Comparison of Prim and Kruskal’s Algorithm

The goal of this research is to compare the performance of the common Prim and the Kruskal of the minimum spanning tree in building up super metric space We suggested using complexity analysis and experimental methods to evaluate these two methods After analysing daily sample data from the Shanghai and Shenzhen 300 indexes from the second half of 2005 to the second half of 2007 the results revealed that when the number of shares is less than 100 the Kruskal algorithm is relatively superior to the Prim algorithm in terms of space complexity however when the number of shares is greater than 100 the Prim algorithm is more superior in terms of time complexity A spanning tree is defined in the glossary as a connected graph with non-negative weights on its edges and the challenge is to identify a maz weight spanning tree Surprisingly the greedy algorithm yields an answer For the problem of finding a min weight spanning tree we propose greedy algorithms based on Prim and Kruskal respectively Graham and Hell provide a history of the issue which began with Czekanowski s work in 1909 The information presented here is based on Rose

On the approximability of robust spanning tree problems

In this paper the minimum spanning tree problem with uncertain edge costs is discussed. In order to model the uncertainty a discrete scenario set is specified and a robust framework is adopted to choose a solution. The min-max, min-max regret and 2-stage min-max versions of the problem are discussed. The complexity and approximability of all these problems are explored. It is proved that the min-max and min-max regret versions with nonnegative edge costs are hard to approximate within $O(\log^{1-\epsilon} n)$ for any $\epsilon>0$ unless the problems in NP have quasi-polynomial time algorithms. Similarly, the 2-stage min-max problem cannot be approximated within $O(\log n)$ unless the problems in NP have quasi-polynomial time algorithms. In this paper randomized LP-based approximation algorithms with performance ratio of $O(\log^2 n)$ for min-max and 2-stage min-max problems are also proposed

Principles of Dataset Versioning: Exploring the Recreation/Storage Tradeoff

The relative ease of collaborative data science and analysis has led to a proliferation of many thousands or millions of $versions$ of the same datasets in many scientific and commercial domains, acquired or constructed at various stages of data analysis across many users, and often over long periods of time. Managing, storing, and recreating these dataset versions is a non-trivial task. The fundamental challenge here is the $storage-recreation\;trade-off$: the more storage we use, the faster it is to recreate or retrieve versions, while the less storage we use, the slower it is to recreate or retrieve versions. Despite the fundamental nature of this problem, there has been a surprisingly little amount of work on it. In this paper, we study this trade-off in a principled manner: we formulate six problems under various settings, trading off these quantities in various ways, demonstrate that most of the problems are intractable, and propose a suite of inexpensive heuristics drawing from techniques in delay-constrained scheduling, and spanning tree literature, to solve these problems. We have built a prototype version management system, that aims to serve as a foundation to our DATAHUB system for facilitating collaborative data science. We demonstrate, via extensive experiments, that our proposed heuristics provide efficient solutions in practical dataset versioning scenarios