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368
Approximating cycles in a shortest basis of the first homology group from point data. Inverse Problems
, 2012
"... Inference of topological and geometric attributes of a hidden manifold from its point data is a fundamental problem arising in many scientific studies and engineering applications. In this paper we present an algorithm to compute a set of cycles from a point data that presumably sample a smooth mani ..."
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Cited by 4 (4 self)
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manifold M ⊂ R d. These cycles approximate a shortest basis of the first homology group H1(M) over coefficients in finite field Z2. Previous results addressed the issue of computing the rank of the homology groups from point data, but there is no result on approximating the shortest basis of a manifold
Minimal realizations of linear systems: The “shortest Basis” approach. Preprint 2009. ArXiv: 0910.4336
"... ar ..."
PowerAware Localized Routing in Wireless Networks
, 2000
"... Recently, a cost aware metric for wireless networks based on remaining battery power at nodes was proposed for shortestcost routing algorithms, assuming constant transmission power. Power aware metrics where transmission power depends on distance between nodes, and corresponding shortestpower algo ..."
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Cited by 298 (33 self)
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Recently, a cost aware metric for wireless networks based on remaining battery power at nodes was proposed for shortestcost routing algorithms, assuming constant transmission power. Power aware metrics where transmission power depends on distance between nodes, and corresponding shortest
Approximating loops in a shortest homology basis from point data
 arXiv:0909.5654v2[cs.CG] (2009), Online. URL http://arxiv.org/abs/0909.5654
"... Inference of topological and geometric attributes of a hidden manifold from its point data is a fundamental problem arising in many scientific studies and engineering applications. In this paper we present an algorithm to compute a set of loops from a point data that presumably sample a smooth manif ..."
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Cited by 12 (4 self)
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manifold M ⊂ R d. These loops approximate a shortest basis of the one dimensional homology group H1(M) over coefficients in finite field Z2. Previous results addressed the issue of computing the rank of the homology groups from point data, but there is no result on approximating the shortest basis of a
Congestionoriented shortest multipath routing
, 1995
"... We present a framework for the modeling of multipath routing in connectionless networks that dynamically adapt to network congestion. The basic routing protocol uses a shortterm metric based on hopbyhop credits to reduce congestion over a given link, and a longterm metric based on endtoend pa ..."
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Cited by 38 (0 self)
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permitbucket filter is used at each router to regulate traffic flow on a per destination basis, and all paths are loop free. The shortest multipath routing protocol regulates the parameters of the destinationoriented permit buckets and guarantees that all portions of a multipath are loop free. 1.
Balancing Minimum Spanning and Shortest Path Trees
, 1993
"... Efficient algorithms are known for computing a minimum spann.ing tree, or a shortest path. tree (with a fixed vertex as the root). The weight of a shortest path tree can be much more than the weight of a minimum spa,nning tree. Conversely, the distance bet,ween the root, and any vertex in a minimum ..."
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Cited by 65 (1 self)
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Efficient algorithms are known for computing a minimum spann.ing tree, or a shortest path. tree (with a fixed vertex as the root). The weight of a shortest path tree can be much more than the weight of a minimum spa,nning tree. Conversely, the distance bet,ween the root, and any vertex in a minimum
Shortest Vector Problem
, 2003
"... The Shortest Vector Problem (SVP) is the most famous and widely studied computational problem on lattices. Given a lattice L (typically represented by a basis), SVP asks to find the shortest nonzero vector in L. The problem can be defined with respect to any norm, but the Euclidean norm is the most ..."
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The Shortest Vector Problem (SVP) is the most famous and widely studied computational problem on lattices. Given a lattice L (typically represented by a basis), SVP asks to find the shortest nonzero vector in L. The problem can be defined with respect to any norm, but the Euclidean norm is the most
Trapdoors for Hard Lattices and New Cryptographic Constructions
, 2007
"... We show how to construct a variety of “trapdoor ” cryptographic tools assuming the worstcase hardness of standard lattice problems (such as approximating the shortest nonzero vector to within small factors). The applications include trapdoor functions with preimage sampling, simple and efficient “ha ..."
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Cited by 191 (26 self)
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We show how to construct a variety of “trapdoor ” cryptographic tools assuming the worstcase hardness of standard lattice problems (such as approximating the shortest nonzero vector to within small factors). The applications include trapdoor functions with preimage sampling, simple and efficient
On finding a cycle basis with a shortest maximal cycle
, 1995
"... The Shortest Maximal Cycle Basis (SMCB) problem is that of nding a cycle basis B of a given graph G such that the length of the longest cycle included in B is the smallest among all bases of G. We show that any cycle basis B 0 of G such that the sum of the lengths of the cycles included in B 0 is th ..."
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Cited by 12 (0 self)
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The Shortest Maximal Cycle Basis (SMCB) problem is that of nding a cycle basis B of a given graph G such that the length of the longest cycle included in B is the smallest among all bases of G. We show that any cycle basis B 0 of G such that the sum of the lengths of the cycles included in B 0
A Shortest 2Basis for Boolean Algebra in Terms of the Sheffer Stroke
 J. Automated Reasoning
, 2003
"... In this article, we present a short 2basis for Boolean algebra in terms of the Sheffer stroke and prove that no such 2basis can be shorter. We also prove that the new 2basis is unique (for its length) up to applications of commutativity. Our proof of the 2basis was found by using the method of p ..."
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Cited by 8 (5 self)
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In this article, we present a short 2basis for Boolean algebra in terms of the Sheffer stroke and prove that no such 2basis can be shorter. We also prove that the new 2basis is unique (for its length) up to applications of commutativity. Our proof of the 2basis was found by using the method
Results 1  10
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368