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Online Network Optimization Problems
 In Developments from a
, 1998
"... . We survey results on online versions of the standard network optimization problems, including the minimum spanning tree problem, the minimum Steiner tree problem, the weighted and unweighted matching problems, and the traveling salesman problem. The goal in these problems is to maintain, with mini ..."
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. We survey results on online versions of the standard network optimization problems, including the minimum spanning tree problem, the minimum Steiner tree problem, the weighted and unweighted matching problems, and the traveling salesman problem. The goal in these problems is to maintain, with minimal changes, a low cost subgraph of some type in a dynamically changing network. 1 Introduction In the early 1920's Otakar Bor uvka was asked by the Electric Power Company of Western Moravia (EPCWM) to assist in EPCWM's electrification of southern Moravia by solving from a mathematical standpoint the question of how to construct the most economical electric power network [9]. In 1926 Bor uvka initiated the study of network optimization problems, by publishing an efficient algorithm for constructing a minimum spanning tree of a fixed network [9]. Certainly since the 1920's the underlying collection of sites that require electrification in southern Moravia has changed frequently as new sites ...
A learning automatabased heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs
, 2010
"... During the last decades, a host of efficient algorithms have been developed for solving the minimum spanning tree problem in deterministic graphs, where the weight associated with the graph edges is assumed to be fixed. Though it is clear that the edge weight varies with time in realistic applicatio ..."
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During the last decades, a host of efficient algorithms have been developed for solving the minimum spanning tree problem in deterministic graphs, where the weight associated with the graph edges is assumed to be fixed. Though it is clear that the edge weight varies with time in realistic applications and such an assumption is wrong, finding the minimum spanning tree of a stochastic graph has not received the attention it merits. This is due to the fact that the minimum spanning tree problem becomes incredibly hard to solve when the edge weight is assumed to be a random variable. This becomes more difficult, if we assume that the probability distribution function of the edge weight is unknown. In this paper, we propose a learning automata‐based heuristic algorithm to solve the minimum spanning tree problem in stochastic graphs wherein the probability distribution function of the edge weight is unknown. The proposed algorithm taking advantage of learning automata determines the edges that must be sampled at each stage. As the presented algorithm proceeds, the sampling process is concentrated on the edges that constitute the spanning tree with the minimum expected weight. The proposed learning automata‐based sampling method decreases the number of samples that need to be taken from the graph by reducing the rate of unnecessary samples. Experimental results show the superiority of the proposed algorithm over the well‐known existing methods both in terms of the number of samples and the running time of algorithm.
An Autonomous and Decentralized Protocol for Delay Sensitive Overlay Multicast Tree
 Proc. of ICDCS’04
, 2004
"... In this paper, we present a protocol for dynamically maintaining a degreebounded delay sensitive spanning tree in a decentralized way on overlay networks. The protocol aims at repairing the spanning tree autonomously even if multiple nodes ’ leave operations or failures (disappearances) occur simul ..."
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In this paper, we present a protocol for dynamically maintaining a degreebounded delay sensitive spanning tree in a decentralized way on overlay networks. The protocol aims at repairing the spanning tree autonomously even if multiple nodes ’ leave operations or failures (disappearances) occur simultaneously or continuously in a specified period. It also aims at maintaining the diameter (maximum delay) of the tree as small as possible. The simulation results using ns2 have shown that the protocol could keep reasonable diameters compared with the existing centralized static algorithm even if many nodes ’ participations and disappearances occur frequently. 1
Excavator: a computer program for efficiently mining gene expression data
 Nucleic Acids Research
, 2003
"... Massive geneexpression data are generated using microarrays, and clustering geneexpression data is useful for studying functional relationship among genes in a biological process. We have developed a computer package, EXCAVATOR ..."
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Cited by 6 (0 self)
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Massive geneexpression data are generated using microarrays, and clustering geneexpression data is useful for studying functional relationship among genes in a biological process. We have developed a computer package, EXCAVATOR
Two Linear Time Algorithms for MST on Minor Closed Graph Classes
, 2002
"... This article presents two simple deterministic algorithms for finding the Minimum Spanning Tree in O(V + E) time for any proper class of graphs closed on graph minors, which includes planar graphs and graphs of bounded genus. Both algorithms require no a priori knowledge of the structure of th ..."
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This article presents two simple deterministic algorithms for finding the Minimum Spanning Tree in O(V + E) time for any proper class of graphs closed on graph minors, which includes planar graphs and graphs of bounded genus. Both algorithms require no a priori knowledge of the structure of the class except for its density; edge weights are only compared and no random access to data is needed.
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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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.
The Diameter of the Minimum Spanning Tree of a Complete Graph
"... } be independent identically distributed weights for the edges of Kn. If Xi � = Xj for i � = j, then ..."
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} be independent identically distributed weights for the edges of Kn. If Xi � = Xj for i � = j, then
Randomized Minimum Spanning Tree Algorithms Using Exponentially Fewer Random Bits
"... For many fundamental problems there exist randomized algorithms that are asymptotically optimal and are superior to the best known deterministic algorithm. Among these are the minimum spanning tree (MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel mi ..."
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Cited by 5 (1 self)
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For many fundamental problems there exist randomized algorithms that are asymptotically optimal and are superior to the best known deterministic algorithm. Among these are the minimum spanning tree (MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel minimum spanning tree problems, and the local sorting and set maxima problems. (For the first two problems there are provably optimal deterministic algorithms with unknown, and possibly superlinear running times.) One downside of the randomized methods for solving these problems is that they use a number of random bits linear in the size of the input. In this paper we develop some general methods for reducing exponentially the consumption of random bits in comparison based algorithms. In some cases we are able to reduce the number of random bits from linear to nearly constant without affecting the expected running time. Most of our results are obtained by adjusting or reorganizing existing randomized algorithms to work well with a pairwise or O(1)wise independent sampler. The prominent exception — and the main focus of this paper — is a lineartime randomized minimum spanning tree algorithm that is not derived from the well known KargerKleinTarjan algorithm. In many ways it resembles more closely the deterministic minimum spanning tree algorithms based on Soft Heaps. Further,