Union-find Research Articles

A Path-Compression Approach for Improving Shortest-Path Algorithms

Given a weighted directed graph G=(V;E;w), where w is non-negative weight function, G’ is a graph obtained from G by an application of path compression. Path compression reduces the graph G to a critical set of vertices and edges that affect the generation of shortest trees. The main contribution of this paper is finding shortest path between two selected vertices by applying a new algorithm that reduces number of nodes that needs to be traversed in the graph while preserving all graph properties. The main method of the algorithm is restructuring the graph in a way that only critical/relevant nodes are considered while all other neutral vertices and weights are preserved as sub paths' properties. Our algorithm can compress the graph paths into considerable improved percentage especially when the graph is sparse and hence improves performance significantly.

The longest common substring problem

Given a set$\mathcal{D}$ofqdocuments, the Longest Common Substring (LCS) problem asks, for any integer 2 ⩽k⩽q, the longest substring that appears inkdocuments. LCS is a well-studied problem having a wide range of applications in Bioinformatics: from microarrays to DNA sequences alignments and analysis. This problem has been solved by Hui (2000International Journal of Computer Science and Engineering1573–76) by using a famous constant-time solution to the Lowest Common Ancestor (LCA) problem in trees coupled with the use of suffix trees.In this article, we present a simple method for solving the LCS problem by using suffix trees (STs) and classical union-find data structures. In turn, we show how this simple algorithm can be adapted in order to work with other space efficient data structures such as the enhanced suffix arrays (ESA) and the compressed suffix tree.

Reliability Evaluation of the Minimum Spanning Tree on Uncertain Graph

Minimum spanning tree is a minimum-cost spanning tree connecting the whole network, but it couldn't be directly obtained on uncertain graph. In this paper, we define the reliability as the existence probability of all minimum spanning trees and present an algorithm for evaluating reliability of the minimum spanning tree on uncertain graph. The time complexity of the algorithm is O(Nmn), where n, m and N stand for the number of vertices, edges and minimum spanning trees, respectively. Because this algorithm spends more time finding minimum spanning tree, we propose an improved algorithm whose time complexity is O(Nm). The improved algorithm uses disjoint set data structure so that the average time complexity on finding a new minimum spanning tree is O(m/n). The two algorithms are analyzed in detail and the experiment results agree with theoretical analysis.

Not solving problems, managing messes

EU 2020, the current strategic framework of the European Union (European Commission, 2010) sets ambitious policy goals based on a rather bleak analysis of a complex crisis scenario the Union finds itself in. A key role is given to early childhood education and care to achieve these goals, and ‘highest benefits’ are predicted for children and society provided that ECEC services are of ‘high quality’ (Council of the European Union, 2010). Recent European and international research emphasizes the importance of systemic, trans-sectoral and trans-disciplinary approaches to developing and improving early childhood experiences for all children, families and communities (Urban et al., 2011a, 2012). Drawing on findings of the study, the article outlines the concept of ‘competent systems’ in early childhood and discusses implications for governance. It questions the persistent use of a ‘language of technology and normalisation’ (Dahlberg et al., 2007) in policy documents and argues for alternatives that recognize and embrace the relational, political and uncertain characteristics of early childhood professional practice.

Union-Find with Constant Time Deletions

A union-find data structure maintains a collection of disjoint sets under the operations makeset, union, and find. Kaplan, Shafrir, and Tarjan [SODA 2002] designed data structures for an extension of the union-find problem in which items of the sets maintained may be deleted. The cost of a delete operation in their implementations is essentially the same as the cost of a find operation; namely, O (log n ) worst-case and O (α ⌈ M / N ⌉ ( n )) amortized, where n is the number of items in the set returned by the find operation, N is the total number of makeset operations performed, M is the total number of find operations performed, and α ⌈ M / N ⌉ ( n ) is a functional inverse of Ackermann’s function. They left open the question whether delete operations can be implemented more efficiently than find operations, for example, in o (log n ) worst-case time. We resolve this open problem by presenting a relatively simple modification of the classical union-find data structure that supports delete, as well as makeset and union operations, in constant worst-case time, while still supporting find operations in O (log n ) worst-case time and O (α ⌈ M/N⌉ ( n )) amortized time. Our analysis supplies, in particular, a very concise potential-based amortized analysis of the standard union-find data structure that yields an O (α ⌈ M / N ⌉ ( n )) amortized bound on the cost of find operations. All previous potential-based analyses yielded the weaker amortized bound of O (α ⌈ M / N ⌉ ( N )). Furthermore, our tighter analysis extends to one-path variants of the path compression technique such as path splitting .

