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Dynamic Programming: a different perspective
 Algorithmic Languages and Calculi
, 1997
"... Dynamic programming has long been used as an algorithm design technique, with various mathematical theories proposed to model it. Here we take a different perspective, using a relational calculus to model the problems and solutions using dynamic programming. This approach serves to shed new light on ..."
Abstract

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Dynamic programming has long been used as an algorithm design technique, with various mathematical theories proposed to model it. Here we take a different perspective, using a relational calculus to model the problems and solutions using dynamic programming. This approach serves to shed new light on the different styles of dynamic programming, representing them by different search strategies of the treelike space of partial solutions. 1 INTRODUCTION AND HISTORY Dynamic programming is an algorithm design technique for solving many different types of optimization problem, applicable to such diverse fields as operations research (Ecker and Kupferschmid, 1988) and neutron transport theory (Bellman, Kagiwada and Kalaba, 1967). The mathematical theory of the subject dates back to 1957, when Richard Bellman (Bellman, 1957) first popularized the idea, producing a mathematical theory to model multistage decision processes and to solve related optimization problems. He was also the first to i...
Greedylike algorithms in Kleene algebra
 PARTICIPANTS’ PROCEEDINGS 7TH RELMICS/2ND KLEENE WORKSHOP, MALENTE, MAY 12–17, 2003
, 2003
"... This paper provides an algebraic background for the formal derivation of greedylike algorithms. Such derivations have previously been done in various frameworks including relation algebra. We propose Kleene algebra as a particularly simple alternative. Instead of converse and residuation we use mo ..."
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This paper provides an algebraic background for the formal derivation of greedylike algorithms. Such derivations have previously been done in various frameworks including relation algebra. We propose Kleene algebra as a particularly simple alternative. Instead of converse and residuation we use modal operators that are definable in a wide class of algebras, based on domain/codomain or image/preimage operations. By abstracting from earlier approaches we arrive at a very general theorem about the correctness of loops that covers particular forms of greedy algorithms as special cases.