Tabling with Answer Subsumption: Implementation, Applications and Performance

Swift, Terrance; Warren, David S.

doi:10.1007/978-3-642-15675-5_26

Cited by 27 publications

(27 citation statements)

References 10 publications

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“…However, (Van Gelder 1993) pointed out that automatically determining the correct lattices would be difficult in practice, and this was one of the causes that prevented the deployment of the monotonic-aggregate idea in query languages for the following twenty years. Interestingly, a similar idea (with similar limitations) was more recently proposed in (Swift and Warren 2010) and in several other works e.g., (Zhou et al 2010;Zhou et al 2015) in the context of tabling in Prolog. Also here is programmer's duty to make sure that a proper partial order / lattice type is used for the program at hand.…”

Section: Related Workmentioning

confidence: 85%

“…However it used different lattices for different aggregates and thus incurred in the problems described in (Van Gelder 1993). Therefore, the search for general solutions has motivated several approaches that have addressed the problem using powerful semantics, such as answer-set semantics, that however require higher levels of computational complexity (Pelov et al 2007;Son and Pontelli 2007;Swift and Warren 2010;Faber et al 2011;Gelfond and Zhang 2014).…”

Section: Arxiv:170705681v2 [Csdb] 21 Jul 2017mentioning

confidence: 99%

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Fixpoint semantics and optimization of recursive Datalog programs with aggregates

Zaniolo¹,

Yang²,

Das³

et al. 2017

Theory and Practice of Logic Programming

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A very desirable Datalog extension investigated by many researchers in the last thirty years consists in allowing the use of the basic SQL aggregates min, max, count and sum in recursive rules. In this paper, we propose a simple comprehensive solution that extends the declarative least-fixpoint semantics of Horn Clauses, along with the optimization techniques used in the bottom-up implementation approach adopted by many Datalog systems. We start by identifying a large class of programs of great practical interest in which the use of min or max in recursive rules does not compromise the declarative fixpoint semantics of the programs using those rules. Then, we revisit the monotonic versions of count and sum aggregates proposed in (Mazuran et al. 2013b) and named, respectively, mcount and msum. Since mcount, and also msum on positive numbers, are monotonic in the lattice of set-containment, they preserve the fixpoint semantics of Horn Clauses. However, in many applications of practical interest, their use can lead to inefficiencies, that can be eliminated by combining them with max, whereby mcount and msum become the standard count and sum. Therefore, the semantics and optimization techniques of Datalog are extended to recursive programs with min, max, count and sum, making possible the advanced applications of superior performance and scalability demonstrated by BigDatalog (Shkapsky et al. 2016) and Datalog-MC (Yang et al. 2017). This paper is under consideration for acceptance in TPLP.

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Section: Related Workmentioning

confidence: 85%

Section: Arxiv:170705681v2 [Csdb] 21 Jul 2017mentioning

confidence: 99%

Fixpoint semantics and optimization of recursive Datalog programs with aggregates

Zaniolo¹,

Yang²,

Das³

et al. 2017

Theory and Practice of Logic Programming

View full text Add to dashboard Cite

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“…There has been much work on annotated logic programming and we have built on the syntax and semantics of annotated LP. [Swift 1999] describes how lattice answer subsumption can implement GAPs whereas [Swift and Warren 2010] describes its implementation (as well as the implementation of partial order answer subsumption) in XSB and analyzes its performance showing scalability for applications in social network analysis, abstract interpretation, and query justification. We also note that possibilistic logic [Dubois and Prade 1990;Dubois et al 1991] might be extended to handle the types of calculations GAPs support.…”

Section: Related Work In Logic Programmingmentioning

confidence: 99%

Using Generalized Annotated Programs to Solve Social Network Diffusion Optimization Problems

Shakarian

Broecheler

Subrahmanian

et al. 2013

ACM Trans. Comput. Logic

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There has been extensive work in many different fields on how phenomena of interest (e.g., diseases, innovation, product adoption) "diffuse" through a social network. As social networks increasingly become a fabric of society, there is a need to make "optimal" decisions with respect to an observed model of diffusion. For example, in epidemiology, officials want to find a set of k individuals in a social network which, if treated, would minimize spread of a disease. In marketing, campaign managers try to identify a set of k customers that, if given a free sample, would generate maximal "buzz" about the product. In this article, we first show that the well-known Generalized Annotated Program (GAP) paradigm can be used to express many existing diffusion models. We then define a class of problems called Social Network Diffusion Optimization Problems (SNDOPs). SNDOPs have four parts: (i) a diffusion model expressed as a GAP, (ii) an objective function we want to optimize with respect to a given diffusion model, (iii) an integer k > 0 describing resources (e.g., medication) that can be placed at nodes, (iv) a logical condition VC that governs which nodes can have a resource (e.g., only children above the age of 5 can be treated with a given medication). We study the computational complexity of SNDOPs and show both NP-completeness results as well as results on complexity of approximation. We then develop an exact and a heuristic algorithm to solve a large class of SNDOPproblems and show that our GREEDY-SNDOP algorithm achieves the best possible approximation ratio that a polynomial algorithm can achieve (unless P = NP). We conclude with a prototype experimental implementation to solve SNDOPs that looks at a real-world Wikipedia dataset consisting of over 103,000 edges. ACM Reference Format:Shakarian, P., Broecheler, M., Subrahmanian, V. S. and Molinaro, C. 2013. Using generalized annotated programs to solve social network diffusion optimization problems.

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“…Implementations of mode‐directed tabling are currently available in B‐Prolog and YAP Prolog . A restricted form of mode‐directed tabling can also be reproduced in XSB Prolog by using answer subsumption . In YAP, index arguments are represented with mode index , while arguments with modes first , last , min , max , sum , and all represent output arguments.…”

Section: Introductionmentioning

confidence: 99%

Multi‐dimensional lock‐free arrays for multithreaded mode‐directed tabling in Prolog

Areias

Rocha

2018

Concurrency and Computation

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Summary This work proposes a new design for the supporting data structures used to implement multithreaded tabling in Prolog systems. Tabling is an implementation technique that improves the expressiveness of traditional Prolog systems in dealing with recursion and redundant computations. Mode‐directed tabling is an extension to the tabling technique that supports the definition of alternative criteria for specifying how answers are aggregated, thus being very suitable for problems where the goal is to dynamically calculate optimal or selective answers. In this work, we leverage the intrinsic potential that mode‐directed tabling has to express dynamic programming problems by creating a new design that improves the representation of multi‐dimensional arrays in the context of multithreaded tabling. To do so, we introduce a new mode for indexing arguments in mode‐directed tabled evaluations, named dim, where each dim argument features a uni‐dimensional lock‐free array. Experimental results using well‐known dynamic programming problems on a 32‐core machine show that the new design introduces less overheads and clearly improves the execution time for sequential and multithreaded tabled evaluations.

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Tabling with Answer Subsumption: Implementation, Applications and Performance

Cited by 27 publications

References 10 publications

Fixpoint semantics and optimization of recursive Datalog programs with aggregates

Fixpoint semantics and optimization of recursive Datalog programs with aggregates

Using Generalized Annotated Programs to Solve Social Network Diffusion Optimization Problems

Multi‐dimensional lock‐free arrays for multithreaded mode‐directed tabling in Prolog

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