection methods we propose the introduction of appropriate norm constraints in the subproblems; these actually seem to significantly improve the practical performances of the approach. We present extensive computational results on the MINLPLib, showing the effectiveness and efficiency of our algorithm

Calibration of a Multichannel Water Vapor Raman Lidar through Noncollocated Operational Soundings: Optimization and Characterization of Accuracy and Variability

Abstract This paper presents a parametric automatic procedure to calibrate the multichannel Rayleigh–Mie–Raman lidar at the Institute for Atmospheric Science and Climate of the Italian National Research Council (ISAC-CNR) in Tor Vergata, Rome, Italy, using as a reference the operational 0000 UTC soundings at the WMO station 16245 (Pratica di Mare) located about 25 km southwest of the lidar site. The procedure, which is applied to both channels of the system, first identifies portions of the lidar and radiosonde profiles that are assumed to sample the same features of the water vapor profile, taking into account the different time and space sampling. Then, it computes the calibration coefficient with a best-fit procedure, weighted by the instrumental errors of both radiosounding and lidar. The parameters to be set in the procedure are described, and values adopted are discussed. The procedure was applied to a set of 57 sessions of nighttime 1-min-sampling lidar profiles (roughly about 300 h of measurements) covering the whole annual cycle (February 2007–September 2008). A calibration coefficient is computed for each measurement session. The variability of the calibration coefficients (∼10%) over periods with the same instrumental setting is reduced compared to the values obtained with the previously adopted, operator-assisted, and time-consuming calibration procedure. Reduction of variability, as well as the absence of evident trends, gives confidence both on system stability as well as on the developed procedure. Because of the definition of the calibration coefficient and of the different sampling between lidar and radiosonde, a contribution to the variability resulting from aerosol extinction and to the spatial and temporal variability of the water vapor mixing ratio is expected. A preliminary analysis aimed at identifying the contribution to the variability from these factors is presented. The parametric nature of the procedure makes it suitable for application to similar Raman lidar systems

A new wire patch cell for the exposure of cell cultures to electromagnetic fields at 2.45 GHz: Design and numerical characterization

Studies on the interaction between electromagnetic (EM) fields and biological systems have recently gathered further momentum due to the huge diffusion of wireless networks. In order to investigate possible effects on cultured cells of EM fields, in the frequency range typical of such a kind of communication, an in vitro exposure system has been designed and numerically characterized. The system is a Wire Patch Cell (WPC) operating at 2.45 GHz which enables the contemporary exposure of four 35 mm Petri dishes and can be inserted into a commercial incubator. Numerical dosimetry has been carried out by means of the CST Microwave Studio® simulator. Results indicate a good efficiency, in terms of Specific Absorption Rate (SAR) in the biological sample per 1 W of input power. Moreover, the homogeneity of the SAR distribution inside each Petri dish is around 70%, considered an acceptable value for such a kind of biological experimentsStudies on the interaction between electromagnetic (EM) fields and biological systems have recently gathered further momentum due to the huge diffusion of wireless networks. In order to investigate possible effects on cultured cells of EM fields, in the frequency range typical of such a kind of communication, an in vitro exposure system has been designed and numerically characterized. The system is a Wire Patch Cell (WPC) operating at 2.45 GHz which enables the contemporary exposure of four 35 mm Petri dishes and can be inserted into a commercial incubator. Numerical dosimetry has been carried out by means of the CST Microwave Studio ® simulator. Results indicate a good efficiency, in terms of Specific Absorption Rate (SAR) in the biological sample per 1 W of input power. Moreover, the homogeneity of the SAR distribution inside each Petri dish is around 70%, considered an acceptable value for such a kind of biological experiments