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A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least…
We propose a novel Linear Program (LP) based formula- tion for solving jigsaw puzzles. We formulate jigsaw solving as a set of successive global convex relaxations of the stan- dard NP-hard formulation, that can describe both jigsaws with…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…
We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand side is unspecified. Our formula involves irreducible…
For several decades the dominant techniques for integer linear programming have been branching and cutting planes. Recently, several authors have developed core point methods for solving symmetric integer linear programs (ILPs). An integer…
We consider a random knockout tournament among players $1, \ldots, n$, in which each match involves two players. The match format is specified by the number of matches played in each round, where the constitution of the matches in a round…
We consider the following problem: Given a rational matrix $A \in \setQ^{m \times n}$ and a rational polyhedron $Q \subseteq\setR^{m+p}$, decide if for all vectors $b \in \setR^m$, for which there exists an integral $z \in \setZ^p$ such…
The selection of an appropriate competition format is critical for both the success and credibility of any competition, both real and simulated. In this paper, the automated parallelism offered by the RoboCupSoccer 2D simulation league is…
Register allocation (mapping variables to processor registers or memory) and instruction scheduling (reordering instructions to increase instruction-level parallelism) are essential tasks for generating efficient assembly code in a…
Crucial to an Evolutionary Algorithm's performance is its selection scheme. We mathematically investigate the relation between polynomial rank and probabilistic tournament methods which are (respectively) generalisations of the popular…
Automatically matching reviewers to papers is a crucial step of the peer review process for venues receiving thousands of submissions. Unfortunately, common paper matching algorithms often construct matchings suffering from two critical…
In this paper we present methods for exemplar based clustering with outlier selection based on the facility location formulation. Given a distance function and the number of outliers to be found, the methods automatically determine the…
Tournament solutions are frequently used to select winners from a set of alternatives based on pairwise comparisons between alternatives. Prior work has shown that several common tournament solutions tend to select large winner sets and…
An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…
We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue from the seller side. First, we show that it is not possible to solve this problem…
In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…