Related papers: Decomposing Multiparameter Persistence Modules
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
This paper considers the multi-parametric linear complementarity problem (pLCP) with sufficient matrices. The main result is an algorithm to find a polyhedral decomposition of the set of feasible parameters and to construct a piecewise…
Max-norm regularizer has been extensively studied in the last decade as it promotes an effective low-rank estimation for the underlying data. However, such max-norm regularized problems are typically formulated and solved in a batch manner,…
We show that computing the interleaving distance between two multi-graded persistence modules is NP-hard. More precisely, we show that deciding whether two modules are $1$-interleaved is NP-complete, already for bigraded, interval…
A multi-modal multi-objective optimization problem is a special kind of multi-objective optimization problem with multiple Pareto subsets. In this paper, we propose an efficient multi-modal multi-objective optimization algorithm based on…
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…
In this paper, we consider the problem of estimating parameters of a linear regression model. Using a hybrid systems framework, a hybrid algorithm is proposed allowing the estimate to converge to the exact value of the unknown parameters in…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
New contributions in the field of iterative optimisation heuristics are often made in an iterative manner. Novel algorithmic ideas are not proposed in isolation, but usually as an extension of a preexisting algorithm. Although these…
We present a row reduction algorithm to compute the barcode decomposition of persistence modules. This algorithm dualises the standard persistence one and clarifies the symmetry between clear and compress optimisations.
Reactive synthesis is the task of automatically deriving a correct implementation from a specification. It is a promising technique for the development of verified programs and hardware. Despite recent advances in terms of algorithms and…
We study the influence of a graph parameter called modular-width on the time complexity for optimally solving well-known polynomial problems such as Maximum Matching, Triangle Counting, and Maximum $s$-$t$ Vertex-Capacitated Flow. The…
Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…
We show that a persistence module (for a totally ordered indexing set) consisting of finite-dimensional vector spaces is a direct sum of interval modules. The result extends to persistence modules with the descending chain condition on…
This paper introduces the inverse modeling constrained multi-objective evolutionary algorithm based on decomposition (IM-C-MOEA/D) for addressing constrained real-world optimization problems. Our research builds upon the advancements made…
Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…
We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…