scholarly journals Fact-Alternating Mutex Groups for Classical Planning (Extended Abstract)

2018 ◽  
Author(s):  
Daniel Fišer ◽  
Antonín Komenda
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Experimental Evaluation ◽  
Complexity Analysis ◽  
Finite Domain ◽  
Initial State ◽  
Pruning Algorithm ◽  
Dead End ◽  
New Type ◽  
Np Complete

Mutex groups are defined in the context of STRIPS planning as sets of facts out of which, maximally, one can be true in any state reachable from the initial state. This work provides a complexity analysis showing that inference of mutex groups is as hard as planning itself (PSPACE-Complete) and it also shows a tight relationship between mutex groups and graph cliques. Furthermore, we propose a new type of mutex group called a fact-alternating mutex group (fam-group) of which inference is NP-Complete. We introduce an algorithm for the inference of fam-groups based on integer linear programming that is complete with respect to the maximal fam-groups and we demonstrate that fam-groups can be beneficial in the translation of planning tasks into finite domain representation, for the detection of dead-end state and for the pruning of spurious operators. The experimental evaluation of the pruning algorithm shows a substantial increase in a number of solved tasks in domains from the optimal deterministic track of the last two planning competitions (IPC 2011 and 2014).

scholarly journals Fact-Alternating Mutex Groups for Classical Planning

2018 ◽  
Vol 61 ◽  
pp. 475-521
Author(s):  
Daniel Fišer ◽  
Antonín Komenda
Keyword(s):  
Linear Programming ◽  
Theoretical Analysis ◽  
Complexity Analysis ◽  
Simple Algorithm ◽  
Finite Domain ◽  
Initial State ◽  
Pruning Algorithm ◽  
Dead End ◽  
New Type ◽  
Np Complete

Mutex groups are defined in the context of STRIPS planning as sets of facts out of which, maximally, one can be true in any state reachable from the initial state. The importance of computing and exploiting mutex groups was repeatedly pointed out in many studies. However, the theoretical analysis of mutex groups is sparse in current literature. This work provides a complexity analysis showing that inference of mutex groups is as hard as planning itself (PSPACE-Complete) and it also shows a tight relationship between mutex groups and graph cliques. This result motivates us to propose a new type of mutex group called a fact-alternating mutex group (fam-group) of which inference is NP-Complete. Moreover, we introduce an algorithm for the inference of fam-groups based on integer linear programming that is complete with respect to the maximal fam-groups and we demonstrate how beneficial fam-groups can be in the translation of planning tasks into finite domain representation. Finally, we show that fam-groups can be used for the detection of dead-end states and we propose a simple algorithm for the pruning of operators and facts as a preprocessing step that takes advantage of the properties of fam-groups. The experimental evaluation of the pruning algorithm shows a substantial increase in a number of solved tasks in domains from the optimal deterministic track of the last two planning competitions (IPC 2011 and 2014).

Schema Compliant Consistency Management via Triple Graph Grammars and Integer Linear Programming

2021 ◽  
Author(s):  
Nils Weidmann ◽  
Anthony Anjorin
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Experimental Evaluation ◽  
Graph Grammars ◽  
Model Driven Engineering ◽  
Rule Based ◽  
Consistency Management ◽  
Model Driven ◽  
Triple Graph Grammars ◽  
Domain Constraints

AbstractIn the field of Model-Driven Engineering, Triple Graph Grammars (TGGs) play an important role as a rule-based means of implementing consistency management. From a declarative specification of a consistency relation, several operations including forward and backward transformations, (concurrent) synchronisation, and consistency checks can be automatically derived. For TGGs to be applicable in realistic application scenarios, expressiveness in terms of supported language features is very important. A TGG tool is schema compliant if it can take domain constraints, such as multiplicity constraints in a meta-model, into account when performing consistency management tasks. To guarantee schema compliance, most TGG tools allow application conditions to be attached as necessary to relevant rules. This strategy is problematic for at least two reasons: First, ensuring compliance to a sufficiently expressive schema for all previously mentioned derived operations is still an open challenge; to the best of our knowledge, all existing TGG tools only support a very restricted subset of application conditions. Second, it is conceptually demanding for the user to indirectly specify domain constraints as application conditions, especially because this has to be completely revisited every time the TGG or domain constraint is changed. While domain constraints can in theory be automatically transformed to obtain the required set of application conditions, this has only been successfully transferred to TGGs for a very limited subset of domain constraints. To address these limitations, this paper proposes a search-based strategy for achieving schema compliance. We show that all correctness and completeness properties, previously proven in a setting without domain constraints, still hold when schema compliance is to be additionally guaranteed. An implementation and experimental evaluation are provided to support our claim of practical applicability.

