Related papers: Parameterized Approximation for Maximum Weight Ind…
We study a natural geometric variant of the classic Knapsack problem called 2D-Knapsack: we are given a set of axis-parallel rectangles and a rectangular bounding box, and the goal is to pack as many of these rectangles inside the box…
Minimum Weight Cycle (MWC) is the problem of finding a simple cycle of minimum weight in a graph $G=(V,E)$. This is a fundamental graph problem with classical sequential algorithms that run in $\tilde{O}(n^3)$ and $\tilde{O}(mn)$ time where…
We give a polynomial-time constant-factor approximation algorithm for maximum independent set for (axis-aligned) rectangles in the plane. Using a polynomial-time algorithm, the best approximation factor previously known is $O(\log\log n)$.…
We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a * b rectangles such that the sum of the weights of the points in P…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
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…
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…
Given a weighted bipartite graph $G = (L, R, E, w)$, the maximum weight matching (MWM) problem seeks to find a matching $M \subseteq E$ that maximizes the total weight $\sum_{e \in M} w(e)$. This paper presents a novel algorithm with a time…
In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…
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…
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…
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…
Process Planning and Scheduling (PPS) is an essential and practical topic but a very intractable problem in manufacturing systems. Many research use iterative methods to solve such problems; however, they cannot achieve satisfactory results…
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,…
Given $n$ weighted points (positive or negative) in $d$ dimensions, what is the axis-aligned box which maximizes the total weight of the points it contains? The best known algorithm for this problem is based on a reduction to a related…
The Maximum Weight Independent Set (MWIS) problem is a well-known NP-hard problem. For graphs $G_1, G_2$, $G_1+G_2$ denotes the disjoint union of $G_1$ and $G_2$, and for a constant $l \ge 2$, $lG$ denotes the disjoint union of $l$ copies…
Ellipsoid fitting is of general interest in machine vision, such as object detection and shape approximation. Most existing approaches rely on the least-squares fitting of quadrics, minimizing the algebraic or geometric distances, with…
Given two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ over the same ground set, the matroid intersection problem is to find the maximum cardinality common independent set. In the weighted version of the problem, the goal is to find a…
In the Min $k$-Cut problem, input is an edge weighted graph $G$ and an integer $k$, and the task is to partition the vertex set into $k$ non-empty sets, such that the total weight of the edges with endpoints in different parts is minimized.…
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…