Related papers: The Complexity of Computing Optimal Assignments of…
We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally NP-hard, we show it is polynomial time solvable when a…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
The assignment problem is one of the most well-studied settings in social choice, matching, and discrete allocation. We consider the problem with the additional feature that agents' preferences involve uncertainty. The setting with…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
This paper presents the first study of the complexity of the optimization problem for integer linear-exponential programs which extend classical integer linear programs with the exponential function $x \mapsto 2^x$ and the remainder…
We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these conditions, we propose a…
In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial…
Given a sound first-order p-time theory $T$ capable of formalizing syntax of first-order logic we define a p-time function $g_T$ that stretches all inputs by one bit and we use its properties to show that $T$ must be incomplete. We leave it…
We consider the classical problem of Scheduling on Unrelated Machines. In this problem a set of jobs is to be distributed among a set of machines and the maximum load (makespan) is to be minimized. The processing time $p_{ij}$ of a job $j$…
We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a…
In coding and information theory, it is desirable to construct maximal codes that can be either variable length codes or error control codes of fixed length. However deciding code maximality boils down to deciding whether a given NFA is…
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…
Consider the polynomial optimization problem whose objective and constraints are all described by multivariate polynomials. Under some genericity assumptions, %% on these polynomials, we prove that the optimality conditions always hold on…
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. It is desirable to classify the computational complexity of VCSPs depending on a fixed set of allowed cost functions in the input.…
Constraint satisfaction problem (CSP) is a well-studied combinatorial search problem, in which we are asked to find an assignment of values to given variables so as to satisfy all of given constraints. We study a reconfiguration variant of…
The Possible-Winner problem asks, given an election where the voters' preferences over the set of candidates is partially specified, whether a distinguished candidate can become a winner. In this work, we consider the computational…
Reinforcement learning can greatly benefit from the use of options as a way of encoding recurring behaviours and to foster exploration. An important open problem is how can an agent autonomously learn useful options when solving particular…
We consider the problem of minimal correction of the training set to make it consistent with monotonic constraints. This problem arises during analysis of data sets via techniques that require monotone data. We show that this problem is…