Related papers: Finding Diverse Solutions in Combinatorial Problem…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…
Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like…
We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…
In the past few years, several new matching models have been proposed and studied that take into account complex distributional constraints. Relevant lines of work include (1) school choice with diversity constraints where students have…
We consider an assortment optimization problem under the multinomial logit choice model with general covering constraints. In this problem, the seller offers an assortment that should contain a minimum number of products from multiple…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…
The algebraic diversity framework generalizes temporal averaging over multiple observations to algebraic group action on a single observation for second-order statistical estimation. The central open problem in this framework is…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
This paper presents centralized and distributed Alternating Direction Method of Multipliers (ADMM) frameworks for solving large-scale nonconvex optimization problems with binary decision variables subject to spanning tree or rooted…
The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes…
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
This work explores the relationship between solution space and time complexity in the context of the $\textbf{P}$ vs. $\textbf{NP}$ problem, particularly through the lens of the sliding tile puzzle and root finding algorithms. We focus on…
It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a…
We study the efficient learnability of high-dimensional Gaussian mixtures in the outlier-robust setting, where a small constant fraction of the data is adversarially corrupted. We resolve the polynomial learnability of this problem when the…
We give the first polynomial-time algorithms on graphs of bounded maximum induced matching width (mim-width) for problems that are not locally checkable. In particular, we give $n^{\mathcal{O}(w)}$-time algorithms on graphs of mim-width at…
Seriation methods order a set of descriptions given some criterion (e.g., unimodality or minimum distance between similarity scores). Seriation is thus inherently a problem of finding the optimal solution among a set of permutations of…
We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…