Related papers: Parameterized Inapproximability of Exact Cover and…

Selection of a group of representatives satisfying certain fairness constraints, is a commonly occurring scenario. Motivated by this, we initiate a systematic algorithmic study of a \emph{fair} version of \textsc{Hitting Set}. In the…

In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…

We suggest a new optical solution for solving the YES/NO version of the Exact Cover problem by using the massive parallelism of light. The idea is to build an optical device which can generate all possible solutions of the problem and then…

In the Multiple Allocation $k$-Hub Center (MA$k$HC), we are given a connected edge-weighted graph $G$, sets of clients $\mathcal{C}$ and hub locations $\mathcal{H}$, where ${V(G) = \mathcal{C} \cup \mathcal{H}}$, a set of demands…

For a positive integer $k \ge 1$, a $k$-star ($k^+$-star, $k^-$-star, respectively) is a connected graph containing a degree-$\ell$ vertex and $\ell$ degree-$1$ vertices, where $\ell = k$ ($\ell \ge k$, $1 \le \ell \le k$, respectively).…

We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]-hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This problem is…

Bin Packing with $k$ bins is a fundamental optimisation problem in which we are given a set of $n$ integers and a capacity $T$ and the goal is to partition the set into $k$ subsets, each of total sum at most $T$. Bin Packing is NP-hard…

We study the Steiner Tree problem on the intersection graph of most natural families of geometric objects, e.g., disks, squares, polygons, etc. Given a set of $n$ objects in the plane and a subset $T$ of $t$ terminal objects, the task is to…

In the NP-hard \textsc{Group Closeness Centrality Maximization} problem, the input is a graph $G = (V,E)$ and a positive integer $k$, and the task is to find a set $S \subseteq V$ of size $k$ that maximizes the reciprocal of group farness…

We consider the parameterized complexity of the problem of tracking shortest s-t paths in graphs, motivated by applications in security and wireless networks. Given an undirected and unweighted graph with a source s and a destination t,…

We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…

Most optimization problems are notoriously hard. Considerable efforts must be spent in obtaining an optimal solution to certain instances that we encounter in the real world scenarios. Often it turns out that input instances get modified…

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each…

Let $G=(V,E)$ be a simple undirected graph. The open neighbourhood of a vertex $v$ in $G$ is defined as $N_G(v)=\{u\in V~|~ uv\in E\}$; whereas the closed neighbourhood is defined as $N_G[v]= N_G(v)\cup \{v\}$. For an integer $k$, a subset…

In this paper we initiate a systematic study of exact algorithms for well-known clustering problems, namely $k$-Median and $k$-Means. In $k$-Median, the input consists of a set $X$ of $n$ points belonging to a metric space, and the task is…

We present algorithms for the Max-Cover and Max-Unique-Cover problems in the data stream model. The input to both problems are $m$ subsets of a universe of size $n$ and a value $k\in [m]$. In Max-Cover, the problem is to find a collection…

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…

In the $k$-cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. The current best algorithms are an…

An arithmetic progression is a sequence of integers in which the difference between any two consecutive elements is the same. We investigate the parameterized complexity of two problems related to arithmetic progressions, called Cover by…

Let $H$ be a fixed undirected graph on $k$ vertices. The $H$-hitting set problem asks for deleting a minimum number of vertices from a given graph $G$ in such a way that the resulting graph has no copies of $H$ as a subgraph. This problem…