Frameworks for designing in-place graph algorithms

Chakraborty, Sankardeep; Mukherjee, Anish; Raman, Venkatesh; Satti, Srinivasa Rao

doi:10.1016/j.jcss.2021.07.004

Cited by 3 publications

(3 citation statements)

References 63 publications

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“…The most relevant model of inertial changes is the exponential curve, since it contains the base of the natural logarithm [7], [8], [11]. In addition, this corresponds to many other, less significant, negative impact factors, after which, according to the law of large numbers [2], [3], [7], the total result will approach a normal distribution. Let 𝑎 𝚤 � (𝑡) is an estimate of the state of the i-th business process at a moment in time t, and 𝑎 𝚤 � (𝑡 + ∆𝑡) -assessment at the next point in time that follows the period of duration Δt.…”

Section: Methodsmentioning

confidence: 99%

Assessment of Negative Impact of Operating Environment of the Enterprise on Business Processes and Economic Security

Samborska,

Rudnichenko,

Havlovska

et al. 2024

TEM Journal

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The article examines the peculiarities of influence of operating environment an enterprise on business processes. Considerable attention is paid to negative influence of external environment, in particular, seven factors in the process of growth of inertia are highlighted, namely: 1) fierce competition; 2) limited resources; 3) complexity and high cost of logistics operations; 4) institutional restrictions; 5) destabilization of financial system; 6) change of standards and norms; 7) reduction of target markets. The factors of negative influence of internal environment are singled out as a set of manifestations of economic security destabilization in order of increasing inertia, which are 1) ineffectiveness of research work at an enterprise; 2) problems of responsibility areas distribution; 3) problems of managing operational processes; 4) low efficiency of marketing system; 5) insufficient financial support; 6) absence of effective control system; 7) conflicts; 8) workers’ opportunistic behaviour. The article assesses the deterioration of an enterprise business process, taking into account the listed factors of negative impact. Such assessment is carried out by experts, in particular, experts are asked to give corresponding percentage of decline in the assessment of the state of this process for each business process on a scale of 0, 25%, 50%, 75% or more. The testing was carried out at the "Khmelnitskhezelezobeton" enterprise with 34 experts being involved. The article provides a matrix of average percentages of decline during a month and a matrix of intensities of decline for the enterprise under study. The result of using the model is ensuring the economic security of the enterprise making effective management decisions for minimizing the negative impact of operating environment of the enterprise.

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Section: Methodsmentioning

confidence: 99%

Assessment of Negative Impact of Operating Environment of the Enterprise on Business Processes and Economic Security

Samborska,

Rudnichenko,

Havlovska

et al. 2024

TEM Journal

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“…However, the algorithms are based on random walks and are inherently sequential. Recent work by Chakraborty et al [24][25][26] has studied in-place algorithms for other graph problems, including graph search and connectivity, and it would be interesting to parallelize these algorithms in the future.…”

Section: Relaxed Pip Graph Algorithmsmentioning

confidence: 99%

Parallel In-Place Algorithms: Theory and Practice

Gu¹,

Obeya²,

Shun³

2021

Preprint

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Many parallel algorithms use at least linear auxiliary space in the size of the input to enable computations to be done independently without conflicts. Unfortunately, this extra space can be prohibitive for memory-limited machines, preventing large inputs from being processed. Therefore, it is desirable to design parallel in-place algorithms that use sublinear (or even polylogarithmic) auxiliary space.In this paper, we bridge the gap between theory and practice for parallel in-place (PIP) algorithms. We first define two computational models based on fork-join parallelism, which reflect modern parallel programming environments. We then introduce a variety of new parallel in-place algorithms that are simple and efficient, both in theory and in practice. Our algorithmic highlight is the Decomposable Property introduced in this paper, which enables existing non-in-place but highly-optimized parallel algorithms to be converted into parallel in-place algorithms. Using this property, we obtain algorithms for random permutation, list contraction, tree contraction, and merging that take linear work, 𝑂 (𝑛 1−𝜖 ) auxiliary space, and 𝑂 (𝑛 𝜖 • polylog(𝑛)) span for 0 < 𝜖 < 1. We also present new parallel in-place algorithms for scan, filter, merge, connectivity, biconnectivity, and minimum spanning forest using other techniques.In addition to theoretical results, we present experimental results for implementations of many of our parallel in-place algorithms. We show that on a 72-core machine with twoway hyper-threading, the parallel in-place algorithms usually outperform existing parallel algorithms for the same problems that use linear auxiliary space, indicating that the theory developed in this paper indeed leads to practical benefits in terms of both space usage and running time.

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“…Whereas the Prim's algorithm is commonly said to perform better on dense graphs [12], the Kruskal's algorithm is believed to perform acceptably on sparser graphs [2], [6], [7]. However, the efficiency of the Prim's algorithm on sparse graphs still has not been denied [13]. Both the algorithms have nearly the same asymptotic time complexity varying from linear to polynomial [14].…”

Section: Introductionmentioning

confidence: 99%

Building Minimum Spanning Trees by Limited Number of Nodes Over Triangulated Set of Initial Nodes

Romanuke¹

2023

ITS

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Background. The common purpose of modelling and using minimum spanning trees is to ensure efficient coverage. In many tasks of designing efficient telecommunication networks, the number of network nodes is usually limited. In terms of rational allocation, there are more possible locations than factually active tools to be settled to those locations. Objective. Given an initial set of planar nodes, the problem is to build a minimum spanning tree connecting a given number of the nodes, which can be less than the cardinality of the initial set. The root node is primarily assigned, but it can be changed if needed. Methods. To obtain a set of edges, a Delaunay triangulation is performed over the initial set of nodes. Distances between every pair of the nodes in respective edges are calculated. These distances being the lengths of the respective edges are used as graph weights, and a minimum spanning tree is built over this graph. Results. The problem always has a solution if the desired number of nodes (the number of available recipient nodes) is equal to the number of initially given nodes. If the desired number is lesser, the maximal edge length is found and the edges of the maximal length are excluded while the number of minimum spanning tree nodes is greater than the desired number of nodes. Conclusions. To build a minimum spanning tree by a limited number of nodes it is suggested to use the Delaunay triangulation and an iterative procedure in order to meet the desired number of nodes. Planar nodes of an initial set are triangulated, whereupon the edge lengths are used as weights of a graph. The iterations to reduce nodes are done only if there are redundant nodes. When failed, the root node must be changed before the desired number of nodes is changed.

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Frameworks for designing in-place graph algorithms

Cited by 3 publications

References 63 publications

Assessment of Negative Impact of Operating Environment of the Enterprise on Business Processes and Economic Security

Assessment of Negative Impact of Operating Environment of the Enterprise on Business Processes and Economic Security

Parallel In-Place Algorithms: Theory and Practice

Building Minimum Spanning Trees by Limited Number of Nodes Over Triangulated Set of Initial Nodes

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