최소신장트리를 위한 크루스칼 알고리즘의 효율적인 구현

본 논문에서는 최소신장트리를 구하는 크루스칼 알고리즘의 효율적인 구현 방법을 제시한다. 제시하는 방법은 union-find 자료구조를 이용하며, 노드 집합을 나타내는 각 트리의 깊이를 줄이기 위해 union 연산시 루트까지의 경로에 있는 노드들의 위치를 최종 루트의 자식노드로 직접 이동하여 깊이를 줄이도록 하는 방법이다. 이 방법은 루트까지의 경로를 축소하고 노드의 레벨을 축소시킴으로써 트리의 깊이도 줄일 수 있다. 트리의 깊이가 줄어든다면 노드가 속하는 트리의 루트를 찾는 시간을 줄일 수 있게 되어 효율적인 방법이라 할 수 있다. 본 장에서 제안하는 방법을 그래프로 평가해보고 분석해 본 결과, 기존의 union() 방법이나 경로축소방법인 union2() 보다 트리의 깊이를 작게 유지함을 알 수 있다. In this paper, we present an efficient implementation of Kruskal's algorithm to obtain a minimum spanning tree. The proposed method utilizes the union-find data structure, reducing the depth of the tree of the node set by making the nodes in the path to root be the child node of the root of combined tree. This method can reduce the depth of the tree by shortening the path to the root and lowering the level of the node. This is an efficient method because if the tree's depth reduces, it could shorten the time of finding the root of the tree to which the node belongs. The performance of the proposed method is evaluated through the graphs generated randomly. The results showed that the proposed method outperformed the conventional method in terms of the depth of the tree.

Numerical investigation into the fragmentation efficiency of one coal prism in a roller pulveriser: Homogeneous approach

The aim of this paper is to numerically model the rolling compression induced breakage process of a single coal prism in a roller pulveriser and to quantify the resultant fragmentation efficiency. A coupling approach of the finite element method (FEM) and the smoothed particle hydrodynamics (SPH) method is adopted to examine the complete deformation and progressive fragmentation process involved. A coupled damage-plastic material model is used to simulate the complex deformation and failure behaviour of coal materials. In order to quantify the geometric properties of main fragments by the rolling compression, a numerical approach is developed based on the union-find algorithm. Parametric studies have been conducted considering various factors, including the geometric factors of prismatic coal specimens and the rotating velocity of the rigid roller. Typical modelling results are provided and the fragmentation efficiency is examined and discussed with respect to the corresponding factors.

Finding dominators via disjoint set union

The problem of finding dominators in a directed graph has many important applications, notably in global optimization of computer code. Although linear and near-linear-time algorithms exist, they use sophisticated data structures. We develop an algorithm for finding dominators that uses only a “static tree” disjoint set data structure in addition to simple lists and maps. The algorithm runs in near-linear or linear time, depending on the implementation of the disjoint set data structure. We give several versions of the algorithm, including one that computes loop nesting information (needed in many kinds of global code optimization) and that can be made self-certifying, so that the correctness of the computed dominators is very easy to verify.

