Related papers: Reduction from the partition problem: Dynamic lot …
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
Subset sum is a very old and fundamental problem in theoretical computer science. In this problem, $n$ items with weights $w_1, w_2, w_3, \ldots, w_n$ are given as input and the goal is to find out if there is a subset of them whose weights…
We are given a set of $n$ jobs and a single processor that can vary its speed dynamically. Each job $J_j$ is characterized by its processing requirement (work) $p_j$, its release date $r_j$ and its deadline $d_j$. We are also given a budget…
In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
In this note, we consider the capacitated facility location problem when the transportation costs of the instance satisfy the Monge property. We show that a straightforward dynamic program finds the optimal solution when the demands are…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
This paper presents a method for calculating Region of Attraction of a target set (not necessarily an equilibrium) for controlled polynomial dynamical systems, using a hierarchy of semidefinite programming problems (SDPs). Our approach…
This note provides a simple example demonstrating that, if exact computations are allowed, the number of iterations required for the value iteration algorithm to find an optimal policy for discounted dynamic programming problems may grow…
We consider several subgroup-related algorithmic questions in groups, modeled after the classic computational lattice problems, and study their computational complexity. We find polynomial time solutions to problems like finding a subgroup…
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
We consider the problem of fitting a probability density function when it is constrained to have a given number of modal intervals. We propose a dynamic programming approach to solving this problem numerically. When this number is not…
It is demonstrated how dynamic storage allocation algorithms can be analyzed in terms of finite size scaling. The method is illustrated in the three simple cases of the it first-fit, next-fit and it best-fit algorithms, and the system works…
In this focused technical paper, we present long-awaited algorithmic advances toward the efficient construction of near-optimal replenishment policies for a true inventory management classic, the economic warehouse lot scheduling problem.…
A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.
Subset Sum is a classical optimization problem taught to undergraduates as an example of an NP-hard problem, which is amenable to dynamic programming, yielding polynomial running time if the input numbers are relatively small. Formally,…