Modeling and Optimizing for NP-hard Problems in Graph Theory

This PhD thesis introduces optimization methods for graph problems classified as NP-hard. These are problems for which no deterministic algorithm is capable of solving them in polynomial time. More specifically, three graph problems were addressed, and for each, different optimization methods were used. These methods include standard methods, metaheuristics, and heuristics. In all cases, the performance of these methods was compared with those proposed in the literature, considering factors such as execution time and the quality of the solutions achieved. This comparative analysis aims to demonstrate the effectiveness of the proposed optimization methods

DONS: Dynamic Optimized Neighbor Selection for smart blockchain networks

Blockchain (BC) systems mainly depend on the consistent state of the Distributed Ledger (DL) at different logical and physical places of the network. The majority of network nodes need to be enforced to use one or both of the following approaches to remain consistent: (i) to wait for certain delays (i.e. by requesting a hard puzzle solution as in PoW and PoUW, or to wait for random delays as in PoET, etc.) (ii) to propagate shared data through shortest possible paths within the network. The first approach may cause higher energy consumption and/or lower throughput rates if not optimized, and in many cases these features are conventionally fixed. Therefore, it is preferred to enhance the second approach with some optimization. Previous works for this approach have the following drawbacks: they may violate the identity privacy of miners, only locally optimize the Neighbor Selection method (NS), do not consider the dynamicity of the network, or require the nodes to know the precise size of the network at all times. In this paper, we address these issues by proposing a Dynamic and Optimized NS protocol called DONS, using a novel privacy-aware leader election within the public BC called AnoLE, where the leader anonymously solves the The Minimum Spanning Tree problem (MST) of the network in polynomial time. Consequently, miners are informed about the optimum NS according to the current state of network topology. We analytically evaluate the complexity, the security and the privacy of the proposed protocols against state-of-the-art MST solutions for DLs and well known attacks. Additionally, we experimentally show that the proposed protocols outperform state-of-the-art NS solutions for public BCs. Our evaluation shows that the proposed DONS and AnoLE protocols are secure, private, and they acutely outperform all current NS solutions in terms of block finality and fidelity. © 2021 The Author(s

Exact Methods for the Longest Induced Cycle Problem

The longest induced (or chordless) cycle problem is a graph problem classified as NP-complete and involves the task of determining the largest possible subset of vertices within a graph in such a way that the induced subgraph forms a cycle. Within this paper, we present three integer linear programs specifically formulated to yield optimal solutions for this problem. The branch-and-cut algorithm has been used for two models. To demonstrate the computational efficiency of these methods, we utilize them on a range of real-world graphs as well as random graphs. Additionally, we conduct a comparative analysis against approaches previously proposed in the literature

Symbolic regression for approximating graph geodetic number

Graph properties are certain attributes that could make the structure of the graph understandable. Occasionally, standard methods cannot work properly for calculating exact values of graph properties due to their huge computational complexity, especially for real-world graphs. In contrast, heuristics and metaheuristics are alternatives proved their ability to provide sufficient solutions in a reasonable time. Although in some cases, even heuristics are not efficient enough, where they need some not easily obtainable global information of the graph. The problem thus should be dealt in completely different way by trying to find features that related to the property and based on these data build a formula which can approximate the graph property. In this work, symbolic regression with an evolutionary algorithm called Cartesian Genetic Programming has been used to derive formulas capable to approximate the graph geodetic number which measures the minimal-cardinality set of vertices, such that all shortest paths between its elements cover every vertex of the graph. Finding the exact value of the geodetic number is known to be NP-hard for general graphs. The obtained formulas are tested on random and real-world graphs. It is demonstrated how various graph properties as training data can lead to diverse formulas with different accuracy. It is also investigated which training data are really related to each property

PF-BTS: A Privacy-Aware Fog-enhanced Blockchain-assisted task scheduling

In recent years, the deployment of Cloud Computing (CC) has become more popular both in research and industry applications, arising form various fields including e-health, manufacturing, logistics and social networking. This is due to the easiness of service deployment and data management, and the unlimited provision of virtual resources (VR). In simple scenarios, users/applications send computational or storage tasks to be executed in the cloud, by manually assigning those tasks to the available computational resources. In complex scenarios, such as a smart city applications, where there is a large number of tasks, VRs, or both, task scheduling is exposed as an NP-Hard problem. Consequently, it is preferred and more efficient in terms of time and effort, to use a task scheduling automation technique. As there are many automated scheduling solutions proposed, new possibilities arise with the advent of Fog Computing (FC) and Blockchain (BC) technologies. Accordingly, such automation techniques may help the quick, secure and efficient assignment of tasks to the available VRs. In this paper, we propose an Ant Colony Optimization (ACO) algorithm in a Fog-enabled Blockchain-assisted scheduling model, namely PF-BTS. The protocol and algorithms of PF-BTS exploit BC miners for generating efficient assignment of tasks to be performed in the cloud's VRs using ACO, and award miner nodes for their contribution in generating the best schedule. In our proposal, PF-BTS further allows the fog to process, manage, and perform the tasks to enhance latency measures. While this processing and managing is taking place, the fog is enforced to respect the privacy of system components, and assure that data, location, identity, and usage information are not exposed. We evaluate and compare PF-BTS performance, with a recently proposed Blockchain-based task scheduling protocol, in a simulated environment. Our evaluation and experiments show high privacy awareness of PF-BTS, along with noticeable enhancement in execution time and network load. © 2020 The Author

Does open reduction internal fixation using a volar locking plate and closed reduction percutaneous pinning using K wires provide similar functional and radiological outcomes for unstable distal radius fractures?

Background: Distal radius fractures (DRFs) are a common orthopedic injury, with open reduction internal fixation (ORIF) and closed reduction percutaneous pinning (CRPP) being the two most frequently used methods for treating unstable DRFs. The optimal treatment approach for DRFs is still a matter of debate. Therefore, this retrospective analysis aimed to compare the functional and radiological outcomes of ORIF and CRPP to determine the most effective approach for treating unstable DRFs. Material and Methods: A total of 89 patients were included in this retrospective study; 34 underwent CRPP and 55 underwent ORIF (61 males and 28 females, mean age: 35.5). Radiographic measurements of radial inclination, radial height, and volar tilt, as well as patient-rated wrist evaluation (PRWE) scores for pain and function, were used to evaluate the functional and radiological outcomes during the final follow-up period, ranging from 1 to 4 years. Results: There were significant improvements in the radiographic measurements for both groups, indicating a good reduction. However, the two fixation methods had no significant difference in radiographic measurements during the entire follow-up period. Regarding PRWE scores, there was a significant difference between the two groups, with patients in the CRPP group reporting better wrist function and less pain. Conclusions: Both CRPP and ORIF are effective methods for treating unstable DRFs. Achieving an acceptable reduction did not correlate with better pain management, function, or the ability to carry out day-to-day activities. However, patients treated with CRPP had better wrist function and less pain during follow-up. Radiographic measurements did not differ significantly between the two groups. Clinicians should consider closed-reduction percutaneous pinning as a viable and effective treatment option for distal radius fractures, particularly when optimal wrist function and pain management are important considerations