In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.

Flows in Networks

This paper gives an overview of the open source project Potassco, the Potsdam Answer Set Solving Collection, bundling tools for Answer Set Programming developed at the University of Potsdam.

Potassco: The Potsdam Answer Set Solving Collection

Answer Set Programming (ASP) is a declarative problem solving approach, initially tailored to modeling problems in the area of Knowledge Representation and Reasoning (KRR). More recently, its attractive combination of a rich yet simple modeling language with high-performance solving capacities has sparked interest in many other areas even beyond KRR. This book presents a practical introduction to ASP, aiming at using ASP languages and systems for solving application problems. Starting from the essential formal foundations, it introduces ASP's solving technology, modeling language and methodology, while illustrating the overall solving process by practical examples. Table of Contents: List of Figures / List of Tables / Motivation / Introduction / Basic modeling / Grounding / Characterizations / Solving / Systems / Advanced modeling / Conclusions

/pdf/answer-set-solving-in-practice-vtcfq8bjfw.pdf

Answer Set Solving in Practice

Conflict-driven answer set solving: From theory to practice

This book presents the most up-to-date coverage of procedural content generation (PCG) for games, specifically the procedural generation of levels, landscapes, items, rules, quests, or other types of content. Each chapter explains an algorithm type or domain, including fractal methods, grammar-based methods, search-based and evolutionary methods, constraint-based methods, and narrative, terrain, and dungeon generation. The authors are active academic researchers and game developers, and the book is appropriate for undergraduate and graduate students of courses on games and creativity; game developers who want to learn new methods for content generation; and researchers in related areas of artificial intelligence and computational intelligence.

Procedural Content Generation in Games

Answer Set Programming (ASP) is a model, ground, and solve paradigm. The integration of application- or theory-specific reasoning into ASP systems thus impacts on many if not all elements of its workflow, viz. input language, grounding, intermediate language, solving, and output format. We address this challenge with the fifth generation of the ASP system clingo and its grounding and solving components by equipping them with well-defined generic interfaces facilitating the manifold integration efforts. On the grounder's side, we introduce a generic way of specifying language extensions and propose an intermediate format accommodating their ground representation. At the solver end, this is accompanied by high-level interfaces easing the integration of theory propagators dealing with these extensions.

https://drops.dagstuhl.de/opus/volltexte/2016/6733/pdf/OASIcs-ICLP-2016-2.pdf/

Theory Solving Made Easy with Clingo 5

We present a new approach to integrating Constraint Processing (CP) techniques into Answer Set Programming (ASP). Based on an alternative semantic approach, we develop an algorithmic framework for conflict-driven ASP solving that exploits CP solving capacities. A significant technical issue concerns the combination of conflict information from different solver types. We have implemented our approach, combining ASP solver clingo with the generic CP solver gecode , and we empirically investigate its computational impact.

Constraint Answer Set Solving

Many real-world applications, like planning or model checking, comprise a parameter reflecting the size of a solution. In a propositional formalism like Answer Set Programming (ASP), such problems can only be dealt with in a bounded way, considering one problem instance after another by gradually increasing the bound on the solution size. We thus propose an incremental approach to both grounding and solving in ASP. Our goal is to avoid redundancy by gradually processing the extensions to a problem rather than repeatedly re-processing the entire (extended) problem. We start by furnishing a formal framework capturing our incremental approach in terms of module theory. In turn, we take advantage of this framework for guiding the successive treatment of program slices during grounding and solving. Finally, we describe the first integrated incremental ASP system, iclingo , and provide an experimental evaluation.

/pdf/engineering-an-incremental-asp-solver-e25uql2m1c.pdf

Engineering an Incremental ASP Solver

We elaborate a uniform approach to computing answer sets of disjunctive logic programs based on state-of-the-art Boolean constraint solving techniques. Starting from a constraint-based characterization of answer sets, we develop advanced solving algorithms, featuring backjumping and conflict-driven learning using the First-UIP scheme as well as sophisticated unfounded set checking. As a final result, we obtain a competitive solver for ΣP2-complete problems, taking advantage of Boolean constraint solving technology without using any legacy solvers as black boxes.

/pdf/conflict-driven-disjunctive-answer-set-solving-nk6nxyvcg4.pdf

Max Ostrowski

Papers

Potassco: The Potsdam Answer Set Solving Collection

Theory Solving Made Easy with Clingo 5

Constraint Answer Set Solving

Engineering an Incremental ASP Solver

Conflict-driven disjunctive answer set solving