Related papers: Maximizing the Score in "Ticket to Ride"
2048 is a stochastic single-player game involving 16 cells on a 4 by 4 grid, where a player chooses a direction among up, down, left, and right to obtain a score by merging two tiles with the same number located in neighboring cells along…
We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…
The Team Orienteering Problem (TOP) is an NP-hard routing problem in which a fleet of identical vehicles aims at collecting rewards (prizes) available at given locations, while satisfying restrictions on the travel times. In TOP, each…
Platooning of vehicles is a promising approach for reducing fuel consumption, increasing vehicle safety, and using road space more efficiently. We consider the important but difficult problem of assigning optimal routes and departure…
Many public transportation systems are unable to keep up with growing passenger demand as the population grows in urban areas. The slow or lack of improvements for public transportation pushes people to use private transportation modes,…
We consider the problem of maximizing the minimum (weighted) value of all components of a vector over a polymatroid. This is a special case of the lexicographically optimal base problem introduced and solved by Fujishige. We give an…
Ride-hailing services have expanded the role of shared mobility in passenger transportation systems, creating new markets and creative planning solutions for major urban centers. In this paper, we consider their use for the first-mile or…
This paper presents a data-driven statistical framework to quantify the role of skill in games, addressing the long-standing question of whether success in a game is predominantly driven by skill or chance. We analyze player level data from…
Nowadays, several crowdsourcing projects exploit social choice methods for computing an aggregate ranking of alternatives given individual rankings provided by workers. Motivated by such systems, we consider a setting where each worker is…
Let $G=(V,E)$ be an undirected graph with $n$ vertices and $m$ edges, in which each vertex $u$ is assigned an integer priority in $[1,n]$, with 1 being the "highest" priority. Let $M$ be a matching of $G$. We define the priority score of…
The railway timetables are designed in an optimal manner to maximize the capacity usage of the infrastructure concerning different objectives besides avoiding conflicts. The real-time railway traffic management problem occurs when the…
Connect Four is a two-player game where each player attempts to be the first to create a sequence of four of their pieces, arranged horizontally, vertically, or diagonally, by dropping pieces into the columns of a grid of width seven and…
To study discrimination in automated decision-making systems, scholars have proposed several definitions of fairness, each expressing a different fair ideal. These definitions require practitioners to make complex decisions regarding which…
The traveling salesman problem (TSP) is one of the most prominent combinatorial optimization problems. Given a complete graph G = (V, E) and non-negative distances d for every edge, the TSP asks for a shortest tour through all vertices with…
Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several…
In bike sharing systems the quality of the service to the users strongly depends on the strategy adopted to reposition the bikes. The bike repositioning problem is in general very complex as it involves different interrelated decisions: the…
This paper explores multi-entry strategies for betting pools related to single-elimination tournaments. In such betting pools, participants select winners of games, and their respective score is a weighted sum of the number of correct…
We present a solution to real-world train scheduling problems, involving routing, scheduling, and optimization, based on Answer Set Programming (ASP). To this end, we pursue a hybrid approach that extends ASP with difference constraints to…
This paper addresses the problem of planning time-optimal trajectories for multiple cooperative agents along specified paths through a static road network. Vehicle interactions at intersections create non-trivial decisions, with complex…
Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two…