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Graph Optimization

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lightbulbAbout this topic
Graph optimization is a field of study within computer science and mathematics that focuses on finding the most efficient solutions to problems represented as graphs. It involves optimizing various parameters, such as path lengths, network flows, or resource allocations, to achieve desired outcomes while adhering to specific constraints.
lightbulbAbout this topic
Graph optimization is a field of study within computer science and mathematics that focuses on finding the most efficient solutions to problems represented as graphs. It involves optimizing various parameters, such as path lengths, network flows, or resource allocations, to achieve desired outcomes while adhering to specific constraints.

Key research themes

1. How can graph embeddings and graph neural networks be used to solve combinatorial optimization problems on graphs?

This research area focuses on leveraging graph representation learning, particularly graph embeddings and graph neural networks (GNNs), to effectively solve combinatorial optimization (CO) problems on graphs, which are typically NP-hard. Researchers investigate methods that encode graph structures into low-dimensional vectors suitable for machine learning models, enabling approximate or heuristic solutions that adapt across different CO tasks. This approach offers advantages over classical heuristics by automating feature extraction, adapting to families of problems, and potentially achieving better empirical performance.

Key finding: Provides a comprehensive survey classifying graph embedding methods used for solving CO problems into graph preprocessing and machine learning model stages. It distinguishes between graph embedding methods and end-to-end... Read more
Key finding: Develops a framework employing graph convolutional networks (GCNs) and graph isomorphism networks for decision versions of CO problems tied to vertex counts (minimum vertex cover, maximum clique, minimum dominating set, graph... Read more
Key finding: Introduces NeuLay, a method using GNNs to accelerate force-directed layout algorithms for large networks achieving 10 to 100 times speedup. Analyzes that GNN speedup relates to the eigenspectrum of the adjacency matrix,... Read more

2. What are efficient algorithms and approximation techniques for graph connectivity augmentation and shortest path problems in planar and semidirected graphs?

This theme explores algorithmic and complexity results for enhancing connectivity in planar straight-line graphs (PSLGs) while minimizing added edge length and computing shortest paths in semidirected graphs that model networks with both directed and undirected edges. This includes polynomial-time solutions where possible, hardness results when input graphs are disconnected, and approximation strategies balancing solution quality and computational feasibility. Applications target wireless networks and transportation graphs, addressing connectivity robustness and route optimization.

Key finding: Proves every connected PSLG can be augmented to 2-connectivity by adding edges with total length at most twice the original graph's length, and that an optimal augmentation can be computed in O(|V|^4) time. Establishes... Read more
Key finding: Develops a method applying Floyd-Warshall algorithm to semidirected graphs (combining directed and undirected edges) by transforming undirected edges into bidirectional pairs, enabling shortest path computation in hybrid... Read more
Key finding: Presents deterministic algorithms for all-pairs shortest path approximation offering additive and multiplicative guarantees with improved running times over previous methods. Also introduces near 3/2-approximation... Read more

3. How can evolutionary and heuristic optimization methods enhance geometric graph layouts, especially for weighted graphs with constraints?

Research in this area investigates using genetic algorithms (GAs) and other heuristics to generate graph layouts where geometric placement of vertices respects edge weights and desired shape constraints. This includes improving layouts of weighted graphs to approximate edge lengths accurately while achieving aesthetic and spatial properties. The methodology extends to complex and diverse applications such as circuit design and visualization, combining physical analogies (e.g., springs) with evolutionary search to find consistent and optimized spatial representations.

Key finding: Introduces real-coded genetic algorithms to produce graph layouts for weighted graphs that maintain edge length consistency and can enforce particular geometric shapes. Demonstrates that GA-based approaches outperform... Read more
Key finding: Proposes a tabu search method for automated graph layout optimizing multiple criteria such as edge lengths, smoothness and symmetry of curves, specifically applied to Euler diagrams as graphs with closed curves. Shows this... Read more
Key finding: Presents Telemaco, a flexible tool leveraging language engineering to optimize graph-based models' layouts across diverse formalisms via genetic algorithms targeting customizable metrics. Demonstrates hierarchy-based... Read more

