Related papers: Using Integer Programming to Solve Games, Puzzles,…
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…
We give two graph-theoretic models and a mixed-integer program to calculate the maximum achievable score in the popular board game "Ticket to Ride." In Ticket to Ride, players compete to claim railway routes on a map, with points awarded…
This paper presents an integer programming-based optimization framework designed to effectively address the complex final exam scheduling challenges encountered at Cornell University. With high flexibility, the framework is specifically…
Even though it is well known that for most relevant computational problems different algorithms may perform better on different classes of problem instances, most researchers still focus on determining a single best algorithmic…
We provide a complexity classification of four variants of robust integer programming when the underlying Graver basis is given. We discuss applications to robust multicommodity flows and multidimensional transportation, and describe an…
We consider the problem of selecting a portfolio of entries of fixed cardinality for contests with top-heavy payoff structures, i.e. most of the winnings go to the top-ranked entries. This framework is general and can be used to model a…
Mean-field games (MFGs) have shown strong modeling capabilities for large systems in various fields, driving growth in computational methods for mean-field game problems. However, high order methods have not been thoroughly investigated. In…
Can agents be trained to answer difficult mathematical questions by playing a game? We consider the integer feasibility problem, a challenge of deciding whether a system of linear equations and inequalities has a solution with integer…
Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form…
Quantum computers promise to outperform their classical counterparts at certain tasks. However, existing quantum devices are error-prone and restricted in size. Thus, effective compilation methods are crucial to exploit limited quantum…
The game industry is moving into an era where old-style game engines are being replaced by re-engineered systems with embedded machine learning technologies for the operation, analysis and understanding of game play. In this paper, we…
In this tutorial, we present a computational overview on computing Nash equilibria in Integer Programming Games ($IPG$s), $i.e.$, how to compute solutions for a class of non-cooperative and nonconvex games where each player solves a…
Learning to program has become common in schools, higher education and individual learning. Although testing is an important aspect of programming, it is often neglected in education due to a perceived lack of time and knowledge, or simply…
In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different…
A query game is a pair of a set $Q$ of queries and a set $\mathcal{F}$ of functions, or codewords $f:Q\rightarrow \mathbb{Z}.$ We think of this as a two-player game. One player, Codemaker, picks a hidden codeword $f\in \mathcal{F}$. The…
We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…
It is known that for any general access structure, a secret sharing scheme (SSS) can be constructed from an (m,m)-threshold scheme by using the so-called cumulative map or from a (t,m)-threshold SSS by a modified cumulative map. However,…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
Round robin tournaments are omnipresent in sport competitions and beyond. We propose two new integer programming formulations for scheduling a round robin tournament, one of which we call the matching formulation. We analytically compare…
We consider so-called squaring the square-puzzles where a given square (or rectangle) should be dissected into smaller squares. For a specific instance of such problems we demonstrate that a mathematically rigorous solution can be quite…