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Meta-kernelization theorems are general results that provide polynomial kernels for large classes of parameterized problems. The known meta-kernelization theorems, in particular the results of Bodlaender et al. (FOCS'09) and of Fomin et al.…

Data Structures and Algorithms · Computer Science 2013-04-22 Robert Ganian , Friedrich Slivovsky , Stefan Szeider

Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…

Probability · Mathematics 2014-09-09 Andrew Papanicolaou , Konstantinos Spiliopoulos

The maximum cut problem for a quintic del Pezzo surface ${\rm Bl}_{4}(\mathbb{P}^2)$ asks: Among all partitions of the 10 exceptional curves into two disjoint sets, what is the largest possible number of pairwise intersections? In this…

Combinatorics · Mathematics 2012-07-18 Mauricio Junca Mauricio Velasco

We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size.

Optimization and Control · Mathematics 2020-11-12 Amitabh Basu , Michele Conforti , Marco Di Summa , Hongyi Jiang

In this paper, we are concerned with efficiently solving the sequences of regularized linear least squares problems associated with employing Tikhonov-type regularization with regularization operators designed to enforce edge recovery. An…

Numerical Analysis · Mathematics 2023-06-29 Matthias Bolten , Scott P. MacLachlan , Misha E. Kilmer

We establish the pointwise convergence of the iterative Lloyd algorithm, also known as $k$-means algorithm, when the quadratic quantization error of the starting grid (with size $N\ge 2$) is lower than the minimal quantization error with…

Probability · Mathematics 2014-01-03 Gilles Pagès , Jun Yu

Assuming the AND-distillation conjecture, the Pathwidth problem of determining whether a given graph G has pathwidth at most k admits no polynomial kernelization with respect to k. The present work studies the existence of polynomial…

Data Structures and Algorithms · Computer Science 2015-03-20 Hans L. Bodlaender , Bart M. P. Jansen , Stefan Kratsch

Despite the promise that fault-tolerant quantum computers can efficiently solve classically intractable problems, it remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy,…

Quantum Physics · Physics 2024-11-13 Miguel Murça , Duarte Magano , Yasser Omar

We propose a very simple preprocessing algorithm for semidefinite programming. Our algorithm inspects the constraints of the problem, deletes redundant rows and columns in the constraints, and reduces the size of the variable matrix. It…

Optimization and Control · Mathematics 2016-08-09 Preston Faulk , Gabor Pataki , Quoc Tran-Dinh

Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial…

Computational Complexity · Computer Science 2015-07-14 Michael Etscheid , Stefan Kratsch , Matthias Mnich , Heiko Röglin

We extend kernelized matrix factorization with a fully Bayesian treatment and with an ability to work with multiple side information sources expressed as different kernels. Kernel functions have been introduced to matrix factorization to…

Machine Learning · Statistics 2013-05-10 Mehmet Gönen , Suleiman A. Khan , Samuel Kaski

Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…

Computational Complexity · Computer Science 2017-08-28 Henning Fernau , Till Fluschnik , Danny Hermelin , Andreas Krebs , Hendrik Molter , Rolf Niedermeier

Parameterized analysis provides powerful mechanisms for obtaining fine-grained insights into different types of algorithms. In this work, we combine this field with evolutionary algorithms and provide parameterized complexity analysis of…

Combinatorics · Mathematics 2023-03-22 Samuel Baguley , Tobias Friedrich , Aneta Neumann , Frank Neumann , Marcus Pappik , Ziena Zeif

The computational and storage complexity of kernel machines presents the primary barrier to their scaling to large, modern, datasets. A common way to tackle the scalability issue is to use the conjugate gradient algorithm, which relieves…

Machine Learning · Statistics 2016-05-26 Kurt Cutajar , Michael A. Osborne , John P. Cunningham , Maurizio Filippone

This article presents a method for solving large-scale linear inverse problems regular- ized with a nonlinear, edge-preserving penalty term such as the total variation or Perona-Malik. In the proposed scheme, the nonlinearity is handled…

Numerical Analysis · Mathematics 2013-09-02 Simon R. Arridge , Marta M. Betcke , Lauri Harhanen

The Odd Cycle Transversal problem (OCT) asks whether a given graph can be made bipartite by deleting at most $k$ of its vertices. In a breakthrough result Reed, Smith, and Vetta (Operations Research Letters, 2004) gave a $\BigOh(4^kkmn)$…

Data Structures and Algorithms · Computer Science 2015-03-19 Stefan Kratsch , Magnus Wahlström

We consider a bi-criteria generalization of the pathwidth problem, where, for given integers $k,l$ and a graph $G$, we ask whether there exists a path decomposition $\cP$ of $G$ such that the width of $\cP$ is at most $k$ and the number of…

Data Structures and Algorithms · Computer Science 2021-03-05 Dariusz Dereniowski , Wieslaw Kubiak , Yori Zwols

Due to the COVID-19 pandemic, there is an increasing demand for portable CT machines worldwide in order to diagnose patients in a variety of settings. This has led to a need for CT image reconstruction algorithms that can produce high…

Numerical Analysis · Mathematics 2025-12-10 Mai Phuong Pham Huynh , Manuel Santana , Ana Castillo

Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…

Optimization and Control · Mathematics 2023-11-17 Daniel Porumbel

We introduce a new framework for the analysis of preprocessing routines for parameterized counting problems. Existing frameworks that encapsulate parameterized counting problems permit the usage of exponential (rather than polynomial) time…

Data Structures and Algorithms · Computer Science 2023-08-07 Daniel Lokshtanov , Pranabendu Misra , Saket Saurabh , Meirav Zehavi