All papers in Graph Optimization

Wireless Sensors Networks are widely used to monitor the areas. In many WSN applications it is important to achieve a good coverage of the observed area while the energetic efficiency and the lifetime of the network are high. The task of... more
Abstract. The paper proposes a XOR-based network coded cooperation protocol for the uplink transmission of relay assisted cellular networks and an algorithm for selection and assignment of the relay nodes. The performances of the... more
Non-functional properties evaluation in Service Oriented Architecture (SOA) is still mostly an open challenge. Although this is a problem that has been already partially explored with some success, there is lack of consolidated results... more
Human analysis in images and video is a hard problem due to the large variation in human pose, clothing, camera viewpoints , lighting and other factors. While the explicit modeling of this variability is difficult, the huge amount of... more
System modeling is one of the important tasks to be solved during software development. As more complex software systems become as higher requirements are defined for demonstrative presentation of the system to be developed. To solve this... more
The extended Kalman filter (EKF) is a widely used algorithm for nonlinear estimation of Inertial Navigation Systems (INS) and the Global Position System (GPS) integration. However, EKF has several limitations, such as linearization... more
Multibody simulations are already used in many industries to speed up the development of new products. However, improvements in multibody formulations and the continuous increase of computational power open new fields of applications for... more
Novel Adaptive Unscented Kalman Filter (NAUKF) has been developed and applied to fuse the outputs of strap-down IMU, the measurements of GPS satellites (pseudo-range and Doppler), strap-down magnetometer and a barometric altimeter, using... more
In this paper a brief review on the observability and estimability analysis of GPS/INS is presented. There have been various analysis results on the observability of INS errors. However different INS error dynamics models and reference... more
In the last years some infrastructures and frameworks have been proposed to enable the compositional development of multiformalism models. This effort requires proper techniques and tools to guarantee generality and flexibility when... more
4D or dynamic imaging of the thorax has many potential applications [1, 2]. CT and MRI offer sufficient speed to acquire motion information via 4D imaging. However they have different constraints and requirements. For both modalities both... more
An accurate orientation is crucial to a satisfactory position in pedestrian navigation. The orientation estimation, however, is greatly affected by errors like the biases of gyroscopes. In order to minimize the error in the orientation,... more
Cooperative approaches are becoming of great interest in automotive research. One of the most important ITS applications is cooperative localization. In this paper, the concept of a dynamic base station DGPS (DDGPS) and its application in... more
This work illustrates an educational project flow of an electronic system. This system is developed to support applications in which there are the need to measure motion parameters and transmit them to a remote unit for real-time... more
In this paper we present an analysis of the positioning uncertainty increase rate for a group of mobile robots. The simplified version for a group of N robots moving along one dimension is considered. The one dimension restriction permits... more
The six degrees-of-freedom Stewart platform, or hexapod, is in widespread use in the flight simulation industry for the generation of motion cues that are representative of those experienced in actual flight. For closed-loop control of... more
In this paper, new attitude determination algorithms using pseudolite signal phase measurements are developed and presented with realistic simulations. Pseudolite signals are used to replace GPS signals which are often not available due... more
Measurement and estimation of motion variables is an important feature for autonomous navigation. Since the not-so-distant past, global positioning systems (GPS) and GPS-aided inertial navigation systems (INS) have been the main... more
This paper presents a methodology and its software implementation for the performance evaluation of low-cost accelerometer and magnetometer sensors for use in geomatics applications. A known mathematical calibration model has been... more
Magnetometers are sensors that can sense the earth magnetic field from which heading can be determined. Gyroscopes can provide the angular rate from which the heading can be calculated, they can be available in low-cost and light weight.... more
Using absolute navigation systems (such as global navigation satellite systems) has proved to be insufficient for indoor navigation or when navigating in urban canyons due to multipath and obstruction. This opened the gate widely for... more
This work illustrates an educational project flow of an electronic system. This system is developed to support applications in which there are the need to measure motion parameters and transmit them to a remote unit for real-time... more
In INS/GPS integration system, Euler angle and quaternion are often used to represent attitude. In a tightly-coupled system, both the Euler angle-based and quaternion-based approaches have nonlinear system propagation and observation... more
