We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula F, It is -hard to find a CP refutation of F in time polynomial in the length of the shortest such refutation; and unless Gap-Hitting-Set admits a nontrivial algorithm, ...
The cotangent complex of a map of commutative rings is a central object in deformation theory. Since the 1990s, it has been generalized to the homotopical setting of E-infinity-ring spectra in various ways. In this work we first establish, in the context o ...
We consider the problem of solving integer programs of the form min {c^⊺ x : Ax = b, x ∈ ℤ_{⩾ 0}}, where A is a multistage stochastic matrix in the following sense: the primal treedepth of A is bounded by a parameter d, which means that the columns of A ca ...
Schloss Dagstuhl - Leibniz-Zentrum für Informatik2021
We study the admissibility problem in multivariate algebraic systems, such as ac electrical networks, where the power injection is quadratic in the state. The goal of such systems is to ensure that the state stays in some security set (e.g., magnitudes of ...
We study the computations that Bayesian agents undertake when exchanging opinions over a network. The agents act repeatedly on their private information and take myopic actions that maximize their expected utility according to a fully rational posterior be ...
This thesis focuses on designing spectral tools for graph clustering in sublinear time. With the emergence of big data, many traditional polynomial time, and even linear time algorithms have become prohibitively expensive. Processing modern datasets requir ...
The Ring Learning with Errors (RLWE) problem has become one of the most widely used cryptographic assumptions for the construction of modern cryptographic primitives. Most of these solutions make use of power-of-two cyclotomic rings mainly due to its simpl ...
In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...
We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rul ...
