Related papers: On an optimal constraint aggregation method for in…
We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set…
We present an optimization problem emerging from optimal control theory and situated at the intersection of fractional programming and linear max-min programming on polytopes. A na\"ive solution would require solving four nested, possibly…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
This paper focuses on the study of a mathematical program with equilibrium constraints, where the objective and the constraint functions are all polynomials. We present a method for finding its global minimizers and global minimum using a…
Generally, multi-objective optimisation problems are solved exactly or approximated by solving a series of scalarisations, for example by dichotomic search. In this paper, we take a different approach and attempt to compute the set of all…
A syntactical proof is given that all functions definable in a certain affine linear typed lambda-calculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be…
The famous pancake theorem states that for every finite set $X$ in the plane, there exist two orthogonal lines that divide $X$ into four equal parts. We propose an algorithm whose running time is linear in the number of points in $X$ and…
Data aggregation is a fundamental primitive in distributed computing wherein a network computes a function of every nodes' input. However, while compute time is non-negligible in modern systems, standard models of distributed computing do…
Multi-homogeneous polynomial systems arise in many applications. We provide bit complexity estimates for solving them which, up to a few extra other factors, are quadratic in the number of solutions and linear in the height of the input…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
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…
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
This paper studies the problem of enumerating all maximal collinear subsets of size at least three in a given set of $n$ points. An algorithm for this problem, besides solving degeneracy testing and the exact fitting problem, can also help…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
Let G = (V, E) be a planar triangulated graph (PTG) having every face triangular. A rectilinear dual or an orthogonal floor plan (OFP) of G is obtained by partitioning a rectangle into \mid V \mid rectilinear regions (modules) where two…
We study the problem of computing robust controllable sets for discrete-time linear systems with additive uncertainty. We propose a tractable and scalable approach to inner- and outer-approximate robust controllable sets using constrained…
We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…
We study systems of polynomial equations in several classes of finitely generated rings and algebras. For each ring $R$ (or algebra) in one of these classes we obtain an interpretation by systems of equations of a ring of integers $O$ of a…
We consider integer and linear programming problems for which the linear constraints exhibit a (recursive) block-structure: The problem decomposes into independent and efficiently solvable sub-problems if a small number of constraints is…
The representation of a dynamic ordered set of $n$ integer keys drawn from a universe of size $m$ is a fundamental data structuring problem. Many solutions to this problem achieve optimal time but take polynomial space, therefore preserving…