Fully Dynamic Evaluation of Sequence Pair

In the electronic design automation field, as well as in other areas, problem instances and solutions are often subject to discrete changes. The foundational significance of efficient updates of the criterion value after dynamic updates, instead of recomputing it from scratch each time, has attracted a lot of research. In this paper, motivated by the significance of the sequence pair (SP) representation for floorplanning, we develop a fully dynamic algorithm of SP evaluation, that efficiently updates a criterion value after insertions and deletions of SP elements and after modifications of element weights. Our result is based on a new data structure for the predecessor problem, which maintains the whole history of its dynamic modifications, and the path-compression technique from the union-find problem, which efficiently support predecessor queries. Numerical experiments showed that our algorithm exhibits linear-time behavior and considerably reduces the time of SP evaluation, compared to other approaches.

Continuum percolation thresholds in two dimensions

A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the connected clusters, and (in two dimensions) using exact values from conformal field theory for the probability, at the phase transition, that various kinds of wrapping clusters exist on the torus. We apply this approach to percolation in continuum models, finding overlaps between objects with real-valued positions and orientations. In particular, we find precise values of the percolation transition for disks, squares, rotated squares, and rotated sticks in two dimensions and confirm that these transitions behave as conformal field theory predicts. The running time and memory use of our algorithm are essentially linear as a function of the number of objects at criticality.

Is social movement unionism still relevant? The case of the South African federation COSATU

ABSTRACTIs adopting a social movement role the most effective organisational strategy for organised labour or is it little more than an ideal, in an age of austerity and union defensiveness? This article draws on a national survey of Congress of South African Trade Union (COSATU) members to test perceptions of union activities and finds that COSATU unions largely embrace a social movement role. However, in the context of insecurity, unions need to address the central challenge of declining formal sector employment and precarious jobs.

String Distances for Near-duplicate Detection

Near-duplicate detection is important when dealing with large, noisy databases in data mining tasks. In this paper, we present the results of applying the Rank distance and the Smith-Waterman distance, along with more popular string similarity measures such as the Levenshtein distance, together with a disjoint set data structure, for the problem of near-duplicate detection. HE concept of near-duplicates belongs to the larger class of problems known as knowledge discovery and data mining, that is identifying consistent patterns in large scale data bases of any nature. Any two chunks of text that have possibly different syntactic structure, but identical or very similar semantics, are said to be near duplicates. During the last decade, largely due to low cost storage capacity, the volume of stored data increased at amassing rates; thus, the size of useful and available datasets for almost any task has become very large, prompting the need of scalable methods. Many datasets are noisy, in the very specific sense of having redundant data in the form of identical or nearly identical entries. In an interview for The Metropolitan Corporate Counsel (see http://www.metrocorpcounsel.com/articles/7757/ near-duplicates-elephant-document-review-room), Warwick Sharp, vice-president of Equivio Ltd., a company offering information on retrieval services to law firms with huge legal document databases, noted that 20 to 30 percent of data they work with are actually near-duplicates, and this is after identical duplicate elimination. The most extreme case they handled was made up of 45% near-duplicates. Today it is estimated that around 7% of websites are approximately duplicates of one another, and their number is growing rapidly. On the one hand, near-duplicates have the effect of artificially enlarging the dataset and therefore slowing down any processing; on the other hand, the small variation between them can contain additional information so that, by merging them, we obtain an entry with more information than any of the original near-duplicates on their own. Therefore, the key problems regarding near-duplicates are identification

Technical Barriers to Trade Provisions in Regional Trade Agreements

The proliferation of regional trade agreements (“RTAs”) behoves all WTO members to assess the extent to which RTAs depart from fundamental principles in the WTO such as the most-favoured-nation (“MFN”) treatment in the GATT and in particular, the WTO Agreement on Technical Barriers to Trade. This paper focuses on technical barriers to trade (“TBT”) provisions in RTAs concluded by the United States, European Union, Australia and Singapore and finds that these TBT provisions complement the existing disciplines in the TBT Agreement. To the extent that TBT provisions in RTAs may be inconsistent with the TBT Agreement, this paper examines the extent to which they can be justified under Article XXIV of GATT. This paper concludes that the ambiguity of key terms in Article XXIV of GATT allows WTO Members to adopt an expansive interpretation of the scope of Article XXIV of GATT.

