Related papers: Using Integer Programming to Solve Games, Puzzles,…
We discuss the problem of finding distinct integer sets $\{x_1,x_2,...,x_n\}$ where each sum $x_i+x_j, i \ne j$ is a square, and $n \le 7$. We confirm minimal results of Lagrange and Nicolas for $n=5$ and for the related problem with…
The orienteering problem is a well-studied and fundamental problem in transportation science. In the problem, we are given a graph with prizes on the nodes and lengths on the edges, together with a budget on the overall tour length. The…
We develop a first line of attack for solving programming competition-style problems from input-output examples using deep learning. The approach is to train a neural network to predict properties of the program that generated the outputs…
We consider the solution of linear systems with tensor product structure using a GMRES algorithm. In order to cope with the computational complexity in large dimension both in terms of floating point operations and memory requirement, our…
The following four classes of computational problems are equivalent: solving matrix games, solving linear programs, best $l^{\infty}$ linear approximation, best $l^1$ linear approximation.
We study the reformulation of integer linear programs by means of a mixed integer linear program with fewer integer variables. Such reformulations can be solved efficiently with mixed integer linear programming techniques. We exhibit…
Humans excel in solving complex reasoning tasks through a mental process of moving from one idea to a related one. Inspired by this, we propose Subgoal Search (kSubS) method. Its key component is a learned subgoal generator that produces a…
This paper provides a set of cycling problems in linear programming. These problems should be useful for researchers to develop and test new simplex algorithms. As matter of the fact, this set of problems is used to test a recently proposed…
We study the interplay between chip-firing games and potential theory on graphs, characterizing reduced divisors ($G$-parking functions) on graphs as the solution to an energy (or potential) minimization problem and providing an algorithm…
At the heart of many scientific conferences is the problem of matching submitted papers to suitable reviewers. Arriving at a good assignment is a major and important challenge for any conference organizer. In this paper we propose a…
We present evidence from three student interactions in which two types of common solution methods for solving simple first-order differential equations are used. We describe these using the language of resources, considering epistemic games…
Quantum computing has become an active research field in recent years, as its applications in fields such as cryptography, optimization, and materials science are promising. Along with these developments, challenges and opportunities exist…
Recent work has shown potential in using Mixed Integer Programming (MIP) solvers to optimize certain aspects of neural networks (NNs). However the intriguing approach of training NNs with MIP solvers is under-explored.…
Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…
This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics…
Coalitions naturally exist in many real-world systems involving multiple decision makers such as ridesharing, security, and online ad auctions, but the coalition structure among the agents is often unknown. We propose and study an important…
Designing efficient algorithms to compute Nash equilibria poses considerable challenges in Algorithmic Game Theory and Optimization. In this work, we employ integer programming techniques to compute Nash equilibria in Integer Programming…
Leveraging the prevailing interest in computer games among college students, both for entertainment and as a possible career path, is a major reason for the increasing prevalence of computer game design courses in computer science…
Knowledge graph (KG) embedding is well-known in learning representations of KGs. Many models have been proposed to learn the interactions between entities and relations of the triplets. However, long-term information among multiple triplets…
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…