Related papers: Message-passing for Maximum Weight Independent Set
We study the Maximum Weight Matching (MWM) problem for general graphs through the max-product Belief Propagation (BP) and related Linear Programming (LP). The BP approach provides distributed heuristics for finding the Maximum A Posteriori…
The max-product {belief propagation} (BP) is a popular message-passing heuristic for approximating a maximum-a-posteriori (MAP) assignment in a joint distribution represented by a graphical model (GM). In the past years, it has been shown…
The Maximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. MWIS is known to be $NP$-complete in general, even under various restrictions. Let…
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…
Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely…
While Artificial intelligence (AI), including Generative AI, are effective at generating high-quality traffic data and optimization solutions in intelligent transportation systems (ITSs), these techniques often demand significant training…
Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from…
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,…
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 complexity of classical computational problems in graph classes defined by forbidding induced subgraphs is one of the central topics of algorithmic graph theory. Recently, there has been a growing interest in the complexity of such…
We consider the Maximum Weight Independent Set Problem (MWIS) in $d$-claw free graphs, i.e. 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…
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…
For graphs $G$ and $H$, we say that $G$ is $H$-free if it does not contain $H$ as an induced subgraph. Already in the early 1980s Alekseev observed that if $H$ is connected, then the \textsc{Max Weight Independent Set} problem (MWIS)…
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…
Maximum a posteriori (MAP) inference in discrete-valued Markov random fields is a fundamental problem in machine learning that involves identifying the most likely configuration of random variables given a distribution. Due to the…
Applying the max-product (and belief-propagation) algorithms to loopy graphs is now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there…
A 2-packing set for an undirected, weighted graph G=(V,E,w) is a subset S of the vertices V such that any two vertices are not adjacent and have no common neighbors. The Maximum Weight 2-Packing Set problem that asks for a 2-packing set of…
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…
In this paper, we propose a novel pooling layer for graph neural networks based on maximizing the mutual information between the pooled graph and the input graph. Since the maximum mutual information is difficult to compute, we employ 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…