Related papers: Objective Coefficient Rounding and Almost Symmetri…
We present a novel algorithm for (i) detecting approximate symmetries inherently present among spatially localized molecular orbitals and (ii) enforcing these in numerically exact manners by means of unitary optimization techniques. The…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson has been extensively…
We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
We study a variant of the quantum approximate optimization algorithm [ E. Farhi, J. Goldstone, and S. Gutmann, arXiv:1411.4028] with slightly different parametrization and different objective: rather than looking for a state which…
Quadratic assignment problem is one of the great challenges in combinatorial optimization. It has many applications in Operations research and Computer Science. In this paper, the author extends the most-used rounding approach to a…
This paper presents theoretical and practical results for the bin packing problem with scenarios, a generalization of the classical bin packing problem which considers the presence of uncertain scenarios, of which only one is realized. For…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
This paper considers scheduling on identical machines. The scheduling objective considered in this paper generalizes most scheduling minimization problems. In the problem, there are $n$ jobs and each job $j$ is associated with a…
Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…
Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in…
Automating algorithm configuration is growing increasingly necessary as algorithms come with more and more tunable parameters. It is common to tune parameters using machine learning, optimizing performance metrics such as runtime and…
Studied here is the effect of the presence of symmetry groups in a system of algebraic equations on the numerical resolution with fixed-point algorithms. It is proved that the symmetries imply two important properties of the system: the…
We study the Min-Weighted Sum Bin Packing problem, a variant of the classical Bin Packing problem in which items have a weight, and each item induces a cost equal to its weight multiplied by the index of the bin in which it is packed. This…
Quantum computers can solve semidefinite programs (SDPs) using resources that scale better than state-of-the-art classical methods as a function of the problem dimension. At the same time, the known quantum algorithms scale very unfavorably…
A particularly important substructure in modeling joint linear chance-constrained programs with random right-hand sides and finite sample space is the intersection of mixing sets with common binary variables (and possibly a knapsack…
Suppose that we wish to estimate a vector $\mathbf{x}$ from a set of binary paired comparisons of the form "$\mathbf{x}$ is closer to $\mathbf{p}$ than to $\mathbf{q}$" for various choices of vectors $\mathbf{p}$ and $\mathbf{q}$. The…
In the stochastic submodular cover problem, the goal is to select a subset of stochastic items of minimum expected cost to cover a submodular function. Solutions in this setting correspond to sequential decision processes that select items…
A typical goal of research in combinatorial optimization is to come up with fast algorithms that find optimal solutions to a computational problem. The process that takes a real-world problem and extracts a clean mathematical abstraction of…