In this paper, a new algorithm is developed for attitude estimation using Global Positioning System (GPS) signals. The new algorithm is based on a predictive filtering scheme designed for spacecraft without rate measuring devices. The... more
In this paper, new attitude determination algorithms using pseudolite signal phase measurements are developed and presented with realistic simulations. Pseudolite signals are used to replace GPS signals which are often not available due... more
In this paper, new attitude determination algorithms using pseudolite signal phase measurements are developed and presented with realistic simulations. Pseudolite signals are used to replace GPS signals which are often not available due... more
This article considers the application of Divided Difference Filter (DDF) to the orientation estimation, based on a quaternion-error continuous-discrete time model. DDF is a nonlinear estimator that in contrast to Taylor's expansion of... more
Development of micro-electro mechanical system (MEMS) and micro-electro optical mechanical system (MEOMS) inertial sensors has been driven by the need for inexpensive sensing solutions in military and commercial applications. In addition... more
Contemporary surveying in measurement-whiledrilling (MWD) processes incorporates measurements from three-axes accelerometers and magnetometers. Unfortunately, magnetometer-related problems limit the navigation performance of this... more
by Moriba Jah and 
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This paper presents a new method to determine the mass of an inactive space object from the fusion of photometric and astrometric data. Typically, the effect of solar radiation pressure is used to determine area-to-mass ratio for space... more
This work illustrates an educational project flow of an electronic system. This system is developed to support applications in which there are the need to measure motion parameters and transmit them to a remote unit for real-time... more
Nonlinear system state estimation is a very common task. For non-linear system doesn't exist an optimal Bayesan estimator and so is necessary to use approximate solutions. The most common and used estimator in this case is the Extended... more
Many modern fusion architectures are designed to process and fuse data in networked systems. Alongside the advantages, such as scalability and robustness, distributed fusion techniques particularly have to tackle the problem of... more
Many modern fusion architectures are designed to process and fuse data in networked systems. Alongside the advantages, such as scalability and robustness, distributed fusion techniques particularly have to tackle the problem of... more
A novel concept for determining the full state of a projectile near the muzzle of the gun has been investigated. The methodology relies on the gun system inducing a known spatially varying magnetic field. Using readings from a cluster of... more
When multiple correlated data channels are simultaneously processed, multichannel-autoregressive (M-AR) processes may be combined with optimal filtering such as Kalman or H ∞ for prediction or estimation from noisy observations. However,... more
This work illustrates an educational project flow of an electronic system. This system is developed to support applications in which there are the need to measure motion parameters and transmit them to a remote unit for real-time... more
ABSTRACT Starting with the birth of Web 2.0, the quantity of data managed by large-scale web services has grown exponentially, posing new challenges and infrastructure requirements. This has led to new programming paradigms and... more
This work illustrates an educational project flow of an electronic system. This system is developed to support applications in which there are the need to measure motion parameters and transmit them to a remote unit for real-time... more
This paper considers the question of using a nonlinear complementary filter for attitude estimation of fixed-wing unmanned aerial vehicle (UAV) given only measurements from a low-cost inertial measurement unit. A nonlinear complementary... more
Big Data applications represent an emerging field, which have proved to be crucial in business intelligence and in massive data management. Big Data promises to be the next big thing in the development of strategical computer... more
Progress of ICT is shifting the paradigm of systems organization towards a distributed approach, in which physical deployment of components influences the evaluation of systems properties. This contribution can be considered as a problem... more
This paper deals with the problem of cooperative tracking using large groups of sensor nodes. A Kalman filter-like estimator is implemented and tested for this purpose. The focus of this paper is to examine the effect of the sensor... more
A typical Inertial Navigation System (INS) fuses acceleration and angular rate readings with aiding measurements obtained by GPS and a compass. Here we present a robust state estimation framework based on the Extended Kalman Filter (EKF)... more
The solving of Vehicle Routing Problem (VRP) is a difficult combinatorial optimisation task. The interactive programming environment Venera and programming language Mars, oriented to ease the build up of constructive heuristic algorithms... more
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