Related papers: A QPTAS for Maximum Weight Independent Set of Poly…
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…
We present an $(1+\varepsilon)$-approximation algorithm with quasi-polynomial running time for computing the maximum weight independent set of polygons out of a given set of polygons in the plane (specifically, the running time is $n^{O(…
Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriously hard both in the…
We consider two optimization problems in planar graphs. In Maximum Weight Independent Set of Objects we are given a graph $G$ and a family $\mathcal{D}$ of objects, each being a connected subgraph of $G$ with a prescribed weight, and the…
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 Weight Independent Set (MWIS) problem on finite undirected graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum weight sum. MWIS is one of the most investigated and most important algorithmic…
Given a graph $G$, a non-negative integer $k$, and a weight function that maps each vertex in $G$ to a positive real number, the \emph{Maximum Weighted Budgeted Independent Set (MWBIS) problem} is about finding a maximum weighted…
The Maximum Weight Independent Set (MWIS) problem on finite undirected graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum weight sum. MWIS is one of the most investigated and most important algorithmic…
We study the maximum weight convex polytope problem, in which the goal is to find a convex polytope maximizing the total weight of enclosed points. Prior to this work, the only known result for this problem was an $O(n^3)$ algorithm for the…
Weighted geometric set-cover problems arise naturally in several geometric and non-geometric settings (e.g. the breakthrough of Bansal-Pruhs (FOCS 2010) reduces a wide class of machine scheduling problems to weighted geometric set-cover).…
$\newcommand{\eps}{\varepsilon}$ We observe that a $(1-\eps)$-approximation algorithm to Independent Set, that works for any induced subgraph of the input graph, can be used, via a polynomial time reduction, to provide a…
In the classic Maximum Weight Independent Set problem we are given a graph $G$ with a nonnegative weight function on vertices, and the goal is to find an independent set in $G$ of maximum possible weight. While the problem is NP-hard in…
In rectangle packing problems we are given the task of placing axis-aligned rectangles in a given plane region, so that they do not overlap with each other. In Maximum Weight Independent Set of Rectangles (MWISR), their position is given…
The Maximum Weighted Independent Set (MWIS) problem, which considers a graph with weights assigned to nodes and seeks to discover the "heaviest" independent set, that is, a set of nodes with maximum total weight so that no two nodes in the…
We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local search algorithm yields a \PTAS. For the weighted case,…
We study a natural extension of the Maximum Weight Independent Set Problem (MWIS), one of the most studied optimization problems in Graph algorithms. We are given a graph $G=(V,E)$, a weight function $w: V \rightarrow \mathbb{R^+}$, a…
The area of parameterized approximation seeks to combine approximation and parameterized algorithms to obtain, e.g., (1+eps)-approximations in f(k,eps)n^{O(1)} time where k is some parameter of the input. We obtain the following results on…
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 study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph $G= (A \cup P, E)$ with weights on the edges in $E$, and with lower and upper quotas on the vertices in $P$. We…
We study the Maximum Independent Set of Rectangles (MISR) problem: given a set of $n$ axis-parallel rectangles, find a largest-cardinality subset of the rectangles, such that no two of them overlap. MISR is a basic geometric optimization…