PepMapper: A Collaborative Web Tool for Mapping Epitopes from Affinity-Selected Peptides

Epitope mapping from affinity-selected peptides has become popular in epitope prediction, and correspondingly many Web-based tools have been developed in recent years. However, the performance of these tools varies in different circumstances. To address this problem, we employed an ensemble approach to incorporate two popular Web tools, MimoPro and Pep-3D-Search, together for taking advantages offered by both methods so as to give users more options for their specific purposes of epitope-peptide mapping. The combined operation of Union finds as many associated peptides as possible from both methods, which increases sensitivity in finding potential epitopic regions on a given antigen surface. The combined operation of Intersection achieves to some extent the mutual verification by the two methods and hence increases the likelihood of locating the genuine epitopic region on a given antigen in relation to the interacting peptides. The Consistency between Intersection and Union is an indirect sufficient condition to assess the likelihood of successful peptide-epitope mapping. On average from 27 tests, the combined operations of PepMapper outperformed either MimoPro or Pep-3D-Search alone. Therefore, PepMapper is another multipurpose mapping tool for epitope prediction from affinity-selected peptides. The Web server can be freely accessed at: http://informatics.nenu.edu.cn/PepMapper/

The dynamic effects of a currency union on trade

The response of trade to a monetary union is a dynamic process. An empirical study of the European monetary union finds that the extensive margin of trade in new goods responded several years ahead of EMU implementation and ahead of overall trade volume. A dynamic rational expectations trade model shows that early entry of new firms in anticipation is explainable as a rational forward-looking response to news. The model helps identify which types of trading frictions are reduced by a currency union, and shows how new entry can be affected by uncertainty about EMU.

Delegated isolation

Isolation---the property that a task can access shared data without interference from other tasks---is one of the most basic concerns in parallel programming. In this paper, we present Aida, a new model of isolated execution for parallel programs that perform frequent, irregular accesses to pointer-based shared data structures. The three primary benefits of Aida are dynamism, safety and liveness guarantees, and programmability. First, Aida allows tasks to dynamically select and modify, in an isolated manner, arbitrary fine-grained regions in shared data structures, all the while maintaining a high level of concurrency. Consequently, the model can achieve scalable parallelization of regular as well as irregular shared-memory applications. Second, the model offers freedom from data races, deadlocks, and livelocks. Third, no extra burden is imposed on programmers, who access the model via a simple, declarative isolation construct that is similar to that for transactional memory. The key new insight in Aida is a notion of delegation among concurrent isolated tasks (known in Aida as assemblies). Each assembly A is equipped with a region in the shared heap that it owns---the only objects accessed by A are those it owns, guaranteeing race-freedom. The region owned by A can grow or shrink flexibly---however, when A needs to own a datum owned by B, A delegates itself, as well as its owned region, to B. From now on, B has the responsibility of re-executing the task A set out to complete. Delegation as above is the only inter-assembly communication primitive in Aida. In addition to reducing contention in a local, data-driven manner, it guarantees freedom from deadlocks and livelocks. We offer an implementation of Aida on top of the Habanero Java parallel programming language. The implementation employs several novel ideas, including the use of a union-find data structure to represent tasks and the regions that they own. A thorough evaluation using several irregular data-parallel benchmarks demonstrates the low overhead and excellent scalability of Aida, as well as its benefits over existing approaches to declarative isolation. Our results show that Aida performs on par with the state-of-the-art customized implementations of irregular applications and much better than coarse-grained locking and transactional memory approaches.

