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We investigate the practical aspects of computing the necessary and possible winners in elections over incomplete voter preferences. In the case of the necessary winners, we show how to implement and accelerate the polynomial-time algorithm…
We study the general integer programming problem where the number of variables $n$ is a variable part of the input. We consider two natural parameters of the constraint matrix $A$: its numeric measure $a$ and its sparsity measure $d$. We…
Reconciliation methods aim at recovering macro evolutionary events and at localizing them in the species history, by observing discrepancies between gene family trees and species trees. In this article we introduce an Integer Linear…
The recently introduced polynomial time integration framework proposes a novel way to construct time integrators for solving systems of first-order ordinary differential equation by using interpolating polynomials in the complex time plane.…
We investigate the relationship between several enumeration complexity classes and focus in particular on problems having enumeration algorithms with incremental and polynomial delay (IncP and DelayP respectively). We show that, for some…
In this paper, we develop a simple and fast online algorithm for solving a class of binary integer linear programs (LPs) arisen in general resource allocation problem. The algorithm requires only one single pass through the input data and…
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
This paper studies generalized semi-infinite programs (GSIPs) given by polynomials. We propose a hierarchy of polynomial optimization relaxations to solve them. They are based on Lagrange multiplier expressions and polynomial extensions.…
In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…
Given a set of integers, one can easily construct the set of their pairwise distances. We consider the inverse problem: given a set of pairwise distances, find the integer set which realizes the pairwise distance set. This problem arises in…
Round robin tournaments are omnipresent in sport competitions and beyond. We propose two new integer programming formulations for scheduling a round robin tournament, one of which we call the matching formulation. We analytically compare…
We give a deterministic, polynomial-time algorithm for approximately counting the number of {0,1}-solutions to any instance of the knapsack problem. On an instance of length n with total weight W and accuracy parameter eps, our algorithm…
This paper investigates several cost-sparsity induced optimal input selection problems for structured systems. Given are an autonomous system and a prescribed set of input links, where each input link has a non-negative cost. The problems…
Positive semidefinite programs are an important subclass of semidefinite programs in which all matrices involved in the specification of the problem are positive semidefinite and all scalars involved are non-negative. We present a parallel…
This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we…
Solving linear systems and quadratic programming (QP) problems are both ubiquitous tasks in the engineering and computing fields. Direct methods for solving systems, such as Cholesky, LU, and QR factorizations, exhibit data-independent time…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…
This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are…
Interval-valued computing is a relatively new computing paradigm. It uses finitely many interval segments over the unit interval in a computation as data structure. The satisfiability of Quantified Boolean formulae and other hard problems,…