Generation of Efficient Programs for Solving Maximum Multi-marking Problems

Sasano, Isao; Hu, Zhenjiang; Takeichi, Masato

doi:10.1007/3-540-44806-3_5

Cited by 9 publications

(11 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It can be shown that this problem is also in HSG and has a linear-time solution by using a very similar idea to that used earlier (the maximum width of the tree is di erent (3) but still constant) The results of comparing the run-time (in seconds) of our program with that generated by [SHT01] on sequences of randomly generated numbers of varying lengths is shown in the following …”

Section: Abs(x I )mentioning

confidence: 95%

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

Nedunuri

Smith

Cook

2012

FM 2012: Formal Methods

View full text Add to dashboard Cite

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...

show abstract

Section: Abs(x I )mentioning

confidence: 95%

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

Nedunuri

Smith

Cook

2012

FM 2012: Formal Methods

View full text Add to dashboard Cite

show abstract

“…Can we also derive a linear-time algorithm from this specification? In fact, the approach for maximum marking problems developed by Sasano and Hu et al [29,28] suggests a O(nU) algorithm, where n is the length of the input list. We are, however, aiming for an algorithm whose complexity is independent from U.…”

Section: Maximum Segment Sum With Bounded Lengthsmentioning

confidence: 99%

“…Curtis analysed dynamic programming [11] and greedy algorithms [12] in a relational setting. Sasano and Hu et al [29,28] studied a useful class of maximum marking problems and proposed linear time algorithms for them.…”

Section: Introductionmentioning

confidence: 99%

Maximum segment sum is back

2008

Proceedings of the 2008 ACM SIGPLAN Symposium on Partial Evaluation and Semantics-Based Program Manipulation

View full text Add to dashboard Cite

It may be surprising that variations of the maximum segment sum (MSS) problem, a textbook example for the squiggolists, are still active topics for algorithm designers. In this paper we examine the new developments from the view of relational program calculation. It turns out that, while the classical MSS problem is solved by the Greedy Theorem, by applying the Thinning Theorem, we get a linear-time algorithm for MSS with upper bound on length. To derive a linear-time algorithm for the maximum segment density problem, on the other hand, we purpose a variation of thinning based on an extended notion of monotonicity. The concepts of left-negative and right-screw segments emerge from the search for monotonicity conditions. The efficiency of the resulting algorithms crucially relies on exploiting properties of the set of partial solutions and design efficient data structures for them.

show abstract

“…Second, transform checking to the form with f oldSP by tupling transformation [18]. Then, if w is homomorphic, Optimization Theorem (Theorem 1 [27,26]) automatically gives how to detect an optimal register allocation with certain generic dynamic programming (i.e., a single traversal on an SP Term), assuming the live variables are pre-computed. Note that we restrict ourselves to control flow graphs with bounded tree width, and do not intend P = NP, where the conventional optimal register allocation based on graph coloring [10] is NP-complete.…”

Section: Register Allocation For Flowchart Programmentioning

confidence: 99%

“…We solve it as an instance of maximum marking problems [26,27,5]; mark the nodes of a control flow graph under a certain condition such that the sum of weight of marked nodes is maximum (or, minimum). We make use of Optimization Theorem from our previous work [26,27], and show how it works to find an optimal register allocation as a certain dynamic programming on SP Terms. The rest of the paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Iterative-free program analysis

Ogawa

Sasano

2003

Proceedings of the Eighth ACM SIGPLAN International Conference on Functional Programming

Self Cite

View full text Add to dashboard Cite

Program analysis is the heart of modern compilers. Most control flow analyses are reduced to the problem of finding a fixed point in a certain transition system, and such fixed point is commonly computed through an iterative procedure that repeats tracing until convergence. This paper proposes a new method to analyze programs through recursive graph traversals instead of iterative procedures, based on the fact that most programs (without spaghetti GOTO) have wellstructured control flow graphs, graphs with bounded tree width. Our main techniques are; an algebraic construction of a control flow graph, called SP Term, which enables control flow analysis to be defined in a natural recursive form, and the Optimization Theorem, which enables us to compute optimal solution by dynamic programming. We illustrate our method with two examples; dead code detection and register allocation. Different from the traditional standard iterative solution, our dead code detection is described as a simple combination of bottom-up and top-down traversals on SP Term. Register allocation is more interesting, as it further requires optimality of the result. We show how the Optimization Theorem on SP Terms works to find an optimal register allocation as a certain dynamic programming.

show abstract

Generation of Efficient Programs for Solving Maximum Multi-marking Problems

Cited by 9 publications

References 10 publications

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

Theory and Techniques for Synthesizing Efficient Breadth-First Search Algorithms

Maximum segment sum is back

Iterative-free program analysis

Contact Info

Product

Resources

About