Almost-Tight Distributed Minimum Cut Algorithms

We study the problem of computing the minimum cut in a weighted distributed message-passing networks (the CONGEST model). Let $\lambda$ be the minimum cut, $n$ be the number of nodes in the network, and $D$ be the network diameter. Our algorithm can compute $\lambda$ exactly in $O((\sqrt{n} \log^{*} n+D)\lambda^4 \log^2 n)$ time. To the best of our knowledge, this is the first paper that explicitly studies computing the exact minimum cut in the distributed setting. Previously, non-trivial sublinear time algorithms for this problem are known only for unweighted graphs when $\lambda\leq 3$ due to Pritchard and Thurimella's $O(D)$-time and $O(D+n^{1/2}\log^* n)$-time algorithms for computing $2$-edge-connected and $3$-edge-connected components. By using the edge sampling technique of Karger's, we can convert this algorithm into a $(1+\epsilon)$-approximation $O((\sqrt{n}\log^{*} n+D)\epsilon^{-5}\log^3 n)$-time algorithm for any $\epsilon>0$. This improves over the previous $(2+\epsilon)$-approximation $O((\sqrt{n}\log^{*} n+D)\epsilon^{-5}\log^2 n\log\log n)$-time algorithm and $O(\epsilon^{-1})$-approximation $O(D+n^{\frac{1}{2}+\epsilon} \mathrm{poly}\log n)$-time algorithm of Ghaffari and Kuhn. Due to the lower bound of $\Omega(D+n^{1/2}/\log n)$ by Das Sarma et al. which holds for any approximation algorithm, this running time is tight up to a $\mathrm{poly}\log n$ factor. To get the stated running time, we developed an approximation algorithm which combines the ideas of Thorup's algorithm and Matula's contraction algorithm. It saves an $\epsilon^{-9}\log^{7} n$ factor as compared to applying Thorup's tree packing theorem directly. Then, we combine Kutten and Peleg's tree partitioning algorithm and Karger's dynamic programming to achieve an efficient distributed algorithm that finds the minimum cut when we are given a spanning tree that crosses the minimum cut exactly once

On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure

The effect of vent size and congestion in large-scale vented natural gas/air explosions

A typical building consists of a number of rooms; often with windows of different size and failure pressure and obstructions in the form of furniture and décor, separated by partition walls with interconnecting doorways. Consequently, the maximum pressure developed in a gas explosion would be dependent upon the individual characteristics of the building. In this research, a large-scale experimental programme has been undertaken at the DNV GL Spadeadam Test Site to determine the effects of vent size and congestion on vented gas explosions. Thirty-eight stoichiometric natural gas/air explosions were carried out in a 182 m3 explosion chamber of L/D = 2 and KA = 1, 2, 4 and 9. Congestion was varied by placing a number of 180 mm diameter polyethylene pipes within the explosion chamber, providing a volume congestion between 0 and 5% and cross-sectional area blockages ranging between 0 and 40%. The series of tests produced peak explosion overpressures of between 70 mbar and 3.7 bar with corresponding maximum flame speeds in the range 35 - 395 m/s at a distance of 7 m from the ignition point. The experiments demonstrated that it is possible to generate overpressures greater than 200 mbar with volume blockages of as little as 0.57%, if there is not sufficient outflow through the inadvertent venting process. The size and failure pressure of potential vent openings, and the degree of congestion within a building, are key factors in whether or not a building will sustain structural damage following a gas explosion. Given that the average volume blockage in a room in a UK inhabited building is in the order of 17%, it is clear that without the use of large windows of low failure pressure, buildings will continue to be susceptible to significant structural damage during an accidental gas explosion

Medical and Surgical Care of Patients With Mesothelioma and Their Relatives Carrying Germline BAP1 Mutations

The most common malignancies that develop in carriers of BAP1 germline mutations include diffuse malignant mesothelioma, uveal and cutaneous melanoma, renal cell carcinoma, and less frequently, breast cancer, several types of skin carcinomas, and other tumor types. Mesotheliomas in these patients are significantly less aggressive, and patients require a multidisciplinary approach that involves genetic counseling, medical genetics, pathology, surgical, medical, and radiation oncology expertise. Some BAP1 carriers have asymptomatic mesothelioma that can be followed by close clinical observation without apparent adverse outcomes: they may survive many years without therapy. Others may grow aggressively but very often respond to therapy. Detecting BAP1 germline mutations has, therefore, substantial medical, social, and economic impact. Close monitoring of these patients and their relatives is expected to result in prolonged life expectancy, improved quality of life, and being cost-effective. The co-authors of this paper are those who have published the vast majority of cases of mesothelioma occurring in patients carrying inactivating germline BAP1 mutations and who have studied the families affected by the BAP1 cancer syndrome for many years. This paper reports our experience. It is intended to be a source of information for all physicians who care for patients carrying germline BAP1 mutations. We discuss the clinical presentation, diagnostic and treatment challenges, and our recommendations of how to best care for these patients and their family members, including the potential economic and psychosocial impact. (C) 2022 International Association for the Study of Lung Cancer. Published by Elsevier Inc