相关论文: Maximal Closed Set and Half-Space Separations in F…

In this paper, we study the parameterized complexity of the MaxMin versions of two fundamental separation problems: Maximum Minimal $st$-Separator and Maximum Minimal Odd Cycle Transversal (OCT), both parameterized by the solution size. In…

Optimization problems with constraints in the form of a partial differential equation arise frequently in the process of engineering design. The discretization of PDE-constrained optimization problems results in large-scale linear systems…

Based on the needs of convergence proofs of preconditioned proximal point methods, we introduce notions of partial strong submonotonicity and partial (metric) subregularity of set-valued maps. We study relationships between these two…

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analogue random-field Potts model corresponds to a multi-terminal…

Collective communications are ubiquitous in parallel applications. We present two new algorithms for performing a reduction. The operation associated with our reduction needs to be associative and commutative. The two algorithms are…

We present a generalization of the well known Next-Closure algorithm working on semilattices. We prove the correctness of the algorithm and apply it on the computation of the intents of a formal context.

Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the…

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…

In recent years, finding new satisfiability algorithms for various circuit classes has been a very active line of research. Despite considerable progress, we are still far away from a definite answer on which circuit classes allow fast…

This letter studies the problem of minimizing increasing set functions, or equivalently, maximizing decreasing set functions, over the base of a matroid. This setting has received great interest, since it generalizes several applied…

In this paper, we describe how to get Janet decomposition for a finite set of terms and detect completeness of that set by means of the associated Bar Code. Moreover, we explain an algorithm to find a variable ordering (if it exists) s.t. a…

A fundamental open problem in learning theory is to characterize the best-case teaching dimension $\operatorname{TS}_{\min}$ of a concept class $\mathcal{C}$ with finite VC dimension $d$. Resolving this problem will, in particular, settle…

Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating…

Finding maximum-weight independent sets in graphs is an important NP-hard optimization problem. Given a vertex-weighted graph $G$, the task is to find a subset of pairwise non-adjacent vertices of $G$ with maximum weight. Most recently…

We propose a Greedy strategy to solve the problem of Graph Cut, called GGC. It starts from the state where each data sample is regarded as a cluster and dynamically merges the two clusters which reduces the value of the global objective…

Finding independent sets of maximum size in fixed graphs is well known to be an NP-hard task. Using scaling limits, we characterise the asymptotics of sequential degree-greedy explorations and provide sufficient conditions for this…

Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…

This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…

We develop an experimental algorithm for the exact solving of the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set…

MapReduce has become the de facto standard model for designing distributed algorithms to process big data on a cluster. There has been considerable research on designing efficient MapReduce algorithms for clustering, graph optimization, and…