105 research outputs found
Characterizing Block Graphs in Terms of their Vertex-Induced Partitions
Given a finite connected simple graph with vertex set and edge
set , we will show that
the (necessarily unique) smallest block graph with vertex set whose
edge set contains is uniquely determined by the -indexed family of the various partitions
of the set into the set of connected components of the
graph ,
the edge set of this block graph coincides with set of all -subsets
of for which and are, for all , contained
in the same connected component of ,
and an arbitrary -indexed family of
partitions of the set is of the form for some
connected simple graph with vertex set as above if and only if,
for any two distinct elements , the union of the set in
that contains and the set in that contains coincides with
the set , and holds for all .
As well as being of inherent interest to the theory of block graphs, these
facts are also useful in the analysis of compatible decompositions and block
realizations of finite metric spaces
Characterizing block graphs in terms of their vertex-induced partitions
Block graphs are a generalization of trees that arise in areas such as metric graph theory, molecular graphs, and phylogenetics. Given a finite connected simple graph with vertex set and edge set , we will show that the (necessarily unique) smallest block graph with vertex set whose edge set contains is uniquely determined by the -indexed family \Pp_G =\big(\pi_v)_{v \in V} of the partitions of the set into the set of connected components of the graph . Moreover, we show that an arbitrary -indexed family \Pp=(\p_v)_{v \in V} of partitions \p_v of the set is of the form \Pp=\Pp_G for some connected simple graph with vertex set as above if and only if, for any two distinct elements , the union of the set in \p_v that contains and the set in \p_u that contains coincides with the set , and \{v\}\in \p_v holds for all . As well as being of inherent interest to the theory of block graphs,these facts are also useful in the analysis of compatible decompositions of finite metric spaces
FaaSter, better, cheaper : the prospect of serverless scientific computing and HPC
The adoption of cloud computing facilities and programming models differs vastly between different application domains. Scalable web applications, low-latency mobile backends and on-demand provisioned databases are typical cases for which cloud services on the platform or infrastructure level exist and are convincing when considering technical and economical arguments. Applications with specific processing demands, including high-performance computing, high-throughput computing and certain flavours of scientific computing, have historically required special configurations such as compute- or memory-optimised virtual machine instances. With the rise of function-level compute instances through Function-as-a-Service (FaaS) models, the fitness of generic configurations needs to be re-evaluated for these applications. We analyse several demanding computing tasks with regards to how FaaS models compare against conventional monolithic algorithm execution. Beside the comparison, we contribute a refined FaaSification process for legacy software and provide a roadmap for future work
A MAPE-K Approach to Autonomic Microservices
Microservices are an emerging architectural style advocating for small loosely-coupled services in order to maximize scalability and adaptability. In order to help IT personnel, adaptability can be put (completely or partially) under the responsibility of the system using autonomic techniques, e.g., underpinned by a MAPE-K control loop. This paper discusses possible trade-offs, challenges and support techniques for soft-ware architects involved in building autonomic microservice-based systems
On a Linear Program for Minimum-Weight Triangulation
Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time
constant-factor approximation algorithm, and a variety of effective polynomial-
time heuristics that, for many instances, can find the exact MWT. Linear
programs (LPs) for MWT are well-studied, but previously no connection was known
between any LP and any approximation algorithm or heuristic for MWT. Here we
show the first such connections: for an LP formulation due to Dantzig et al.
(1985): (i) the integrality gap is bounded by a constant; (ii) given any
instance, if the aforementioned heuristics find the MWT, then so does the LP.Comment: To appear in SICOMP. Extended abstract appeared in SODA 201
Усовершенствование механизмов обеспечения производственной безопасности при бурении скважин
Объектом исследования является производственная безопасность при бурении скважин. Цель работы – усовершенствование механизмов обеспечения производственной безопасности при бурении скважин. Предмет исследования – механизмы обеспечения производственной безопасности при бурении скважин.
В процессе исследования были изучены общие требования безопасности на объектах бурения, рассматривалась система производственной безопасности в ООО "СГК-Бурение", был проведен анализ состояния несчастных случаев при бурении скважин (по состоянию с 2014 по 2018 гг.) и выявлены основные их причины. Были раскрыты механизмы обеспечения производственной безопасности на объектах бурения.The object of the study is production safety when drilling wells. The purpose of the work is to improve the mechanisms of ensuring production safety while drilling wells. The subject of the study is the mechanisms for ensuring production safety while drilling wells.
In the course of the study, general safety requirements for drilling sites were studied, the production safety system at LLC "SGC-Burenie" was considered, an analysis of the state of accidents during drilling of wells (as from 2014 to 2018) was carried out and their main causes were identified. The mechanisms for ensuring production safety at drilling facilities were disclosed
A polynomial bound for untangling geometric planar graphs
To untangle a geometric graph means to move some of the vertices so that the
resulting geometric graph has no crossings. Pach and Tardos [Discrete Comput.
Geom., 2002] asked if every n-vertex geometric planar graph can be untangled
while keeping at least n^\epsilon vertices fixed. We answer this question in
the affirmative with \epsilon=1/4. The previous best known bound was
\Omega((\log n / \log\log n)^{1/2}). We also consider untangling geometric
trees. It is known that every n-vertex geometric tree can be untangled while
keeping at least (n/3)^{1/2} vertices fixed, while the best upper bound was
O(n\log n)^{2/3}. We answer a question of Spillner and Wolff [arXiv:0709.0170
2007] by closing this gap for untangling trees. In particular, we show that for
infinitely many values of n, there is an n-vertex geometric tree that cannot be
untangled while keeping more than 3(n^{1/2}-1) vertices fixed. Moreover, we
improve the lower bound to (n/2)^{1/2}.Comment: 14 pages, 7 figure
Recognizing Treelike k-Dissimilarities
A k-dissimilarity D on a finite set X, |X| >= k, is a map from the set of
size k subsets of X to the real numbers. Such maps naturally arise from
edge-weighted trees T with leaf-set X: Given a subset Y of X of size k, D(Y) is
defined to be the total length of the smallest subtree of T with leaf-set Y .
In case k = 2, it is well-known that 2-dissimilarities arising in this way can
be characterized by the so-called "4-point condition". However, in case k > 2
Pachter and Speyer recently posed the following question: Given an arbitrary
k-dissimilarity, how do we test whether this map comes from a tree? In this
paper, we provide an answer to this question, showing that for k >= 3 a
k-dissimilarity on a set X arises from a tree if and only if its restriction to
every 2k-element subset of X arises from some tree, and that 2k is the least
possible subset size to ensure that this is the case. As a corollary, we show
that there exists a polynomial-time algorithm to determine when a
k-dissimilarity arises from a tree. We also give a 6-point condition for
determining when a 3-dissimilarity arises from a tree, that is similar to the
aforementioned 4-point condition.Comment: 18 pages, 4 figure
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