Related papers: Maximum weighted independent sets with a budget
The parameterized complexity of problems is often studied with respect to the size of their optimal solutions. However, for a maximization problem, the size of the optimal solution can be very large, rendering algorithms parameterized by it…
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover Problem in which the frequency of every…
The Partitioning Min-Max Weighted Matching (PMMWM) problem is an NP-hard problem that combines the problem of partitioning a group of vertices of a bipartite graph into disjoint subsets with limited size and the classical Min-Max Weighted…
We present the problem of finding a maximal independent set (MIS) (named as \emph{MIS Filling problem}) of an arbitrary connected graph having $n$ vertices with luminous myopic mobile robots. The robots enter the graph one after another…
In an undirected graph $G=(V,E)$, we say $(A,B)$ is a pair of perfectly matched sets if $A$ and $B$ are disjoint subsets of $V$ and every vertex in $A$ (resp. $B$) has exactly one neighbor in $B$ (resp. $A$). The size of a pair of perfectly…
We present a weighted approach to compute a maximum cardinality matching in an arbitrary bipartite graph. Our main result is a new algorithm that takes as input a weighted bipartite graph $G(A\cup B,E)$ with edge weights of $0$ or $1$. Let…
A maximal independent set is an independent set that is not a subset of any other independent set. It is also the key problem of mathematics, computer science, and other fields. A counting problem is a type of computational problem that…
We introduce and study a new optimization problem on digraphs, termed Maximum Weighted Digraph Partition (MWDP) problem. We prove three complexity dichotomies for MWDP: on arbitrary digraphs, on oriented digraphs, and on symmetric digraphs.…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
In this paper, we study the parameterized complexity and inapproximability of the {\sc Induced Matching} problem in hamiltonian bipartite graphs. We show that, given a hamiltonian cycle in a hamiltonian bipartite graph, the problem is…
We introduce a novel multivariate approach for solving weighted parameterized problems. In our model, given an instance of size $n$ of a minimization (maximization) problem, and a parameter $W \geq 1$, we seek a solution of weight at most…
Mim-width and sim-width are among the most powerful graph width parameters, with sim-width more powerful than mim-width, which is in turn more powerful than clique-width. While several $\mathsf{NP}$-hard graph problems become tractable for…
We propose improved exact and heuristic algorithms for solving the maximum weight clique problem, a well-known problem in graph theory with many applications. Our algorithms interleave successful techniques from related work with novel data…
We investigate the so-called recoverable robust assignment problem on balanced bipartite graphs with $2n$ vertices, a mainstream problem in robust optimization: For two given linear cost functions $c_1$ and $c_2$ on the edges and a given…
We study the complexity of finding the \emph{geodetic number} on subclasses of planar graphs and chordal graphs. A set $S$ of vertices of a graph $G$ is a \emph{geodetic set} if every vertex of $G$ lies in a shortest path between some pair…
We consider the algorithmic problem of finding large \textit{balanced} independent sets in sparse random bipartite graphs, and more generally the problem of finding independent sets with specified proportions of vertices on each side of the…
This paper introduces the \emph{$d$-distance $b$-matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges, an integer $d\in\mathbb{Z}_+$ and a degree bound function…
A graph $G$ is called B$_k$-VPG (resp., B$_k$-EPG), for some constant $k\geq 0$, if it has a string representation on a grid such that each vertex is an orthogonal path with at most $k$ bends and two vertices are adjacent in $G$ if and only…
In this paper we study a maximization version of the classical Feedback Vertex Set (FVS) problem, namely, the Max Min FVS problem, in the realm of parameterized complexity. In this problem, given an undirected graph $G$, a positive integer…
We study polynomial-time approximation algorithms for the Quantum Max-Cut (QMC) problem. Given an edge-weighted graph $G$ on n vertices, the QMC problem is to determine the largest eigenvalue of a particular $2^n \times 2^n$ matrix that…