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The Greedy Algorithms Class: Formalization, Synthesis and Generalization
, 1995
"... On the first hand, this report studies the class of Greedy Algorithms in order to find an as systematic as possible strategy that could be applied to the specification of some problems to lead to a correct program solving that problem. On the other hand, the standard formalisms underlying the G ..."
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On the first hand, this report studies the class of Greedy Algorithms in order to find an as systematic as possible strategy that could be applied to the specification of some problems to lead to a correct program solving that problem. On the other hand, the standard formalisms underlying the Greedy Algorithms (matroid, greedoid and matroid embedding) which are dependent on the particular type set are generalized to a formalism independent of any data type based on an algebraic specification setting.
Synthesis Of Greedy Algorithms Using Dominance Relations
"... Greedy algorithms exploit problem structure and constraints to achieve lineartime performance. Yet there is still no completely satisfactory way of constructing greedy algorithms. For example, the Greedy Algorithm of Edmonds depends upon translating a problem into an algebraic structure called a ma ..."
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Greedy algorithms exploit problem structure and constraints to achieve lineartime performance. Yet there is still no completely satisfactory way of constructing greedy algorithms. For example, the Greedy Algorithm of Edmonds depends upon translating a problem into an algebraic structure called a matroid, but the existence of such a translation can be as hard to determine as the existence of a greedy algorithm itself. An alternative characterization of greedy algorithms is in terms of dominance relations, a wellknown algorithmic technique used to prune search spaces. We demonstrate a process by which dominance relations can be methodically derived for a number of greedy algorithms, including activity selection, and prefixfree codes. By incorporating our approach into an existing framework for algorithm synthesis, we demonstrate that it could be the basis for an effective engineering method for greedy algorithms. We also compare our approach with other characterizations of greedy algorithms. 1