An Exact Characterization of Greedy Structures

Helman, Paul; Moret, Bernard M. E.; Shapiro, Herbert

doi:10.1137/0406021

Cited by 60 publications

(32 citation statements)

References 7 publications

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“…Now we can state the following characterization due to Helman, Mont and Shapiro [HeMS93]: Now we can state the following characterization due to Helman, Mont and Shapiro [HeMS93]:…”

Section: Accessible Set Systemsmentioning

confidence: 99%

See 1 more Smart Citation

Graphs, Networks and Algorithms

Jungnickel

2008

Algorithms and Computation in Mathematics

237

122

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“…Now we can state the following characterization due to Helman, Mont and Shapiro [HeMS93]: Now we can state the following characterization due to Helman, Mont and Shapiro [HeMS93]:…”

Section: Accessible Set Systemsmentioning

confidence: 99%

“…Alternatively, we recommend a look at the original paper [HeMS93], which contains some further interesting results. Alternatively, we recommend a look at the original paper [HeMS93], which contains some further interesting results.…”

Section: Accessible Set Systemsmentioning

confidence: 99%

Graphs, Networks and Algorithms

Jungnickel

2008

Algorithms and Computation in Mathematics

237

122

View full text Add to dashboard Cite

“…[ HMS93] showed that a structure known as a matroid embedding was both necessary and su cient. Matroid embeddings relax the Exchange axiom of greedoids but add two more axioms, so they are simultaneously a generalization and a specialization of greedoids.…”

Section: Related Workmentioning

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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“…Previous attempts formulate optimal greedy algorithms through connections to matroids [Edm71], greedoids [KL81] and matroid embeddings [HMS93]. Observe that the greedy algorithm for matroids is a priority algorithm whereas the optimal priority algorithm "Earliest Finishing Time First" does not have natural formulations as a matroid-related subset system (see [CLR00] p.345).…”

Section: Introductionmentioning

confidence: 99%

On the Structure of Optimal Greedy Computation (for Job Scheduling)

Papakonstantinou

2009

Mathematical Foundations of Computer Science 2009

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We consider Priority Algorithm [BNR03] as a syntactic model of formulating the concept of greedy algorithm for Job Scheduling, and we study the computation of optimal priority algorithms. A Job Scheduling subproblem S is determined by a (possibly infinite) set of jobs, every finite subset of which potentially forms an input to a scheduling algorithm. An algorithm is optimal for S, if it gains optimal profit on every input. To the best of our knowledge there is no previous work about such arbitrary subproblems of Job Scheduling. For a finite S, it is coNP-hard to decide whether S admits an optimal priority algorithm [PR07]. This indicates that meaningful characterizations of subproblems admitting optimal priority algorithms may not be possible. In this paper we consider those S that do admit optimal priority algorithms, and we show that the way in which all such algorithms compute has non-trivial and interesting structural features.

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An Exact Characterization of Greedy Structures

Cited by 60 publications

References 7 publications

Graphs, Networks and Algorithms

Graphs, Networks and Algorithms

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

On the Structure of Optimal Greedy Computation (for Job Scheduling)

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