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The Maximum Weight Independent Set of Polygons problem is a fundamental problem in computational geometry. Given a set of weighted polygons in the 2-dimensional plane, the goal is to find a set of pairwise non-overlapping polygons with…
The Maximum Weight Independent Set (MWIS) Problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. Being one of the most investigated and most important problems on graphs, it is well…
Computing maximum weight independent sets in graphs is an important NP-hard optimization problem. The problem is particularly difficult to solve in large graphs for which data reduction techniques do not work well. To be more precise,…
The Maximum Weight Independent Set (MWIS) problem, as well as its related problems such as Minimum Weight Vertex Cover, are fundamental NP-hard problems with numerous practical applications. Due to their computational complexity, a variety…
We design new deterministic CONGEST approximation algorithms for \emph{maximum weight independent set (MWIS)} in \emph{sparse graphs}. As our main results, we obtain new $\Delta(1+\epsilon)$-approximation algorithms as well as algorithms…
A powerful technique for solving combinatorial optimization problems is to reduce the search space without compromising the solution quality by exploring intrinsic mathematical properties of the problems. For the maximum weight independent…
Given an undirected node-weighted graph, the Maximum-Weight Connected Subgraph problem (MWCS) is to identify a subset of nodes of maximalsum of weights that induce a connected subgraph. MWCS is closely related to the well-studied Prize…
Maximum Independent Set (MIS for short) is in general graphs the paradigmatic $W[1]$-hard problem. In stark contrast, polynomial-time algorithms are known when the inputs are restricted to structured graph classes such as, for instance,…
We address the realization of Maximum Weighted Independent Set (MWIS) and quantum Maximum Independent Set (MIS) problems under Pasqal's neutral-atom QPU constraints: limited qubit number, bounds on {\Omega} and {\Delta}, sequence duration,…
A hole in a graph is an induced cycle of length at least $4$, and an antihole is the complement of an induced cycle of length at least $4$. A hole or antihole is long if its length is at least $5$. For an integer $k$, the $k$-prism is the…
In the Maximum Independent Set problem we are asked to find a set of pairwise nonadjacent vertices in a given graph with the maximum possible cardinality. In general graphs, this classical problem is known to be NP-hard and hard to…
We consider the classic budgeted maximum weight independent set (BMWIS) problem. The input is a graph $G = (V,E)$, a weight function $w:V \rightarrow \mathbb{R}_{\geq 0}$, a cost function $c:V \rightarrow \mathbb{R}_{\geq 0}$, and a budget…
The Maximum Weight Independent Set Problem (WIS) is a well-known NP-hard problem. A popular way to study WIS is to detect graph classes for which WIS can be solved in polynomial time, with particular reference to hereditary graph classes,…
In the Maximum Weight Independent Set of Rectangles problem (MWISR) we are given a weighted set of $n$ axis-parallel rectangles in the plane. The task is to find a subset of pairwise non-overlapping rectangles with the maximum possible…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of…
Given a vertex-weighted connected graph $G = (V, E)$, the maximum weight internal spanning tree (MwIST for short) problem asks for a spanning tree $T$ of $G$ such that the total weight of the internal vertices in $T$ is maximized. The…
The Maximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. The complexity of the MWIS problem for $P_6$-free graphs is unknown. In this note, we…
In the Maximum Weight Independent Set of Rectangles (MWISR) problem we are given a set of n axis-parallel rectangles in the 2D-plane, and the goal is to select a maximum weight subset of pairwise non-overlapping rectangles. Due to many…
The Partitioning Min-Max Weighted Matching (PMMWM) problem, being a practical NP-hard problem, integrates the task of partitioning the vertices of a bipartite graph into disjoint sets of limited size with the classical Maximum-Weight…