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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
Algebraic Dynamic Programming Algebraic Dynamic Programming
"... Abstract. Dynamic programming is a classic programming technique, applicable in a wide variety of domains, like stochastic systems analysis, operations research, combinatorics of discrete structures, flow problems, parsing with ambiguous grammars, or biosequence analysis. Yet, no methodology is avai ..."
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Abstract. Dynamic programming is a classic programming technique, applicable in a wide variety of domains, like stochastic systems analysis, operations research, combinatorics of discrete structures, flow problems, parsing with ambiguous grammars, or biosequence analysis. Yet, no methodology is available for designing such algorithms. The matrix recurrences that typically describe a dynamic programming algorithm are difficult to construct, errorprone to implement, and almost impossible to debug. This article introduces an algebraic style of dynamic programming over sequence data. We define the formal framework including a formalization of Bellmanâ€™s principle, specify an executable specification language, and show how algorithm design decisions and tuning for efficiency can be describedonaconvenientlevelofabstraction.
Partitions Revisited
, 1993
"... Problems involving list partitions are found in many areas of computer science. This paper states theorems about programs that use strategies such as dynamic programming or greedy strategies to solve optimization problems, and applies the theorems to the solving of partition problems. The reasoning ..."
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Problems involving list partitions are found in many areas of computer science. This paper states theorems about programs that use strategies such as dynamic programming or greedy strategies to solve optimization problems, and applies the theorems to the solving of partition problems. The reasoning is in an equational style, using a calculus of relations and associated laws. Contents 1 Introduction 1 1.1 Partition Problems \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta 2 2 A Calculus of Relations 4 2.1 Relations \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta 4 2.2 Relators \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Delta \Del...