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18
Nearest Common Ancestors: A survey and a new distributed algorithm
, 2002
"... Several papers describe linear time algorithms to preprocess a tree, such that one can answer subsequent nearest common ancestor queries in constant time. Here, we survey these algorithms and related results. A common idea used by all the algorithms for the problem is that a solution for complete ba ..."
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Cited by 76 (12 self)
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Several papers describe linear time algorithms to preprocess a tree, such that one can answer subsequent nearest common ancestor queries in constant time. Here, we survey these algorithms and related results. A common idea used by all the algorithms for the problem is that a solution for complete balanced binary trees is straightforward. Furthermore, for complete balanced binary trees we can easily solve the problem in a distributed way by labeling the nodes of the tree such that from the labels of two nodes alone one can compute the label of their nearest common ancestor. Whether it is possible to distribute the data structure into short labels associated with the nodes is important for several applications such as routing. Therefore, related labeling problems have received a lot of attention recently.
Verification and Sensitivity Analysis Of Minimum Spanning Trees In Linear Time
 SIAM J. Comput
, 1992
"... . Koml'os has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree. The total computational work required by his method is much larger than linear, however. We describe a lineartime algorithm for verif ..."
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Cited by 54 (2 self)
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. Koml'os has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree. The total computational work required by his method is much larger than linear, however. We describe a lineartime algorithm for verifying a minimum spanning tree. Our algorithm combines the result of Koml'os with a preprocessing and table lookup method for small subproblems and with a previously known almostlineartime algorithm. Additionally, we present an optimal deterministic algorithm and a lineartime randomized algorithm for sensitivity analysis of minimum spanning trees. 1. Introduction. Suppose we wish to solve some problem for which we know in advance the size of the input data, using an algorithm from some welldefined class of algorithms. For example, consider sorting n numbers, when n is fixed in advance, using a binary comparison tree. Given a sufficient amount of preprocessing time and storage space, we ca...
Inequalities for quantum entropy. A review with conditions with equality
"... This paper presents selfcontained proofs of the strong subadditivity inequality for von Neumann’s quantum entropy, S(ρ), and some related inequalities for the quantum relative entropy, most notably its convexity and its monotonicity under stochastic maps. Moreover, the approach presented here, whic ..."
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Cited by 33 (7 self)
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This paper presents selfcontained proofs of the strong subadditivity inequality for von Neumann’s quantum entropy, S(ρ), and some related inequalities for the quantum relative entropy, most notably its convexity and its monotonicity under stochastic maps. Moreover, the approach presented here, which is based on Klein’s inequality and Lieb’s theorem that the function A → Tr e K+log A is concave, allows one to obtain conditions for equality. In the case of strong subadditivity, which states that S(ρ123)+S(ρ2) ≤ S(ρ12) + S(ρ23) where the subscripts denote subsystems of a composite system, equality holds if and only if log ρ123 = log ρ12 − log ρ2 + log ρ23. Using the fact that the Holevo bound on the accessible information in a quantum ensemble can be obtained as a consequence of the monotonicity of relative entropy, we show that equality can be attained for that bound only when the states in the ensemble commute. The paper concludes with an Appendix giving a short description of Epstein’s elegant proof of Lieb’s
A linearwork parallel algorithm for finding . . .
, 1994
"... We give the first linearwork parallel algorithm for finding a minimum spanning tree. It is a randomized algorithm, and requires O(2log \Lambda n log n) expected time. It is a modification of the sequential lineartime algorithm of Klein and Tarjan. ..."
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Cited by 14 (1 self)
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We give the first linearwork parallel algorithm for finding a minimum spanning tree. It is a randomized algorithm, and requires O(2log \Lambda n log n) expected time. It is a modification of the sequential lineartime algorithm of Klein and Tarjan.
Providing Motor Impaired Users with Access to Standard Graphical User Interface (GUI) Software via Eyebased Interaction
 Proceedings of the 1st European Conference on Disability, Virtual Reality and Associated Technologies (ECDVRAT ’96
, 1996
"... We have designed an onscreen keyboard, operated by eyegaze, for use by motorimpaired users. It enables interaction with unmodified standard Graphic User Interface (GUI) software written for ablebodied users, and it is not solely designed around the need to enter text. The keyboard will adapt auto ..."
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Cited by 9 (0 self)
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We have designed an onscreen keyboard, operated by eyegaze, for use by motorimpaired users. It enables interaction with unmodified standard Graphic User Interface (GUI) software written for ablebodied users, and it is not solely designed around the need to enter text. The keyboard will adapt automatically to the application context by, for example, loading a specific set of keys designed for use with particular menus whenever a menu is displayed in the target application. Results of initial evaluation trials are presented and the implications for improvements in design are discussed.
Identifying Nearest Common Ancestors in a Distributed Environment
, 2001
"... We give a simple algorithm that labels the nodes of a rooted tree such that from the labels of two nodes alone one can compute in constant time the label of their nearest common ancestor. The labels assigned by our algorithm are of size O(log n) bits where n is the number of nodes in the tree. The a ..."
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Cited by 7 (2 self)
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We give a simple algorithm that labels the nodes of a rooted tree such that from the labels of two nodes alone one can compute in constant time the label of their nearest common ancestor. The labels assigned by our algorithm are of size O(log n) bits where n is the number of nodes in the tree. The algorithm runs in O(n) time.
Factors Determining the Failure of Global Systems
 in the Air Cargo Community”, Proc Conf “HICSS29"—29th Hawaii International Conference on Systems Sciences, Maui
, 1996
"... Air cargo parties are becoming increasingb aware of the ..."
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Cited by 3 (0 self)
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Air cargo parties are becoming increasingb aware of the
MUON COLLIDERS
"... Abstract. Muon CoUiders have unique technical and physics advantages and disadvantages when compared with both hadron and electron machines. They should thus be regarded as complementary. Parameters are given of 4 TeV and 0.5 TeV high luminosity p+ttcolliders, and of a 0.5 TeV lower luminosity demo ..."
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Cited by 1 (0 self)
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Abstract. Muon CoUiders have unique technical and physics advantages and disadvantages when compared with both hadron and electron machines. They should thus be regarded as complementary. Parameters are given of 4 TeV and 0.5 TeV high luminosity p+ttcolliders, and of a 0.5 TeV lower luminosity demonstration machine. We discuss the various systems in such muon colliders, starting from the proton accelerator needed to generate the muons and proceeding through muon cooling, acceleration and storage in a collider ring. Problems of detector background are also discussed.