This work estimates the complexity of Uruguayan Truco, an imperfect-information two-team card game, by computing a lower bound on the total number of information sets in its extensive-form representation. We adapt the HyperLogLog (HLL) probabilistic counting algorithm to support arbitrarily long hashes, enabling its use in this new domain. This adapted version is combined with Monte Carlo rollouts to handle the intractable size of the game tree. To validate our approach, we introduce mini-Truco, a simplified and tractable variant of the original game. Our experiments show that, in expectation, this approach yields accurate estimates of the underlying set size while providing horizontal scalability across multiple nodes. After running this game-agnostic method for 100 days (totaling 4.8×105core-hours), we establish that a 20-point 2-player game of Uruguayan Truco contains at least 1.49×1012information sets, providing a concrete lower bound on the game’s complexity.

Network reliability computation is an NP-hard problem which has attracted much attention in literature. This problem consists in, given a network where the links may fail or operate with known probabilities, to compute the probability that a given subset of nodes (known as terminals) are connected by the operational links. Given the difficulty to compute the exact value of the network reliability, an alternative which has been much explored in the literature is the use of Monte Carlo estimation methods. In this work, we discuss the Permutation Monte Carlo method, which is an estimation algorithm which has shown much promise but that is prone to numerical problems in the case of networks with a large number of links. We discuss this situation and we present a simple way to rewrite the algorithm's computations which is more numerically stable. We present some computational results showing that the method is more efficient that the standard Monte Carlo method for highly reliable networks, and that it can be applied to topologies with hundreds of links.

Nowadays, the assimilation of workers with disabilities is recognized as both a challenge and an opportunity in terms of staff diversity and of corporate social responsibility of different organizations. In this context, achieving a fair and efficient task distribution is an essential aspect of guaranteeing the effective and full involvement of all the workers, independently from their cognitive and physical capacities. A task distribution model is a method for assigning and managing tasks within a work team, organization or group of persons, usually aiming to optimize productivity and efficiency. The main objective is to ensure that the correct tasks are assigned to the appropriate persons, taking into account their abilities, experience and current work charge. Task distribution models are particularly relevant when including people with disabilities, where they must be flexible and adaptable enough to guarantee the full integration of all the team members. In this work, we present a Mathematical Programming model for task distribution in the context of hiring people with disabilities. We discuss a practical case study at the Intendencia de Montevideo (IdeM - the municipality of the city of Montevideo), as part of a project for improving the integration of people with disabilities in its staff (currently the IdeM staff only includes about 1.5% of employees with disabilities; while applicable laws state that this percentage should raise to at least 4%). We present the results of applying the Mathematical Programming model, comparing the results against manual assignments. Different objective functions are also taken into account, as the various stakeholders also have specific goals that are important to take into account. The results show that mathematical programming models are an effective tool that can be used to support decision making and improve the integration of workers with disabilities in an organization.

Uruguayan Truco is a positive-sum and imperfect information card game with 2, 4 and 6 player variants. Finding the Nash equilibria of such games is very hard, so we approximate them using Computational Game Theory and Deep Reinforcement Learning methods. We implement Counterfactual Regret Minimization (CFR) and some of its variants, and Deep Monte Carlo (DMC). We also propose two levels of manual abstraction to reduce the number of information sets, which are sets of indistinguishable game states. We evaluate our methods on T1K22, a dataset of 79,000 random hands of Uruguayan Truco, against two baseline agents and a human player. We find that CFR-based methods outperform DMC, especially External Sampling Monte Carlo CFR, which converges faster and achieves a higher win rate. It is remarkable that, after 2 weeks of training (totaling 4,032 core hours), starting from scratch and without using any human knowledge, the best agents defeated every baseline, with win rates significantly higher than 50%.

This state of the art discusses the problem of reliability estimation for highly reliable stochastic flow networks. There are algorithms to compute this reliability exactly, but they have exponential complexity, making the problem intractable for large or even medium sized networks. In this case Monte Carlo simulation is a simple and straightforward alternative tool to provide a reliability estimation. However, standard Monte Carlo is efficient only if the reliability is not extremely high, otherwise variance reduction techniques are required. This work explores different methods designed to reduce the variance of the estimators in this context. These methods are introduced together with a brief review of the algorithms in which they are based. Also, their precision and computational efficiency is discussed, giving some insights on their relative performance and suitability.

This work presents an application of mathematical programming methods and their implementation in free software tools to develop a support tool for the assignment of habitational units in a cooperative. In Uruguay building and housing cooperatives have a history of developing housing solutions, at lower prices and higher quality levels than possible with traditional approaches. In these cooperatives, it is usual that, once the houses are built, the assignment to members is done randomly (ie, holding a lottery). In this work we develop a computational tool that can take into account the stated preferences of the cooperative members and generate assignments that maximize their satisfaction, with results of much higher satisfaction levels than those achieved using the traditional lottery method.