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23
Ambivalent Data Structures For Dynamic 2EdgeConnectivity And k Smallest Spanning Trees
 SIAM J. Comput
, 1991
"... . Ambivalent data structures are presented for several problems on undirected graphs. These data structures are used in finding the k smallest spanning trees of a weighted undirected graph in O(m log #(m, n) + min{k 3/2 ,km 1/2 }) time, where m is the number of edges and n the number of vertice ..."
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Cited by 83 (1 self)
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. Ambivalent data structures are presented for several problems on undirected graphs. These data structures are used in finding the k smallest spanning trees of a weighted undirected graph in O(m log #(m, n) + min{k 3/2 ,km 1/2 }) time, where m is the number of edges and n the number of vertices in the graph. The techniques are extended to find the k smallest spanning trees in an embedded planar graph in O(n + k(log n) 3 ) time. Ambivalent data structures are also used to dynamically maintain 2edgeconnectivity information. Edges and vertices can be inserted or deleted in O(m 1/2 ) time, and a query as to whether two vertices are in the same 2edgeconnected component can be answered in O(log n) time, where m and n are understood to be the current number of edges and vertices, respectively. Key words. analysis of algorithms, data structures, embedded planar graph, fully persistent data structures, k smallest spanning trees, minimum spanning tree, online updating, topology tr...
Combinatorial algorithms for DNA sequence assembly
 Algorithmica
, 1993
"... The trend towards very large DNA sequencing projects, such as those being undertaken as part of the human genome initiative, necessitates the development of efficient and precise algorithms for assembling a long DNA sequence from the fragments obtained by shotgun sequencing or other methods. The seq ..."
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Cited by 42 (3 self)
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The trend towards very large DNA sequencing projects, such as those being undertaken as part of the human genome initiative, necessitates the development of efficient and precise algorithms for assembling a long DNA sequence from the fragments obtained by shotgun sequencing or other methods. The sequence reconstruction problem that we take as our formulation of DNA sequence assembly is a variation of the shortest common superstring problem, complicated by the presence of sequencing errors and reverse complements of fragments. Since the simpler superstring problem is NPhard, any efficient reconstruction procedure must resort to heuristics. In this paper, however, a four phase approach based on rigorous design criteria is presented, and has been found to be very accurate in practice. Our method is robust in the sense that it can accommodate high sequencing error rates and list a series of alternate solutions in the event that several appear equally good. Moreover it uses a limited form ...
Algorithms for Enumerating All Spanning Trees of Undirected and Weighted Graphs
 SIAM J. Comput
, 1995
"... In this paper, we present algorithms for enumeration of spanning trees in undirected graphs, with and without weights. ..."
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Cited by 21 (0 self)
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In this paper, we present algorithms for enumeration of spanning trees in undirected graphs, with and without weights.
Finding the k Smallest Spanning Trees
, 1992
"... We give improved solutions for the problem of generating the k smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes time O(m log #(m, n)+k 2 ); for planar graphs this bound can be improved to O(n + k 2 ). We also show that the k best spanning trees for a set of ..."
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Cited by 18 (2 self)
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We give improved solutions for the problem of generating the k smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes time O(m log #(m, n)+k 2 ); for planar graphs this bound can be improved to O(n + k 2 ). We also show that the k best spanning trees for a set of points in the plane can be computed in time O(min(k 2 n + n log n, k 2 + kn log(n/k))). The k best orthogonal spanning trees in the plane can be found in time O(n log n + kn log log(n/k)+k 2 ).
Symbolic Analysis of Large Analog Integrated Circuits By Approximation During Expression Generation
, 1994
"... A novel algorithm is presented that generates approximate symbolic expressions for smallsignal characteristics of large analog integrated circuits. The method is based upon the approximation of an expression while it is being computed. The CPU time and memory requirements are reduced drastically wi ..."
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Cited by 9 (1 self)
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A novel algorithm is presented that generates approximate symbolic expressions for smallsignal characteristics of large analog integrated circuits. The method is based upon the approximation of an expression while it is being computed. The CPU time and memory requirements are reduced drastically with regard to previous approaches, as only those terms are calculated which will remain in the final expression. As a consequence, the maximum circuit size amenable to symbolic analysis has largely increased. The simplification procedure explicitly takes into account variation ranges of the symbolic parameters to avoid inaccuracies of conventional approaches which use a single value. The new approach is also able to take into account mismatches between the symbolic parameters. INTRODUCTION Symbolic circuit analysis refers to the calculation of network functions H(s,x) in the form: (1) where x T ={x 1 , x 2 , . . . x Q } is the vector of circuit parameters which remain as symbols, and the...
A Branch and Bound Algorithm for the Robust Spanning Tree Problem With Interval Data
, 2002
"... The robust spanning tree problem is a variation, motivated by telecommunications applications, of the classic minimum spanning tree problem. In the robust spanning tree problem edge costs are interval numbers instead of fixed values. ..."
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Cited by 8 (2 self)
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The robust spanning tree problem is a variation, motivated by telecommunications applications, of the classic minimum spanning tree problem. In the robust spanning tree problem edge costs are interval numbers instead of fixed values.
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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Cited by 6 (0 self)
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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...
An Algorithm for Enumerating All Spanning Trees of a Directed Graph
 Algorithmica
, 2000
"... We present an O(NV +V ) time algorithm for enumerating all spanning trees of a directed graph. This improves the previous best known bound of O(NE +V +E) ([1]) when V = o(N ), which will be true for most graphs. Here, N refers to the number of spanning trees of a graph having V vertices and ..."
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Cited by 5 (0 self)
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We present an O(NV +V ) time algorithm for enumerating all spanning trees of a directed graph. This improves the previous best known bound of O(NE +V +E) ([1]) when V = o(N ), which will be true for most graphs. Here, N refers to the number of spanning trees of a graph having V vertices and E edges. The algorithm is based on the technique of obtaining one spanning tree from another by a series of edge swaps. This result complements the result in the companion paper ([2]) which enumerates all spanning trees in an undirected graph in O(N + V +E) time.
Applying General Bayesian Techniques to Improve TAN Induction
 In Proceedings of the International Conference on Knowledge Discovery and Data Mining
, 1999
"... Tree Augmented Naive Bayes (TAN) has shown to be competitive with stateoftheart machine learning algorithms [9]. However, the TAN induction algorithm that appears in [9] can be improved in several ways. In this paper we identify three weak points in it and introduce two ideas to overcome those pro ..."
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Cited by 4 (3 self)
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Tree Augmented Naive Bayes (TAN) has shown to be competitive with stateoftheart machine learning algorithms [9]. However, the TAN induction algorithm that appears in [9] can be improved in several ways. In this paper we identify three weak points in it and introduce two ideas to overcome those problems: the multinomial sampling approach to learning bayesian networks and local bayesian model averaging. These ideas are generic and can thus be reused to improve other learning algorithms. We empirically test the new algorithms, and conclude that in many cases they lead to an improvement in accuracy in the classification and in the quality of the probabilities given as predictions.
Reliability in Layered Networks with Random Link Failures
"... Abstract—We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the ..."
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Cited by 4 (0 self)
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Abstract—We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the multilayer setting. Using random sampling techniques, we develop polynomial time approximation algorithms for the failure polynomial. Our approach gives an approximate expression for reliability as a function of the link failure probability, eliminating the need to resample for different values of the failure probability. Furthermore, it gives insight on how the routings of the logical topology on the physical topology impact network reliability. We show that maximizing the min cut of the (layered) network maximizes reliability in the low failure probability regime. Based on this observation, we develop algorithms for routing the logical topology to maximize reliability. I.