TH-A-220-06: Four-Dimensional MRI/CT Based Auto-Adaptive Segmentation for Real-Time Radiotherapy in Lung Cancer Treatment

Purpose: To enable real-time magnetic resonance (MR)/computer tomography (CT) image-guided radiotherapy (IGRT) and to reduce treatment planning durations in the radiotherapy of lung cancer through the design and implementation of computationally efficient four-dimensional (4D) MR/CT based automated segmentation algorithms. Methods: Hyperpolarized helium-3 (HP3He) and proton-density 4DMRI lung data was acquired for six subjects. Thoracic 4DCT data often subjects with lung cancer was also acquired. Automated segmentation was performed using a novel Morphological Processing and Successive Localization (MPSL) approach. Three different MPSL segmentation algorithms were developed to segment the regions of tumor, body and lung respectively. MPSL segmentation: A mask that includes the intensity range of the region-of-interest was generated. Then morphological processing (and/or reconstruction) was performed to separate the target volume(s) from other regions. Then the different connected regions were labeled using the union-find algorithm and their areas/volumes were calculated. A limit on the maximum/minimum possible area/volume of the target volume was used as a filter to segment the target volume. Morphological processing/reconstruction were performed again to create the final contours. Results: MPSL was shown to successfully segment the regions-of-interest (tumors, lung and body) from the images with both high and low signal-to- noise ratio. With the use of 3D processing and successive localization MPSL was shown to separately classify tumor and diaphragm (that may appear within the 2D contours of the lung). MPSL segmentation was compared with manual segmentation. Average computational time for achieving automated lung segmentation using MPSL on one phase volume (128×128×128) of 4D HP3He MR data was 0.5s. For proton-density 4DMRI data, the average time for automated segmentation of body and lung on one phase volume (128×128×128) was 2s. Conclusions: With the computation speed of the order of seconds for achieving automated segmentation, MPSL has realistic potential for application in real-time image-guidance for adaptive radiotherapy.

Double-Row Cascade Labeling Algorithm for Hyper-Scale Issue

An efficient algorithm is presented to label the connected components in the case that the primary memory is smaller than the image data. Our algorithm uses only the memory of two image rows to label the huge image or any image larger than the available memory. The search path compression is a applied for improving the performance further. An extensive comparison with the state-of-art algorithms is proposed, both on random and real datasets. Our algorithm shows an impressive speedup, while the auxiliary memory is not required at all comparing with all competitors.

A simple and efficient Union–Find–Delete algorithm

The Union–Find data structure for maintaining disjoint sets is one of the best known and widespread data structures, in particular the version with constant-time Union and efficient Find. Recently, the question of how to handle deletions from the structure in an efficient manner has been taken up, first by Kaplan et al. (2002) [2] and subsequently by Alstrup et al. (2005) [1]. The latter work shows that it is possible to implement deletions in constant time, without affecting adversely the asymptotic complexity of other operations, even when this complexity is calculated as a function of the current size of the set. In this note we present a conceptual and technical simplification of the algorithm, which has the same theoretical efficiency, and is probably more attractive in practice.

I/O-efficient batched union-find and its applications to terrain analysis

In this article we present an I/O-efficient algorithm for the batched (off-line) version of the union-find problem. Given any sequence of N union and find operations, where each union operation joins two distinct sets, our algorithm uses O (SORT( N )) = O ( N / B log M/B N / B ) I/Os, where M is the memory size and B is the disk block size. This bound is asymptotically optimal in the worst case. If there are union operations that join a set with itself, our algorithm uses O (SORT( N ) + MST( N )) I/Os, where MST( N ) is the number of I/Os needed to compute the minimum spanning tree of a graph with N edges. We also describe a simple and practical O (SORT( N ) log( N / M ))-I/O algorithm for this problem, which we have implemented. We are interested in the union-find problem because of its applications in terrain analysis. A terrain can be abstracted as a height function defined over R 2 , and many problems that deal with such functions require a union-find data structure. With the emergence of modern mapping technologies, huge amount of elevation data is being generated that is too large to fit in memory, thus I/O-efficient algorithms are needed to process this data efficiently. In this article, we study two terrain-analysis problems that benefit from a union-find data structure: (i) computing topological persistence and (ii) constructing the contour tree. We give the first O (SORT( N ))-I/O algorithms for these two problems, assuming that the input terrain is represented as a triangular mesh with N vertices.