Related papers: Parameterized Matroid-Constrained Maximum Coverage
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
In this paper, we study the minimum dominating set (MDS) problem and the minimum total dominating set MTDS) problem which have many applications in real world. We propose a new idea to compute approximate MDS and MTDS. Next, we give an…
For numerous graph problems in the realm of parameterized algorithms, using the size of a smallest deletion set (called a modulator) into well-understood graph families as parameterization has led to a long and successful line of research.…
We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…
We consider the synthesis problem of Compressed Sensing - given s and an MXn matrix A, extract from it an mXn submatrix A', certified to be s-good, with m as small as possible. Starting from the verifiable sufficient conditions of…
We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased…
In the maximum satisfiability problem (MAX-SAT) we are given a propositional formula in conjunctive normal form and have to find an assignment that satisfies as many clauses as possible. We study the parallel parameterized complexity of…
Maximizing a submodular function is a fundamental task in machine learning and in this paper we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary of the…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
In an instance of the minimum eigenvalue problem, we are given a collection of $n$ vectors $v_1,\ldots, v_n \subset {\mathbb{R}^d}$, and the goal is to pick a subset $B\subseteq [n]$ of given vectors to maximize the minimum eigenvalue of…
In the maximum coverage problem, we are given subsets $T_1, \ldots, T_m$ of a universe $[n]$ along with an integer $k$ and the objective is to find a subset $S \subseteq [m]$ of size $k$ that maximizes $C(S) := \Big|\bigcup_{i \in S}…
We study the problem of maximizing a monotone submodular function subject to a matroid constraint, and present for it a deterministic non-oblivious local search algorithm that has an approximation guarantee of $1 - 1/e - \varepsilon$ (for…
Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements…
The Minimum Vertex Cover problem, a classical NP-complete problem, presents significant challenges for exact solution on large graphs. Fixed-Parameter Tractability (FPT) offers a powerful paradigm to address such problems by exploiting a…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
A Fixed-Parameter Tractable (\FPT) $\rho$-approximation algorithm for a minimization (resp. maximization) parameterized problem $P$ is an FPT algorithm that, given an instance $(x, k)\in P$ computes a solution of cost at most $k \cdot…
A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…
The $k$-ExactCover problem is a parameterized version of the ExactCover problem, in which we are given a universe $U$, a collection $S$ of subsets of $U$, and an integer $k$, and the task is to determine whether $U$ can be partitioned into…
We study the classic NP-Hard problem of finding the maximum $k$-set coverage in the data stream model: given a set system of $m$ sets that are subsets of a universe $\{1,\ldots,n \}$, find the $k$ sets that cover the most number of distinct…
We consider the problem of maximizing the multilinear extension of a submodular function subject a single matroid constraint or multiple packing constraints with a small number of adaptive rounds of evaluation queries. We obtain the first…