Computing a directed minimum spanning tree, called arborescence, is a fundamental algorithmic problem, although not as common as its undirected counterpart. In 1967, Edmonds discussed an elegant solution. It was refined to run in O(min(n2,m log n)) by Tarjan which is optimal for very dense and very sparse graphs. Gabow et al. gave a version of Edmonds' algorithm that runs in O(n log n + m), thus asymptotically beating the Tarjan variant in the regime between sparse and dense. Despite the attention the problem received theoretically, there exists, to the best of our knowledge, no empirical evaluation of either of these algorithms. In fact, the version by Gabow et al. has never been implemented and, aside from coding competitions, all readily available Tarjan implementations run in O(n2). In this paper, we provide the first implementation of the version by Gabow et al. as well as five variants of Tarjan's version with different underlying data structures. We evaluate these algorithms and existing solvers on a large set of real-world and random graphs. * The full version of the paper can be accessed at https://arxiv.org/abs/2208.02590

Solid-state drives (SSDs) have improved database system performance significantly due to the higher bandwidth that they provide over traditional hard disk drives. Persistent memory (PMem) is a new storage technology that offers DRAM-like speed at SSD-like capacity. Due to its byte-addressability, research has mainly treated PMem as a replacement of, or an addition to DRAM, e.g., by proposing highly-optimized, DRAM-PMem-hybrid data structures and system designs. However, PMem can also be used via a regular file system interface and standard Linux I/O operations. In this paper, we analyze PMem as a drop-in replacement for Non-Volatile Memory Express (NVMe) SSDs and evaluate possible performance gains while requiring no or only minor changes to existing applications. This drop-in approach speeds-up database systems like Postgres, without requiring any code changes. We systematically evaluate PMem and NVMe SSDs in three database microbenchmarks and the widely used TPC-H benchmark on Postgres. Our experiments show that PMem outperforms a RAID of four NVMe SSDs in read-intensive OLAP workloads by up to 4x without any modifications while achieving similar performance in write-intensive workloads. Finally, we give four practical insights to aid decision-making on when to use PMem as an SSD drop-in replacement and how to optimize for it.

Traditional navigation services find the fastest route for a single driver. Though always using the fastest route seems desirable for every individual, selfish behavior can have undesirable effects such as higher energy consumption and avoidable congestion, even leading to higher overall and individual travel times. In contrast, strategic routing aims at optimizing the traffic for all agents regarding a global optimization goal. We introduce a framework to formalize real-world strategic routing scenarios as algorithmic problems and study one of them, which we call Single Alternative Path (SAP), in detail. There, we are given an original route between a single origin--destination pair. The goal is to suggest an alternative route to all agents that optimizes the overall travel time under the assumption that the agents distribute among both routes according to a psychological model, for which we introduce the concept of Pareto-conformity. We show that the SAP problem is NP-complete, even for such models. Nonetheless, assuming Pareto-conformity, we give multiple algorithms for different variants of SAP, using multi-criteria shortest path algorithms as subroutines. Moreover, we prove that several natural models are in fact Pareto-conform. The implementation of our algorithms serves as a proof of concept, showing that SAP can be solved in reasonable time even though the algorithms have exponential running time in the worst case.