scholarly journals Stable Divisorial Gonality is in NP

2020 ◽  
Author(s):  
Hans L. Bodlaender ◽  
Marieke van der Wegen ◽  
Tom C. van der Zanden
Keyword(s):  
Linear Programming ◽  
Algebraic Geometry ◽  
Integer Linear Programming ◽  
Connected Graph ◽  
Np Hard ◽  
Chip Firing ◽  
Np Complete ◽  
Graph Parameters

AbstractDivisorial gonality and stable divisorial gonality are graph parameters, which have an origin in algebraic geometry. Divisorial gonality of a connected graph G can be defined with help of a chip firing game on G. The stable divisorial gonality of G is the minimum divisorial gonality over all subdivisions of edges of G. In this paper we prove that deciding whether a given connected graph has stable divisorial gonality at most a given integer k belongs to the class NP. Combined with the result that (stable) divisorial gonality is NP-hard by Gijswijt et al., we obtain that stable divisorial gonality is NP-complete. The proof consists of a partial certificate that can be verified by solving an Integer Linear Programming instance. As a corollary, we have that the total number of subdivisions needed for minimum stable divisorial gonality of a graph with m edges is bounded by mO(mn).

On-line verification of initial-state opacity by Petri nets and integer linear programming

2019 ◽  
Vol 93 ◽  
pp. 108-114 ◽  
Author(s):  
Xuya Cong ◽  
Maira Pia Fanti ◽  
Agostino Marcello Mangini ◽  
Zhiwu Li
Keyword(s):  
Linear Programming ◽  
Petri Nets ◽  
Integer Linear Programming ◽  
Initial State ◽  
On Line

scholarly journals Solving Integer Linear Programs by Exploiting Variable-Constraint Interactions: A Survey

Algorithms ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 248
Author(s):  
Robert Ganian ◽  
Sebastian Ordyniak
Keyword(s):  
Linear Programming ◽  
Computer Science ◽  
Integer Linear Programming ◽  
Systematic Study ◽  
Optimization Problems ◽  
Linear Programs ◽  
Integer Linear Programs ◽  
Diverse Backgrounds ◽  
Recent Developments ◽  
Np Complete

Integer Linear Programming (ILP) is among the most successful and general paradigms for solving computationally intractable optimization problems in computer science. ILP is NP-complete, and until recently we have lacked a systematic study of the complexity of ILP through the lens of variable-constraint interactions. This changed drastically in recent years thanks to a series of results that together lay out a detailed complexity landscape for the problem centered around the structure of graphical representations of instances. The aim of this survey is to summarize these recent developments, put them into context and a unified format, and make them more approachable for experts from many diverse backgrounds.

scholarly journals FINDING AND ANALYZING THE MINIMUM SET OF DRIVER NODES IN CONTROL OF BOOLEAN NETWORKS

2016 ◽  
Vol 19 (03) ◽  
pp. 1650006 ◽  
Author(s):  
WENPIN HOU ◽  
TAKEYUKI TAMURA ◽  
WAI-KI CHING ◽  
TATSUYA AKUTSU
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Boolean Network ◽  
Boolean Networks ◽  
Np Hard ◽  
Initial State ◽  
Random Boolean Networks ◽  
Minimum Number ◽  
Average Size ◽  
Theoretical Analyses

We study the minimum number of driver nodes control of which leads a Boolean network (BN) from an initial state to a target state in a specified number of time steps. We show that the problem is NP-hard and present an integer linear programming-based method that solves the problem exactly. We mathematically analyze the average size of the minimum set of driver nodes for random Boolean networks with bounded in-degree and with a small number of time steps. The results of computational experiments using randomly generated BNs show good agreements with theoretical analyses. A further examination in realistic BNs demonstrates the efficiency and generality of our theoretical analyses.

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