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Compression of Correlated BitVectors
 Information Systems
, 1990
"... : Bitmaps are data structures occurring often in information retrieval. They are useful; they are also large and expensive to store. For this reason, considerable effort has been devoted to finding techniques for compressing them. These techniques are most effective for sparse bitmaps. We propose a ..."
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: Bitmaps are data structures occurring often in information retrieval. They are useful; they are also large and expensive to store. For this reason, considerable effort has been devoted to finding techniques for compressing them. These techniques are most effective for sparse bitmaps. We propose a preprocessing stage, in which bitmaps are first clustered and the clusters used to transform their member bitmaps into sparser ones, that can be more effectively compressed. The clustering method efficiently generates a graph structure on the bitmaps. In some situations, it is desired to impose restrictions on the graph; finding the optimal graph satisfying these restrictions is shown to be NPcomplete. The results of applying our algorithm to the Bible is presented: for some sets of bitmaps, our method almost doubled the compression savings. 1. Introduction Textual Information Retrieval Systems (IRS) are voracious consumers of computer storage resources. Most conspicuous, of course, is the...
A Flexible Algorithm For Generating All The Spanning Trees In Undirected Graphs
 Algorithmica
, 1997
"... . In this paper, we propose an algorithm for generating all the spanning trees in undirected graphs. The algorithm requires O(n + m + øn) time where the given graph has n vertices, m edges and ø spanning trees. For outputting all the spanning trees explicitly, this time complexity is optimal. Our a ..."
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. In this paper, we propose an algorithm for generating all the spanning trees in undirected graphs. The algorithm requires O(n + m + øn) time where the given graph has n vertices, m edges and ø spanning trees. For outputting all the spanning trees explicitly, this time complexity is optimal. Our algorithm follows a special rooted tree structure on the skeleton graph of the spanning tree polytope. The rule by which the rooted tree structure is traversed is irrelevant to the time complexity. In this sense, our algorithm is flexible. If we employ the depthfirst search rule, we can save the memory requirement to O(n + m): A breadthfirst implementation requires as much as O(m + øn) space, but when a parallel computer is available, this might have an advantage. When a given graph is weighted, the bestfirst search rule provides a ranking algorithm for the minimum spanning tree problem. The ranking algorithm requires O(n +m + øn) time and O(m + øn) space when we have a minimum spanning tr...
A Few Remarks On The History Of MSTProblem
, 1997
"... On the background of Boruvka's pioneering work we present a survey of the development related to the Minimum Spanning Tree Problem. We also complement the historical paper GrahamHell [GH] by a few remarks and provide an update of the extensive literature devoted to this problem. ..."
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Cited by 6 (0 self)
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On the background of Boruvka's pioneering work we present a survey of the development related to the Minimum Spanning Tree Problem. We also complement the historical paper GrahamHell [GH] by a few remarks and provide an update of the extensive literature devoted to this problem.
Optimal Algorithms to Find the Most Vital Edge of a Minimum Spanning Tree
, 1995
"... The problem of finding the most vital edge with respect to a minimum spanning tree of a given connected and weighted graph (with m edges and n vertices) is considered. New sequential and parallel algorithms (3 each) for the problem are proposed, and a lower bound\Omega\Gamma m) is established. We c ..."
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Cited by 3 (0 self)
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The problem of finding the most vital edge with respect to a minimum spanning tree of a given connected and weighted graph (with m edges and n vertices) is considered. New sequential and parallel algorithms (3 each) for the problem are proposed, and a lower bound\Omega\Gamma m) is established. We characterize the set of entering edges and show that the cardinality of this set is O(n). We show the connection between most vital edge problem and the minimum spanning tree update problems and exploit this idea in developing one of the proposed sequential algorithms. Two of our sequential algorithms are optimal. One of our parallel algorithms is optimal if the underlying graph is dense, or planar. We also consider a related problem for weighted matroids. Keywords: Data structures, design of algorithms, parallel algorithms, minimum spanning trees, most vital edge, complexity, matroids. 1 INTRODUCTION Networks are ubiquitous in many scientific and technological applications. A few examples ...
Finding Minimum Spanning Trees in O(m α(m,n)) Time
, 1999
"... We describe a deterministic minimum spanning tree algorithm running in time O(m α(m; n)), where α is a natural inverse of Ackermann's function and m and n are the number of edges and vertices, respectively. This improves upon the O(m α(m; n) log α(m; n)) bound established by Chazelle in 1997. ..."
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We describe a deterministic minimum spanning tree algorithm running in time O(m α(m; n)), where α is a natural inverse of Ackermann's function and m and n are the number of edges and vertices, respectively. This improves upon the O(m α(m; n) log α(m; n)) bound established by Chazelle in 1997. A similar O(m α(m; n))time algorithm was discovered independently by Chazelle, predating the algorithm presented here by many months. This paper may still be of interest for its alternative exposition.
A Linear Time Algorithm for the Minimum Spanning Tree Problem on a Planar Graph
, 1994
"... : In this paper, we propose a linear time algorithm for finding a minimum spanning tree on a planar graph. Keywords: Combinatorial problems; graphs; spanning trees; planar graphs 1 Introduction Finding a spanning tree of minimum weight is one of the best known graph problems. Several efficient algor ..."
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: In this paper, we propose a linear time algorithm for finding a minimum spanning tree on a planar graph. Keywords: Combinatorial problems; graphs; spanning trees; planar graphs 1 Introduction Finding a spanning tree of minimum weight is one of the best known graph problems. Several efficient algorithms exist for solving this problem [1, 3, 4, 5, 6, 9, 11, 13]. This paper presents a liner time algorithm for the minimum spanning tree problem on a planar graph. In [1], Cheriton and Tarjan have proposed a linear time algorithm for this problem. The time complexity of our algorithm is the same as that of Cheriton and Tarjan's algorithm. Different from Cheriton and Tarjan's algorithm, our algorithm does not require the cleanup activity. So, the implementation of our algorithm is very easy. Our algorithm maintains a pair of a planar graph and its dual graph and breeds both a minimum spanning tree of original graph and a maximum spanning tree of a dual graph. In each iteration of our algor...