Distance-regular graphs

This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A., Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page

Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010

Peer Reviewe

Properties of Opportunistic Routing in the Argo Underwater Sensor Network

Underwater Acoustic Sensor Networks (UASN) represent a novel technology for monitoring the underwater environment. However, underwater communications through acoustic modems rise several networking challenges for UASN. In our work, we study the possibility to use Opportunistic Routing to overcome the limitations posed by the acoustic communication channel in UASN. For our study, we used a real-world mobility dataset obtained from the Argo project. In particular, we used data produced by the 51 free-drifting floats deployed on the Mediterranean Sea for approximately one year to build a fictitious network called the Argo Underwater Sensor Network. Then we analyse some important properties of the underwater network we built. Specifically, we analyse the network degree, density, properties of the connected components, properties of contact and inter-contact time while varying the connectivity degree of the whole network. We then consider four known opportunistic routing algorithms, namely Epidemic, PROPHET, SprayAndWait and Direct Delivery, with the goal of measuring their performance in real conditions for UASN. We finally discuss the opportunities arising from the adoption of opportunistic routing in UASN showing that, even in a very sparse and strongly disconnected network, it is still possible to build a limited but working networking framework

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Navigation Recommender:Real-Time iGNSS QoS Prediction for Navigation Services

Global Navigation Satellite Systems (GNSSs), especially Global Positioning System (GPS), have become commonplace in mobile devices and are the most preferred geo-positioning sensors for many location-based applications. Besides GPS, other GNSSs under development or deployment are GLONASS, Galileo, and Compass. These four GNSSs are planned to be integrated in the near future. It is anticipated that integrated GNSSs (iGNSSs) will improve the overall satellite-based geo-positioning performance. However, one major shortcoming of any GNSS and iGNSSs is Quality of Service (QoS) degradation due to signal blockage and attenuation by the surrounding environments, particularly in obstructed areas. GNSS QoS uncertainty is the root cause of positioning ambiguity, poor localization performance, application freeze, and incorrect guidance in navigation applications. In this research, a methodology, called iGNSS QoS prediction, that can provide GNSS QoS on desired and prospective routes is developed. Six iGNSS QoS parameters suitable for navigation are defined: visibility, availability, accuracy, continuity, reliability, and flexibility. The iGNSS QoS prediction methodology, which includes a set of algorithms, encompasses four modules: segment sampling, point-based iGNSS QoS prediction, tracking-based iGNSS QoS prediction, and iGNSS QoS segmentation. Given that iGNSS QoS prediction is data- and compute-intensive and navigation applications require real-time solutions, an efficient satellite selection algorithm is developed and distributed computing platforms, mainly grids and clouds, for achieving real-time performance are explored. The proposed methodology is unique in several respects: it specifically addresses the iGNSS positioning requirements of navigation systems/services; it provides a new means for route choices and routing in navigation systems/services; it is suitable for different modes of travel such as driving and walking; it takes high-resolution 3D data into account for GNSS positioning; and it is based on efficient algorithms and can utilize high-performance and scalable computing platforms such as grids and clouds to provide real-time solutions. A number of experiments were conducted to evaluate the developed methodology and the algorithms using real field test data (GPS coordinates). The experimental results show that the methodology can predict iGNSS QoS in various areas, especially in problematic areas

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282