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Fast SharedMemory Algorithms for Computing the Minimum Spanning Forest of Sparse Graphs
, 2006
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Engineering an External Memory Minimum Spanning Tree Algorithm
 IN PROC. 3RD IFIP INTL. CONF. ON THEORETICAL COMPUTER SCIENCE
, 2004
"... We develop an external memory algorithm for computing minimum spanning trees. The algorithm is considerably simpler than previously known external memory algorithms for this problem and needs a factor of at least four less I/Os for realistic inputs. Our implementation indicates that this algorithm ..."
Abstract

Cited by 14 (3 self)
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We develop an external memory algorithm for computing minimum spanning trees. The algorithm is considerably simpler than previously known external memory algorithms for this problem and needs a factor of at least four less I/Os for realistic inputs. Our implementation indicates that this algorithm processes graphs only limited by the disk capacity of most current machines in time no more than a factor 2–5 of a good internal algorithm with sufficient memory space.
Optimal incremental sorting
 In Proc. 8th Workshop on Algorithm Engineering and Experiments (ALENEX
, 2006
"... Let A be a set of size m. Obtaining the first k ≤ m elements of A in ascending order can be done in optimal O(m+k log k) time. We present an algorithm (online on k) which incrementally gives the next smallest element of the set, so that the first k elements are obtained in optimal time for any k. We ..."
Abstract

Cited by 7 (5 self)
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Let A be a set of size m. Obtaining the first k ≤ m elements of A in ascending order can be done in optimal O(m+k log k) time. We present an algorithm (online on k) which incrementally gives the next smallest element of the set, so that the first k elements are obtained in optimal time for any k. We also give a practical algorithm with the same complexity on average, which improves in practice the existing online algorithm. As a direct application, we use our technique to implement Kruskal’s Minimum Spanning Tree algorithm, where our solution is competitive with the best current implementations. We finally show that our technique can be applied to several other problems, such as obtaining an interval of the sorted sequence and implementing heaps. 1
The filterkruskal minimum spanning tree algorithm
, 2009
"... We present FilterKruskal – a simple modification of Kruskal’s algorithm that avoids sorting edges that are “obviously” not in the MST. For arbitrary graphs with random edge weights FilterKruskal runs in time O (m + n lognlog m n, i.e. in linear time for not too sparse graphs. Experiments indicate ..."
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Cited by 6 (0 self)
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We present FilterKruskal – a simple modification of Kruskal’s algorithm that avoids sorting edges that are “obviously” not in the MST. For arbitrary graphs with random edge weights FilterKruskal runs in time O (m + n lognlog m n, i.e. in linear time for not too sparse graphs. Experiments indicate that the algorithm has very good practical performance over the entire range of edge densities. An equally simple parallelization seems to be the currently best practical algorithm on multicore machines.
On sorting, heaps, and minimum spanning trees
 Algorithmica
"... Let A be a set of size m. Obtaining the first k ≤ m elements of A in ascending order can be done in optimal O(m + k log k) time. We present Incremental Quicksort (IQS), an algorithm (online on k) which incrementally gives the next smallest element of the set, so that the first k elements are obtaine ..."
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Cited by 1 (1 self)
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Let A be a set of size m. Obtaining the first k ≤ m elements of A in ascending order can be done in optimal O(m + k log k) time. We present Incremental Quicksort (IQS), an algorithm (online on k) which incrementally gives the next smallest element of the set, so that the first k elements are obtained in optimal expected time for any k. Based on IQS, we present the Quickheap (QH), a simple and efficient priority queue for main and secondary memory. Quickheaps are comparable with classical binary heaps in simplicity, yet are more cachefriendly. This makes them an excellent alternative for a secondary memory implementation. We show that the expected amortized CPU cost per operation over a Quickheap of m elements is O(log m), and this translates into O((1/B)log(m/M)) I/O cost with main memory size M and block size B, in a cacheoblivious fashion. As a direct application, we use our techniques to implement classical Minimum Spanning Tree (MST) algorithms. We use IQS to implement Kruskal’s MST algorithm and QHs to implement Prim’s. Experimental results show that IQS, QHs, external QHs, and our Kruskal’s and Prim’s MST variants are competitive, and in many cases better in practice than current stateoftheart alternative (and much more sophisticated) implementations.
PROTOTYPE TO DESIGN A LEASED LINE TELEPHONE NETWORK CONNECTING LOCATIONS TO MINIMIZE THE INSTALLATION COST Abstract
"... Network flows have many reallife applications and leasedline installation for telephone network is one of them. In the leased line a major concern is to provide connection of telephone to all the locations. It is required to install the leased line network that reaches all the locations at the min ..."
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Network flows have many reallife applications and leasedline installation for telephone network is one of them. In the leased line a major concern is to provide connection of telephone to all the locations. It is required to install the leased line network that reaches all the locations at the minimum cost. This chapter deals with this situation with the help of a network diagram in which each node represents the locations and the edge between each node represents leased line. Each edge has a number attached to it which represents the cost associated with installing that link. Aim of the paper is to determine the leased line network connecting all the locations at minimum cost of installation.
Clustering the Labeled and Unlabeled Datasets using New MST based Divide and Conquer Technique
"... Abstract: Clustering is the process of partitioning the data set into subsets called clusters, so that the data in each subset share some properties in common. Clustering is an important tool to explore the hidden structures of modern large Databases. Because of the huge variety of the problems and ..."
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Abstract: Clustering is the process of partitioning the data set into subsets called clusters, so that the data in each subset share some properties in common. Clustering is an important tool to explore the hidden structures of modern large Databases. Because of the huge variety of the problems and data distributions, different classical clustering algorithms, such as hierarchical, partitional, densitybased and modelbased clustering approaches, have been developed and no techniques are completely satisfactory for all the cases. Sufficient empirical evidences have shown that a New Minimum Spanning Tree (NMST) representation is quite invariant to the detailed geometric changes in cluster boundaries. Therefore, the shape of a cluster has little impact on the performance of MST based clustering algorithms, which allows us to overcome many of the problems faced by the classical clustering algorithms. NMSTbased clustering algorithms also have the ability to detect clusters with irregular boundaries and so they are being widely used in practice. In these MST based clustering algorithms, search for nearest neighbour is to be done in the construction of NMST. This search is the main source of computation and the standard solutions take O(N 2) time. In our paper, we present a fast minimum spanning treeinspired clustering algorithm. This algorithm uses an efficient implementation of the cut and the cycle property of the NMST, that can have much better performance than O(N 2) time.