Related papers: A fixed-parameter tractable algorithm for combinat…
In combinatorial optimization, partial variable assignments are called persistent if they agree with some optimal solution. We propose persistency criteria for the multicut and max-cut problem as well as fast combinatorial routines to…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
The concept of space-bounded computability has become significantly important in handling vast data sets on memory-limited computing devices. To replenish the existing short list of NL-complete problems whose instance sizes are dictated by…
Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in…
Combinatorial optimization is one of the fundamental research fields that has been extensively studied in theoretical computer science and operations research. When developing an algorithm for combinatorial optimization, it is commonly…
This study addresses a distributed optimization with a novel class of coupling of variables, called clique-wise coupling. A clique is a node set of a complete subgraph of an undirected graph. This setup is an extension of pairwise coupled…
We study the computational problem of computing a fair means clustering of discrete vectors, which admits an equivalent formulation as editing a colored matrix into one with few distinct color-balanced rows by changing at most $k$ values.…
An enumeration kernel as defined by Creignou et al. [Theory Comput. Syst. 2017] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a…
This paper investigates, from information theoretic grounds, a learning problem based on the principle that any regularity in a given dataset can be exploited to extract compact features from data, i.e., using fewer bits than needed to…
Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…
Feedback Vertex Set is a classic combinatorial optimization problem that asks for a minimum set of vertices in a given graph whose deletion makes the graph acyclic. From the point of view of parameterized algorithms and fixed-parameter…
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…
The advent of new special-purpose hardware such as FPGA or ASIC-based annealers and quantum processors has shown potential in solving certain families of complex combinatorial optimization problems more efficiently than conventional CPUs.…
In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints.…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…
We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank…
In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a_1,\ldots,a_n} over \Sigma^m, where \Sigma is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median…
A left-corner parsing algorithm with top-down filtering has been reported to show very efficient performance for unification-based systems. However, due to the nontermination of parsing with left-recursive grammars, top-down constraints…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…