Results 1  10
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24
SEMIRING FRAMEWORKS AND ALGORITHMS FOR SHORTESTDISTANCE PROBLEMS
, 2002
"... We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorit ..."
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Cited by 73 (20 self)
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We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the kshortest distances in a directed graph. It can be used to solve singlesource shortestdistance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.
Parameter Estimation for Probabilistic FiniteState Transducers
 Proc. of the Annual Meeting of the Association for Computational Linguistics
, 2002
"... Weighted finitestate transducers suffer from the lack of a training algorithm. Training is even harder for transducers that have been assembled via finitestate operations such as composition, minimization, union, concatenation, and closure, as this yields tricky parameter tying. We formulate a &qu ..."
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Cited by 49 (4 self)
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Weighted finitestate transducers suffer from the lack of a training algorithm. Training is even harder for transducers that have been assembled via finitestate operations such as composition, minimization, union, concatenation, and closure, as this yields tricky parameter tying. We formulate a "parameterized FST" paradigm and give training algorithms for it, including a general bookkeeping trick ("expectation semirings") that cleanly and efficiently computes expectations and gradients.
Graph Kernels
, 2007
"... We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexit ..."
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Cited by 40 (4 self)
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We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n 6) to O(n 3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixedpoint methods that take O(dn 3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for ddimensional edge kernels, and O(n 4) in the infinitedimensional case; on sparse graphs these algorithms only take O(n 2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to Rconvolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semidefinite.
The correspondence principle for Idempotent Calculus and some computer applications // Gunawardena
 Idempotency: Publ. of the I. Newton Institute
, 1998
"... This paper is devoted to heuristic aspects of the socalled idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers ..."
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Cited by 36 (16 self)
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This paper is devoted to heuristic aspects of the socalled idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers
Algorithmic Aspects of Symbolic Switch Network Analysis
 IEEE Trans. CAD/IC
, 1987
"... A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean eq ..."
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Cited by 16 (5 self)
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A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean equations. For the class of networks that arise when analyzing digital metaloxide semiconductor (MOS) circuits, a simple pivot selection rule guarantees that most s switch networks encountered in practice can be solved with O(s) operations. When represented by a directed acyclic graph, the set of Boolean formulas generated by the analysis has total size bounded by the number of operations required by the Gaussian elimination. This paper presents the mathematical basis for systems of Boolean equations, their solution by Gaussian elimination, and data structures and algorithms for representing and manipulating Boolean formulas.
Efficient computation of the relative entropy of probabilistic automata
 In LATIN’06, LNCS 3887
, 2006
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On the computation of the relative entropy of probabilistic automata
 Int. J. Found. Comput. Sci
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A unified construction of the Glushkov, Follow, and Antimirov automata
 In Proceedings of MFCS’06, volume 4162 of LNCS
, 2006
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