Related papers: Efficient edge-skeleton computation for polytopes …
We consider a version of geometric programming problem consisting in minimizing a function given by the maximum of finitely many log-Laplace transforms of discrete nonnegative measures on a Euclidean space. Under a coerciveness assumption,…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
Tightness is a generalisation of the notion of convexity: a space is tight if and only if it is "as convex as possible", given its topological constraints. For a simplicial complex, deciding tightness has a straightforward exponential time…
Motivated by the problem of enumerating all tree decompositions of a graph, we consider in this article the problem of listing all the minimal chordal completions of a graph. In \cite{carmeli2020} (\textsc{Pods 2017}) Carmeli \emph{et al.}…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
Electric vehicles with multiple motors provide a flexibility in meeting the driver torque demand, which calls for minimizing the battery energy consumption through torque allocation. In this paper, we present an approach to this problem…
We introduce the concept of an obstacle skeleton which is a set of line segments inside a polygonal obstacle $\omega$ that can be used in place of $\omega$ when performing intersection tests for obstacle-avoiding network problems in the…
This paper provides an alternate characterization of type-two polynomial-time computability, with the goal of making second-order complexity theory more approachable. We rely on the usual oracle machines to model programs with subroutine…
We study the fundamental problem of polytope membership aiming at large convex polytopes, i.e. in high dimension and with many facets, given as an intersection of halfspaces. Standard data-structures as well as brute force methods cannot…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
This papers studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs). It presents a new framework using discrete ODEs as a central tool for computation and provides several implicit characterizations…
This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…
The mixed volume counts the roots of generic sparse polynomial systems. Mixed cells are used to provide starting systems for homotopy algorithms that can find all those roots, and track no unnecessary path. Up to now, algorithms for that…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimality. This setting generalizes many…
We report on the implementation of an algorithm for computing the set of all regular triangulations of finitely many points in Euclidean space. This algorithm, which we call down-flip reverse search, can be restricted, e.g., to computing…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…