Related papers: Boosting Data Reduction for the Maximum Weight Ind…
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…
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…
The maximum independent set problem is a classic optimization problem that has also been studied quite intensively in the distributed setting. While the problem is hard to approximate in general, there are good approximation algorithms…
Motivated by a real-world vehicle routing application, we consider the maximum-weight independent set problem: Given a node-weighted graph, find a set of independent (mutually nonadjacent) nodes whose node-weight sum is maximum. Some of the…
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…
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…
The maximum edge-weight clique problem is to find a clique whose sum of edge-weight is the maximum for a given edge-weighted undirected graph. The problem is NP-hard and some branch-and-bound algorithms have been proposed. In this paper, we…
The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
We revisit the recent polynomial-time algorithm for the MAX WEIGHT INDEPENDENT SET (MWIS) problem in bounded-degree graphs that do not contain a fixed graph whose every component is a subdivided claw as an induced subgraph [Abrishami,…
Akiba and Iwata [TCS, 2016] demonstrated that a branch and reduce (B&R) solver for the vertex cover problem can compete favorably with integer linear programming solvers (e.g., CPLEX). Our research question is are there graph…
In this paper, we consider the task of computing an independent set of maximum weight in a given $d$-claw free graph $G=(V,E)$ equipped with a positive weight function $w:V\rightarrow\mathbb{R}^+$. In doing so, $d\geq 2$ is considered a…
The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in…
The Generalized Independent Set (GIS) problem extends the classical maximum independent set problem by incorporating profits for vertices and penalties for edges. This generalized problem has been identified in diverse applications in…
The problem of finding the maximum-weight, planar subgraph of a finite, simple graph with nonnegative real edge weights is well known in industrial and electrical engineering, systems biology, sociology and finance. As the problem is known…
The (\textsc{Weighted}) \textsc{Subset Feedback Vertex Set} problem is a generalization of the classical \textsc{Feedback Vertex Set} problem and asks for a vertex set of minimum (weighted) size that intersects all cycles containing a…
We revisit recent developments for the Maximum Weight Independent Set problem in graphs excluding a subdivided claw $S_{t,t,t}$ as an induced subgraph [Chudnovsky, Pilipczuk, Pilipczuk, Thomass\'{e}, SODA 2020] and provide a…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
Data augmentation is an effective technique to improve the generalization of deep neural networks. However, previous data augmentation methods usually treat the augmented samples equally without considering their individual impacts on the…
Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find…