Related papers: A general class of combinatorial filters that can …
In this work, we consider robust submodular maximization with matroid constraints. We give an efficient bi-criteria approximation algorithm that outputs a small family of feasible sets whose union has (nearly) optimal objective value. This…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…
We present a definition of the class NP in combinatorial context as the set of languages of structures defined by finitely many forbidden lifted substructures. We apply this to special syntactically defined subclasses and show how they…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
Budget Minimization is a scheduling problem with precedence constraints, i.e., a scheduling problem on a partially ordered set of jobs $(N, \unlhd)$. A job $j \in N$ is available for scheduling, if all jobs $i \in N$ with $i \unlhd j$ are…
We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version,…
In this paper we consider two problems concerning string factorisation. Specifically given a string $w$ and an integer $k$ find a factorisation of $w$ where each factor has length bounded by $k$ and has the minimum (the FmD problem) or the…
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…
The problem of approximating a dense matrix by a product of sparse factors is a fundamental problem for many signal processing and machine learning tasks. It can be decomposed into two subproblems: finding the position of the non-zero…
In this paper, we consider the optimal design of networked estimators to minimize the communication/measurement cost under the networked observability constraint. This problem is known as the minimum-cost networked estimation problem, which…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…
For a graph (undirected, directed, or mixed), a cycle-factor is a collection of vertex-disjoint cycles covering the entire vertex set. Cycle-factors subject to parity constraints arise naturally in the study of structural graph theory and…
The Minimum Dominating Set (MDS) problem is a well-established combinatorial optimization problem with numerous real-world applications. Its NP-hard nature makes it increasingly difficult to obtain exact solutions as the graph size grows.…
Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such problem is maximum clique which -- under standard assumptions in complexity theory -- cannot be solved in…
The exact matching problem is a constrained variant of the maximum matching problem: given a graph with each edge having a weight $0$ or $1$ and an integer $k$, the goal is to find a perfect matching of weight exactly $k$. Mulmuley,…
In this paper, we study an unconventional but practically meaningful reversibility problem of commonly used image filters. We broadly define filters as operations to smooth images or to produce layers via global or local algorithms. And we…
Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to…
In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from exact to approximate solution for a host of such problems. As one (notable)…