A Class of Greedy Algorithms and Its Relation to Greedoids

Nedunuri, Srinivas; Smith, Douglas R.; Cook, William R.

doi:10.1007/978-3-642-14808-8_24

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…Given an appropriate constructive prover (such as the one in KIDS [16]) such a derivation could in fact be automated. Other examples that have been derived using this approach are Activity Selection [11], Integer Linear Programming [15], and variations on the Maximum Segment Sum problem [10].…”

Section: Methodsmentioning

confidence: 99%

Theory and Techniques for Synthesizing a Family of Graph Algorithms

Nedunuri

Cook

Smith

2012

Electron. Proc. Theor. Comput. Sci.

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Although Breadth-First Search (BFS) has several advantages over Depth-First Search (DFS) its prohibitive space requirements have meant that algorithm designers often pass it over in favor of DFS. To address this shortcoming, we introduce a theory of Efficient BFS (EBFS) along with a simple recursive program schema for carrying out the search. The theory is based on dominance relations, a long standing technique from the field of search algorithms. We show how the theory can be used to systematically derive solutions to two graph algorithms, namely the Single Source Shortest Path problem and the Minimum Spanning Tree problem. The solutions are found by making small systematic changes to the derivation, revealing the connections between the two problems which are often obscured in textbook presentations of them

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Section: Methodsmentioning

confidence: 99%

Theory and Techniques for Synthesizing a Family of Graph Algorithms

Nedunuri

Cook

Smith

2012

Electron. Proc. Theor. Comput. Sci.

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“…A version of the material in this section appeared in [NSC10], based on a di erent characterization of the criterion for the greedy choice.…”

Section: Greedy Ebfs Algorithmsmentioning

confidence: 99%

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

Nedunuri

Smith

Cook

2012

FM 2012: Formal Methods

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Guided program synthesis is an existing methodology for systematic development of algorithms. Speci c algorithms are viewed as instances of very general algorithm schemas.For example, the Global Search schema generalizes traditional branch-and-bound search, and includes both depth-rst and breadth-rst strategies. Algorithm development involves systematic specialization of the algorithm schema based on problem-speci c constraints to create e cient algorithms that are correct by construction, obviating the need for a separate veri cation step. Guided program synthesis has been applied to a wide range of algorithms, but there is still no systematic process for the synthesis of large search programs such as AI planners.v Our rst contribution is the specialization of Global Search to a class we call E cient Breadth-First Search (EBFS), by incorporating dominance relations to constrain the size of the frontier of the search to be polynomially bounded. Dominance relations allow two search spaces to be compared to determine whether one dominates the other, thus allowing the dominated space to be eliminated from the search. We further show that EBFS is an e ective characterization of greedy algorithms, when the breadth bound is set to one. Surprisingly, the resulting characterization is more general than the well-known characterization of greedy algorithms, namely the Greedy Algorithm parametrized over algebraic structures called greedoids.Our second contribution is a methodology for systematically deriving dominance relations, not just for individual problems but for families of related problems. The techniques are illustrated on numerous well-known problems. Combining this with the program schema for EBFS results in e cient greedy algorithms.Our third contribution is application of the theory and methodology to the practical problem of synthesizing fast planners. Nearly all the state-of-the-art planners in the planning literature are heuristic domain-independent planners. They generally do not scale well and their space requirements also become quite prohibitive. Planners such as TLPlan that incorporate domain-speci c information in the form of control rules are orders of magnitude faster. However, devising the control rules is labor-intensive task and requires domain expertise and insight. The correctness of the rules is also not guaranteed. We introduce a method by which domain-speci c dominance relations can be systematically derived, which can then be turned into control rules, and demonstrate the method on a planning problem (Logistics).vi Many of the derivations are straightforward enough to be automatable.Our third main contribution is showing how to apply the theory and techniqueswe have introduced to a practical problem, namely synthesizing fast AI planners [GNT04].Many of the state-of-the-art planners in the planning literature are domain-independent heuristic planners. They generally do not scale very well and their space requirements also become quite prohibitive. The key to scalable planners is to incorpora...

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Synthesis of first-order dynamic programming algorithms

Bodík

Srivastava

2011

Proceedings of the 2011 ACM International Conference on Object Oriented Programming Systems Languages and Applications

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A Class of Greedy Algorithms and Its Relation to Greedoids

Cited by 4 publications

References 8 publications

Theory and Techniques for Synthesizing a Family of Graph Algorithms

Theory and Techniques for Synthesizing a Family of Graph Algorithms

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

Synthesis of first-order dynamic programming algorithms

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