Fraudulent claims in the automobile industry pose a significant threat to the financial stability of insurance companies and erode the trust between policyholders and insurers. Organized fraud, which involves intricate schemes and multiple parties, presents a substantial challenge in detection due to imbalanced datasets. While existing techniques such as over-sampling and under-sampling have been proposed to address this issue, they often lead to overfitting, loss of information, and reduced accuracy. However, assigning a suspicious label to each policyholder is more changeable, as it can identify potential risks and prevent fraudulent activities before they occur. In response to these challenges, we propose a novel heuristic approach called Organized Fraud detection with Graph theory and Poisson process (OrFGP) that identifies suspiciously organized fraud groups within an accident network and provides credibility levels for accidents and associated individuals. We first demonstrate that car accidents follow a Poisson random process. We then combine this process with graph theory to introduce an accident network. In the network, our objective is to identify regular behavior between accidents, which, based on the stochastic nature of accidents, can indicate organized fraud. OrFGP uses probabilistic concepts in conjunction with local network connectivity metrics to evaluate the credibility of accidents and individuals. The results indicate that OrFGP outperforms state-of-the-art approaches, particularly in imbalanced datasets. In fact, OrFGP achieves an accuracy of 98% and improves the F1-score by at least 3%.

Workflow scheduling is the process of optimally assigning virtual machines to workflow tasks subject to response time and cost consideration. Since such an optimization problem is NP-compete, providing an effective heuristic approach is essential. In this article, we consider the workflow scheduling problem with the least cost subject to a bound on the response time. We show that existing solutions fundamentally care for the longest execution path within the workflow without appropriately handling non-critical paths. To overcome such a shortcoming, we propose a novel heuristic algorithm based on discrete mathematics. We first demonstrate that a workflow has a bijective relation with a partially ordered set and then introduce two operations on the workflow to show that it is an algebraic structure. We then form a totally ordered set,$(T^{exe}({\mathcal P}), \preccurlyeq)$, of workflow paths where$T^{exe}({\mathcal P})$is the set of path execution times. Based on$(T^{exe}({\mathcal P}), \preccurlyeq),$we identify the path with the maximum cumulative execution time and allocate a virtual machine to each task of the path based on the workflow deadline. We then delete the scheduled path and run our algorithm for each resulting sub-workflow in parallel. The results indicate that the proposed algorithm outperforms the best-known approaches in the literature.

Average distance is an important parameter for measuring the communication cost of computer networks. A popular approach for its computation is to first partition the edge set of a network into convex components using the transitive closure of the Djoković–Winkler's relation and then to compute the average distance from the respective invariants of the components. In this article, we refine this idea further by shrinking the quotient graphs into smaller weighted graph called reduced graph, so that the average distance of the original graph is obtained from the reduced graphs. We demonstrate the significance of this technique by computing the average distance of butterfly and hypertree architectures. Along the way, a computational error from Klavžar and Nadjafi-Arani ((2014) Wiener index in weighted graphs via unification of Θ*-classes⁠, Eur. J. Combin. 36, 71–76) is corrected.