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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 72 (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.
A Logic for Graphs with QoS
 VODCA 2004 PRELIMINARY VERSION
, 2004
"... We introduce a simple graph logic that supports specification of Quality of Service (QoS) properties of applications. The idea is that we are not only interested in representing whether two sites are connected, but we want to express the QoS level of the connection. The evaluation of a formula in th ..."
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Cited by 6 (3 self)
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We introduce a simple graph logic that supports specification of Quality of Service (QoS) properties of applications. The idea is that we are not only interested in representing whether two sites are connected, but we want to express the QoS level of the connection. The evaluation of a formula in the graph logic is a value of a suitable algebraic structure, a csemiring, representing the QoS level of the formula and not just a boolean value expressing whether or not the formula holds. We present some examples and briefly discuss the expressiveness and complexity of our logic.
Expectation Semirings: Flexible EM for Learning FiniteState Transducers
, 2001
"... This paper offers a clean way to combine the two traditions: an ExpectationMaximation (EM) [4] algorithm for training arbitrary FSTs. First the human expert uses domain knowledge to specify the topology and parameterization of the transducer in any convenient way. Then the EM algorithm automaticall ..."
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Cited by 5 (0 self)
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This paper offers a clean way to combine the two traditions: an ExpectationMaximation (EM) [4] algorithm for training arbitrary FSTs. First the human expert uses domain knowledge to specify the topology and parameterization of the transducer in any convenient way. Then the EM algorithm automatically chooses parameter values that (locally) maximize the joint likelihood of fully or partly observed data
2009b) Generating Contenders
"... In Optimality Theory, a contender is a candidate that is optimal under some ranking of the constraints. When the candidate generating function Gen and all of the constraints are rational (i.e., representable with (weighted) finite state automata) it is possible to generate the entire set of contende ..."
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Cited by 3 (3 self)
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In Optimality Theory, a contender is a candidate that is optimal under some ranking of the constraints. When the candidate generating function Gen and all of the constraints are rational (i.e., representable with (weighted) finite state automata) it is possible to generate the entire set of contenders for a given input form in much the same way that optima for a single ranking are generated. This paper gives a brief introduction to rational constraints and provides an algorithm for generating contenders whose complexity, modulo the number of contenders generated, is linear in the length of the underlying form with a multiplicative constant representing the size of the finitestate representation of the constraint set. 1
Violation Semirings in Optimality Theory
"... This paper provides a brief algebraic characterization of constraint violations in Optimality Theory (OT). I show that if violations are taken to be multisets over a fixed basis set Con then the merge operator on multisets and a ‘min ’ operation expressed in terms of harmonic inequality provide a se ..."
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Cited by 1 (1 self)
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This paper provides a brief algebraic characterization of constraint violations in Optimality Theory (OT). I show that if violations are taken to be multisets over a fixed basis set Con then the merge operator on multisets and a ‘min ’ operation expressed in terms of harmonic inequality provide a semiring over violation profiles. This semiring allows standard optimization algorithms to be used for OT grammars with weighted finitestate constraints in which the weights are violationmultisets. Most usefully, because multisets are unordered, the merge operation is commutative and thus it is possible to give a single graph representation of the entire class of grammars (i.e. rankings) for a given constraint set. This allows a neat factorization of the optimization problem that isolates the main source of complexity into a single constant γ denoting the size of the graph representation of the whole constraint set. I show that the computational cost of optimization is linear in the length of the underlying form with the multiplicative constant γ. This perspective thus makes it straightforward to evaluate the complexity of optimization for different constraint sets. 1
Journal of Automata, Languages and Combinatorics u (v) w, x–y c ○ OttovonGuerickeUniversität Magdeburg Semiring Frameworks and Algorithms for ShortestDistance Problems
"... 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 ..."
Abstract
 Add to MetaCart
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.