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Rook polynomials are a powerful tool in the theory of restricted permutations. It is known that the rook polynomial of any board can be computed recursively, using a cell decomposition technique of Riordan. In this paper, we give a new…
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…
Retrosynthesis, which aims to identify viable synthetic pathways for target molecules by decomposing them into simpler precursors, is often treated as a search problem. However, its complexity arises from multi-branched tree-structured…
In computational metabolic design, it is often necessary to modify the original constraint-based metabolic networks to lead to growth-coupled production, where cell growth forces target metabolite production. However, in genome-scale…
We provide efficient replicable algorithms for the problem of learning large-margin halfspaces. Our results improve upon the algorithms provided by Impagliazzo, Lei, Pitassi, and Sorrell [STOC, 2022]. We design the first…
In this paper, we study a general semi-random version of the planted independent set problem in a model initially proposed by Feige and Kilian, which has a large proportion of adversarial edges. We give a new deterministic algorithm that…
This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
We consider some classical optimization problems in path planning and network transport, and we introduce new auction-based algorithms for their optimal and suboptimal solution. The algorithms are based on mathematical ideas that are…
This paper discusses various types of constraints, difficulties and solutions to overcome the challenges regarding university course allocation problem. A hybrid evolutionary algorithm has been defined combining Local Repair Algorithm and…
We develop an efficient algorithm for weak recovery in a robust version of the stochastic block model. The algorithm matches the statistical guarantees of the best known algorithms for the vanilla version of the stochastic block model. In…
Deep graph generative modeling has proven capable of learning the distribution of complex, multi-scale structures characterizing real-world graphs. However, one of the main limitations of existing methods is their large output space, which…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written…
In this paper, we discuss an efficient algorithm for computing the growth distance between two compact convex sets with representable support functions. The growth distance between two sets is the minimum scaling factor such that the sets…
One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformu-lation of the problem of interest and solving the resulting problem…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
{\em Reoptimization} is a setting in which we are given an (near) optimal solution of a problem instance and a local modification that slightly changes the instance. The main goal is that of finding an (near) optimal solution of the…
We investigate the distributed multi-agent sharing optimization problem in a directed graph, with a composite objective function consisting of a smooth function plus a convex (possibly non-smooth) function shared by all agents. While…
In this work, we propose a (linearized) Alternating Direction Method-of-Multipliers (ADMM) algorithm for minimizing a convex function subject to a nonconvex constraint. We focus on the special case where such constraint arises from the…